MEDIEVAL - p. 1
MEDIEVAL CHRONOLOGY
FROM THE GREEKS TO THE RENAISSANCE
Copyright ©2003 Professor David Singmaster
contact via http://puzzlemuseum.com
NOTE. Transcriptions of Sanskrit and Arabic use a number of characters which are not
available in Word. A few of these have close approximations in Word. I use ņ, ş, ţ, to
denote the same letters with a dot . under them, and ʼn to denote n with an overdot. I am
sure that I avoided inserting some of these diacritical marks when I first started this file and
the transcriptions differ considerably. I have not tried to re-examine my sources to determine
what the source used. Some of these marks extend beyond the line and I have used wider line
spacing where they occur, e.g. in this paragraph.
This includes some chronology of the Greeks, Chinese and Hindus, which is covered
more extensively in separate chronologies. This chronology is mainly concerned with the
period of the Arabs and medieval Europe and the transmission of ancient knowledge to the
Renaissance. I have inserted a few major events in China to show the development there.
My chronologies on Number and on Computing relate to this one.
Some topics whose main development is in this period are trigonometry, induction,
calendar reform, time keeping, navigation and discovery and the development of papermaking
and printing. I have included relevant earlier and later material on these topics. For a few of
these, there are too many entries to cross reference, so I have now made an index here for
them.
Dates BC are indicated by - , so 1 BC is -1 and there is no year 0. Intervals BC are
indicated with a / , e.g. c-275/-184. Islamic dates are often given as years AH which fall
into two years AD – these are indicated with a /, e.g. 927/8.
Number systems. -2400, 499, 522, 595, 662, 820, 876, c980, c1000, 973-1048,
980-1037, c1044-1123/4, 1202, early 13C, 1247, 1201-1274, 1318?-1374?, 14C,
Notation, terminology. 1170, early 13C, 1489, 1492, 1525, 1540, 1557, 1540-1603,
1583, 1620, 1626, 1658, 1674,
Abacus, etc. c980, c1000, 1000, 1592, 1617,
House numbering. 1463, c1712.
Double entry book-keeping, banking. 1157, 13C, 1340, 1318?-1374?, 1494,
Compound interest. 1558, 1582,
Negative numbers. c-100, 1202, 1247, c1375, 1484, 1572, 1548-1620, 1629,
Decimal fractions. 263, 952-953, c1000, c1000, c1025, 1172, c1330, ?-1429, 1492,
1585,
Binary system. 1617, 1701,
Number theory. 820, 836-901, c1000, c1010, 1220, c1300, 1510.
Algebra (see also Cubic and higher equations). 820, 820?, c850-930, c1010,
c1044-1123/4, 1145, c1375, 1494, 1557, 1572, 1540-1603, 1548-1620, 1585, 1591, 1629,
Binomial theorem/Pascal's triangle. c1044-1123/4, 1225, 1201-1274, 1261, 1303, 1356,
?-1429, 1548-1620, 1640?,
Induction. 1550, 1640?, 1838,
Exponents and logarithms. c1010, 1172, c1330, 1323-1382, 1484, 1524, 1614, 1615,
1616, 1617, 1619, 1620?, 1620, 1621, 1624, 1620-1632,
Cubic and higher equations. c1044-1123/4, 1202, 1225, 1328, 1344, 1494, c1506,
c1530, 1535, 1539, 1540, 1543, 1545, 1546, 1540-1603,
Euclid's Elements. -300, c390, 754-775, 786-809, 813-833, 830-910, 836-901, 888,
c1130, c1175, 1201-1279, c1270, 1482, 1509, 1533, 1543, 1509-1575, 1562, 1564, 1570.
1537-1612.
Other geometry texts. c1270, 1511, 1509-1575,
Values of π. c-100, c85-c165, 263, c480, 973-1048, 1135-1204, 1202, c1320, ?-1429,
1502, 1551, 1577, 1540-1603, 1546-1601, 1585, 1593, 1610, 1621, 1667, 1699,
Volume and area of a sphere. c-287/-212, c-100, 263, c500, 1150,
Trisection. c85-c165,
Parallel postulate. c85-c165, 836-901, c965-1039, c1044-1123/4, 1201-1274,
MEDIEVAL - p. 2
1537-1612, See my chronology of Greece for more on this.
Projective geometry. 1593-1662, 1640?
Perspective. 1413?, c1425, 1435, 1397-1475, 1478, 1525, 1540, 1600,
Polyhedra, Tessellations, etc. 940-998, 1498, 1525, 1595, 1596, 1619,
Iterative methods. c830, c1225(?), 1247, ?-1429,
Areas. 909-946,
Development of 360 degrees. Mid -5C, c-180, c-180/c-125, c85-c165,
Trigonometry. -300, c-180/c-125, c85-c165, 4C, 499, 505, 724, c830, 858-929,
940-998, 973-1048, Late 10C, c1130, 1145, c1175, 1220, 1201-1274, 1321, c1400, 1464,
1533, 1539-1541, 1540-1603, 1594, 1595, 1667, 1744, 1748, 1759, c1870,
Prosthaphaeresis. 858-929, 1005, 1514, c1585, 1540-1603, 1546-1601,
Trigonometric tables. c-180/c-125, c85-c165, 499, 820, 858-929, 940-998, c1000,
973-1048, ?-1429, 1440, 1551, 1596, 1613, 1620,
Calculus, analysis, series. c-287/-212, c500, 628, 932, 1150, c1350, 1356, 1323-1382,
c1400, 1502, 1592, 1665, 1667, 1699.
Astronomy – see also: Calendars. mid -5C, c-180, c-120?, c85-c165, 531-579, c840,
840, c970, 1005, 973-1048, 980-1037, 1120, 1145, 1201-1274, 1292, c1350, c1428,
1401-1464, 1483, 1539-1541, 1543, 1551, 1509-1575, 1572, 1575, 1576, 1546-1601, 1600,
1564-1642, 1609, 1609-1610, 1616, 1619, 1627, 1632, 1637, 1655, 1655-56, 1659, 1667,
1675, 1838-1840,
Observatories. 813-833, 1005, 1201-1274, c1428, 1440, 1471, 1575, 1546-1601, 1637,
1667, 1675,
Astrolabe. c85-c165, c390, 662, c791, 927/8, c970, 973-1048, 11C, 1145, 1295, 1391,
1484,
Cross-staff, Backstaff, Sextant, Theodolite, etc. 1321, 1484, 1512, 1556, 1551, c1594,
1676, 1731,
Telescope/spectacles/microscope/optics. c965-1039, c1200, 1260, c1280, c1300, 1352,
1352, 1568, 1570, 1571, c1590, 1592, 1608, 1609, 1609-1610, 1660, 1663, 1668, c1673,
Calendars. -3761, -776, -752, mid -5C, -432, -4C, c-275/-194, c-180/c-125, -153, -46,
0, early 4C, 324, 325, 525, 622, 640, 675-735, 724, 768-814, late 10C, 973-1048,
c1044-1123/4, 1247, 1260, 1292, mid 14C, 1436, 1474, 1514, 1582, 1583, 1600, 1649-1660,
1700, 1752, 1793, 19-20C, 1967, 20C,
Sun dials, nocturnals, hourglasses. 606, c840, 909-946,
Hourglasses. 8C, 807, 13C, 1309-1313, 1337-1339,
Clocks, watches and chronometers – see also: Longitude. -1550, c-180, c-180/c-125,
622, 724, 802, 807, c840, 850, c980, 1005, 11C, 1088, Early 12C, c1280, 1290, c1300, c1330,
1335, 1335-1347, mid 14C, 1350, 1364, 1365, 1370, 1406, c1430, 1497-1500, 1502, c1525,
1525, 1530, 1581 or 1583, c1585, 1639, 1641, 1656, 1658 (twice), 1660-1664, 1673, 1675,
1676, 1660-1700, 1714, 1715, 1721, 1725, 1735, 1739, c1755, 1757, 1757-1759, 1762, 1773,
c1790, 1793, 1970s,
Waterclocks. -1550, 724, 802, 11C, 1988, c1280,
Standard time and time zones, etc. 1847, 1869, 1880, 1883, 1883-1884, 1963, 20C,
Magnetic compass. -1C, c1000, 1080, c100, 1116, 12C, Late 12C, c1190, c1200, 1260,
1269, Mid 15C, 1492, 1600.
Size and shape of the earth. c-275/-194, c85-c165, 6C, 622, 724, 820, 825, c830,
973-1048, 1323-1382,
Early travel and other contacts – see also: Exploration. -103, 0-200 (twice), 166,
399-414, 431, 615, 636, c685, 771, 786-809, 800, 863, 915, c1140, 1245, 1252, late 13C,
1271-1295, 1322-1356, 1415, 1453.
Exploration and discovery – see also: Magnetic compass, Size of earth, Early travel,
Longitude and navigation, Maps. c825, c1140, 13C, 1415, 1419, 1405-1433, 1427, 13941460, 1456, 1473?, 1482, 1482, 1487, 1488, 1492, 1494, 1497, 1497, 1500, 1507, 1511, 1513,
1514, 1519-1522, c1594, 1607, 1607, 1616,
Longitude and navigation – see also: Astrolabe; Cross-staff, Back-staff, Sextant, etc.
1295, 1484, c1500, 1514, 1524, 1530, 1545, 1551, 1559, c1594, 1598, 1616, 1622, c1650,
1707, 1714, 1735, 1741, 1761, 1762, 1767, 1773,
Maps. c85-c165, 622, c1140, c1260-1310, 1569, c1594, 1595, c1650.
Date line. 1323-1382, 1519-1522,
Crossbow. 1139,
Gunpowder, cannons, guns, rockets. 668, 9C, c900, 1044, 1118, 1132, 12-13C,
1230 or 1231, 1192-1280, 13C, 1260, 1280, c1290?, c1300, 1301, 1312, 1324, 1326, 1331,
MEDIEVAL - p. 3
1332, 1338, 1346, 1346, 1350, 1356-1377, c1375, 1377, 1380, 1420s, 1453, 1453, 1561,
1613,
Libraries, books, etc. -546/-527, c-315, c-260, -259?, c-150, c-275/-194, -213, -196,
-88/-86, -39, 125, 267, 431, 531-579, 642, c685, 813-833, 863, 969, c970, c987, 1005,
1009-1031, 1258, c1330, 1492, 1608, 1653, 1691, 1701, 1705,
Paper: -196, c105, 751, 794, 874, 952-953, 10C, 1005, 1102, 1150s, 1276, 1348, 1390,
1494, 16C, 1588, early 1700s.
Printing: c750, 770, Late 8C, 868, 10-11C, 1005, 1041-1048, 1083, 14C, 1403, 1423,
1440-1450, 1460, 1461 (thrice), 1462, c1470, 1473?, 1473, 1475, 1476, 1482, 1500, 1638,
1690.
Printing of mathematical works: 1083, 1478, 1482, 1482, 1489, 1491, 1494, 1500,
1509, 1510, 1511, 1512, 1515, 1519, 1525, 1533, 1537, 1538, 1540, 1544, 1509-1575, 1588.
Chess. c500, c550, c600, 802, c840, c890, c880-946, 1010, 1061, c1100, 1062-1167,
c1275 (twice), 1283, 1476,
Cards. 969, 11C, 1120, 1299, 1329, 1367, 1371, 1377, 1379, 1392, 1398, 1423, c1450,
1457, 1617,
Dice. 11C, 1193, 1447, c1564,
Backgammon. 1283,
Probability. 1447, 1494, c1564, 1654, 1657,
Technological innovations.
General: 768-814, 11C.
Agriculture and food technology and use of horse. Stirrup: 4C, c694, 732.
Sugar: 5C, 642. Heavy Plough: 6C. Horse harness: 8-9C. Crop rotation and introduction of
legumes: 768-814. Horseshoes: 9-10C. Rabbits: 1176. Salting herring: 1359.
Use of power. Waterwheels and watermills: 1C, 5C, 768-814, c1000, 1086,
Early 12C, 1515. Windmills: 644, 768-814, c870, 10C, Early 12C, c1200, 15C.
Tidemills: 11C.
Machinery. Crank: c825, Early 12C, c1420, 1480. Treadle: Mid 2C, Late 12C,
1480. Compound crank/carpenter's brace: c1420. Grindstone: c825, 1480. Flywheel: late
11C. Automata: Early 12C, 1299, 1464. Speed Governor: Early 12C. Rudder: c1200.
Spinning wheel: c1280. Drawloom: 14C. Canal lock: 1396, c1487. Metal screws: 1405.
Hooke's Law: 1678.
Glass: 1180, 1277.
Atmospheric pressure: 1654,
Translation of texts. 399-414, 531-579, 662, c685, 771, 775?, 786-809, c791, 813-833,
820, 830-910, 836-901, 840, c870, c890, 940-998, c965-1039, 1085, 1120, c1130, 1145,
c1150, c1160, c1175, 1238, 1201-1274, c1270, 1342, 1476, 1498, 1515, 1517, 1534, 1543,
1509-1575, 1570, 1585, 1588, 1616, 1632, 1636,
Use of vernacular languages. 405, c715, 813, 863, c890, 1328, c1375, 1494, 1509,
1511, 1534, 16C, 1509-1575,
Use of Hebrew, Jewish mathematicians. c791, 1120, 1092-1167, 1135-1204, 1321,
1475, 1498, 1517. (Just added, there are probably more entries, e.g. Bonfils?.)
Academies and journals. 529, 786-809, 813-833, 820, 836-901, c860, c870, 1005,
1582, 1603, 1625, c1645, 17C, 1652, 1660-1662, 1665, 1666, 1682,
Universities. -863, c-390, c-1C, 431, 5-12C, 529, 531-579, 651, 7C, 725, c750,
786-809, 813-833, 825, 859, 969, c970, c1050, 11C, 1065, 1088, 1096, 1109, 1137,
1133-1144, 1167, 1096-1270, 1200, 1209, 1214, Early 13C, 1215, 1221 (twice), 1224,
First half of the 13C, 1227/8, 1231, 1253, 1284, 1287, 1290, 1303, 1308, Early 14C, 1331,
1343, 1348 (twice), 1364, 1365, 1367, 1386, 1388, 1389, 1392, 1409, 1411, 1419, 1425,
1426, 1446, 1450, 1460, 1467, 1472, 1477 (twice), 1490, 1491, 1492, 1498, 1502, c1525,
1526, 1529 or 1530, 1544, 1558, 1559, 1559, 1575, 1581, 1582, 1583, 1585, 1590, 1597,
1614 (twice), 1625, 1632 (twice), 1636 (thrice), 1646, 1647, 1665, 1668, 1678, 1693, 1737,
Religious developments. (I haven't included all details of conquest and reconquest nor
all religious aspects of the calendar.) 64, 303, 312, 313, c320, early 4C, 324, 391, 431,
early 6C, c520, 531-579, 597, 622, 632, 638, 640, 642, 656, 661, 717-718, 725, 8C, 842, 863,
929, 989, 1054, 1095, 1099, 1187, 1202, 1204, 1245, c1266, 1290, 1291, 1302, 1309, 1367,
1378, 1415, 1469, 1477, 1492, 1517, 1521, 1529, 1530, 1534, 1534, 1540, 1545-1563, 1555,
1568, 1572, 1598, 1600, 1616, 1618, 1621, 1625, 1632, 1648, 1685,
Medical developments. 860-932, 1096, 1096-1270, 1137, 1221, 1616, 1660,
Social developments. (I have just added this and may not have entered all dates of
relevance.) 768-814, 1290, 1346-1350, c1360, 1568, 1581, 1621, 1678,
MEDIEVAL - p. 4
Women in Mathematics and Science. 415,
Warning notes. Many dates are speculative. Generally they indicate just when the
person flourished. Older Chinese items are extremely uncertain – it is often argued that the
content is much older than the writing, so the Chou Pei Suan Ching may be dated back to
-800!!. Writers on Hindu mathematics often assert its beginnings may go back several million
(!!) years. Even Greek authors may have dates which are uncertain by 200 years. Islamic
dates may be off due to conversion between AH and AD – the Islamic year is about 11 days
shorter than the solar year – see 640.
Spellings can vary greatly, especially for names which are transliterated. D. E. Smith
gives a useful discussion of transliteration and pronunciation at the beginning of his History
of Mathematics.
Notes:
1 year
= 365.242216 or 365.242199 or 365.242197 or 365.24219870 days.
1 lunar month
= 29.530598 days.
1 year
= 12.368267 lunar months.
π
= 3.14159 26535.
The circumference of the earth is 40,010 km = 24,861 mi.
The length of a degree is 111.14 km or 69.06 mi.
-3761
-2400
-1550?
-863
-776
-752
Date of creation used as the starting point of the Jewish calendar.
Positional notation in Babylonia, base 60. It is conjectured that this evolved
from a system of counting on the joints of the four fingers of one hand –
this makes 12 – and then keeping track of the 12s with the five fingers
of the other hand, making 60 in all. This also gave a count of 12 hours
in the day and 12 in the night.
Earliest waterclocks (clepsydra) invented in Egypt by Amenemhet.
In 570, Merlin of Caledonia mentions a university at Stamford, Lincolnshire,
founded by Prince Bladud in -863. I suspect this is entirely legendary.
First Olympiad, used as the beginning of the Greek calendar developed by
Eratosthenes, c-240. The Athenian Festival Calendar had months of
alternately 29 and 30 days, with occasional intercalary months, but this
was not done systematically and the months were often out of phase
with the seasons.
Legendary date of foundation of Rome and beginning of the Roman calendar,
legendarily established by Romulus. However, Roman scholars already
disagreed over this date, variously putting it at -751 or -754, and I have
seen both -752 and -753 and even -735 (probably a misprint for -753).
Consequently numerical years were never widely used by the Romans.
The calendar had a year of only 304 days in ten months, based on the
growing season, with March as the first month. The rest of the days
were not counted – or else the months drifted through the year??
Romulus's successor, the semi-legendary King Numa Pompilius (c-650
or c-700 or reigned -715/-673) added January at the beginning and
February at the end (or both at the beginning??), extending the year to
354 days with months alternating between 30 and 29 days. An extra
day was added, because odd numbers were luckier, giving a year of 355
days. To correct for the obvious inaccuracy, Numa decreed an
intercalary month of Mercedonius to be added between 23 & 24
February of every third year (or an intercalary month of 22 days every
second year or of alternately 22 and 23 days every second year – ah,
another source says it was 27 or 28 days every other year, but then the
last 5 days of February were dropped, though sometimes the extra
month was omitted when things got out of phase), making a year of 377
or 378 days. The last of the methods gives 1465 days in 4 years,
making a year of 366.25 days, which was later recognised as too long
and supposed to be corrected every 24 years. As can be seen, there is
considerable uncertainty – one source says no one really knows how
many days were in this month. Just to confuse matters, the name
Mercedonius only occurs in Plutarch's Lives, which were written in
Greek – the Romans apparently never had a definite name for it beyond
MEDIEVAL - p. 5
-546/-527
Mid -5C
Mid -5C
-432
c-390
-4C
-336/-323
c-315
-300
c-260
-259?
c-250
c-287/-212
c-275/-194
-213
-196
c-180
c-180/c-125
-153
'mensis intercalaris'. In -452 or -153, February was shifted from 12th to
2nd month, so the beginning of the year was 1 Jan. The intercalations
were done so poorly that the calendar was out by 117 days in -190 and
75 days in -168. Apparently Roman officials often added months in
order to extend their time in office. Caesar reformed the calendar in -46
(qv).
Tyranny of Pisistratus at Athens. He is said to be the first to found a public
library, though this is doubtful – see c-260.
Greeks determine the year is 365+ days long.
Babylonians are asserted to have divided the zodiac into 360 degrees with 60
minutes to the degree.
Meton (and Euctemon?) discovers the 19 year cycle of 235 months. This is the
basis of the Greek astronomical calendar which started on 27 Jun -432,
but doesn't seem to have been used for any ordinary purposes.
The Pythagorean, Archytas of Tarentum (c-430/c-370), establishes the
Quadrivium of Music, Astronomy, Arithmetic and Geometry which
remains the basis of university education until the Renaissance, even to
the 16C.
Callippus adjusts the Metonic cycle (see -432) by omitting the last day of every
fourth cycle. My source claims this makes the year equal to 365 1/4
days, but I can't make this work out.
Reign of Alexander.
Ptolemy I Soter founds Museum (c= a research institute) at Alexandria. This
includes the Library, but the history of these is given in my Greek
Chronology and is too long to carry over to here.
Euclid: Elements of Geometry. This includes a form of the law of cosines,
but it is not clearly stated until Vieta (1593).
Ptolemy II Philadelphus founds first public library in Athens, within a
gymnasium called the Ptolemeion.
Ptolemy II Philadelphus (reigned -282/-247) founds Library at Alexandria with
Demetrios as Librarian, according to some sources – cf c-315. A source
says Ptolemy II acquired Aristotle's library, but I believe it was at
Pergamum, cf -88/-86 below.
Callimachus of Cyrene compiles first library catalogue, for the Library at
Alexandria, comprising 120 rolls.
Archimedes. Volume and surface area of the sphere and primitive integration.
Estimates π by use of a 96-gon as 223/71 < π < 22/7. His Cattle
Problem leads to x2 - 4729494 y2 = 1, the first example of Pell's
equation.
Eratosthenes: director of the library at Alexandria from c-245, his 'sieve' and
measurement of the earth. He gets a circumference of 28,727 miles. He
suggests the calendar adopted by Julius Caesar in -46. He also initiates
the first classical calendar with years numbered, based on the fouryearly Olympiads which began in -776, denoted the first year of the first
Olympiad. This system persisted well into Byzantine times.
Burning of books under Qin Shi Huangdi.
Library founded at Pergamum by Eumenes. In order to discommode these
rivals, Egypt prohibited the export of papyrus (the origin of 'paper'), so
Pergamum developed and perfected the treating of skins for writing –
the word 'parchment' derives from Pergamum.
Hypsicles divides day into 360 parts. (I have seen an assertion that the
Babylonians divided the zodiac into 360 degrees, c-450.)
Hipparchus. He begins trigonometry, using Hypsicles' 360 parts to measure
angles. He clearly gives sin (a + b) and seems to know sin 2a, sin a/2
and sin2 a + cos2 a. Greek trigonometry used chords instead of sines.
He may have made a table of chords. He takes year as 365.247222
days (or 365.246667 = 365 74/300 days). He introduces hours of
equal length in the day and the night, but these are only used in
scientific work.
From this time, Roman years start on 1 Jan, while Greek years continue to start
in midsummer. (This may have started earlier, possibly -452, cf -
MEDIEVAL - p. 6
c-120?
-103
c-100
-88/-86
-1C
c-1C
-46
752.)
Zhou Bi Suan Jing = Chou Pei Suan Ching (The Arithmetical Classic of
the Gnomon and the Circular Paths (of Heaven). Variously claimed
to date from -11C or -4C. It has star positions from between -575 and
-450. Compiled into a book in its present form sometime between -100
and +100. Has the theorem of Pythagoras and applies it.
Chinese ships reach east coast of India.
Jiu Zhang Suan Shu = Chiu Chang Suan Ching (Nine Chapters on the
Mathematical Art. Possibly as late as +50. See also Liu Hui (263) for
more history. 246 solved problems. Finds square and cube roots. Lots
of surveying, area and volume problems. Solves simultaneous linear
equations, both determinate and indeterminate. Earliest known use of
negatives. "The method of positive and negative states: for subtracting
– same signs take away, different signs add together, positive from
nothing makes negative, negative from nothing makes positive; for
addition – different signs take away, same signs add together, positive
and nothing is positive, negative and nothing makes negative." One
problem involves finding a numerical solution of a quadratic by a
method which Needham and Wang identify as Horner's method. Says
area of a circle is the radius times the circumference/2. The volume of
the sphere is found as 9/16 the volume of the circumscribed cube, i.e.
V = 9/2 r3, a traditional ratio based on weighing, corresponding to π =
27/8.
Revolt against Romans in Asia Minor, lead by Mithradates. Sulla defeats
Mithradates and sacks Athens on 1 Mar -86. Aristotle's notebooks are
taken from Pergamum as booty by Sulla. Antikythera mechanism
possibly taken as booty.
Chinese geomancers use a magnetite spoon to indicate north, but the
application to navigation is not made until c1190, cf 1269.
Marseilles was a Greek colony and had a Greek university around -1C, 'the last
refuge of Greek teaching in the West'.
Julius Caesar, advised by Sosigenes of Alexandria, based on Eratosthenes'
suggestion, reforms the calendar to a year of 365.25 days (off by 11 min
14 sec per year). The year -46 (= Roman year 708) has 445 days and is
known as the 'last year of confusion'. This was done by adding 23 days
to February (i.e. intercalating 'Mercedonius') and two extra months
(Undecimber & Duodecimber, having 33 and 34 days) between
November and December. (The confusion was partly due to Caesar –
he had been Pontifex Maximus, and hence in charge of the calendar,
since -52 and he had only inserted one intercalary month which should
have been done every two years.) The vernal equinox is intended to be
on 25 March. The beginning of the year is moved from 1 March to
1 January. March, April, May, June are renamed to the Latin forms
from which the English words are derived (other sources says these
names go back to Romulus or Numa, -8C ??). 8 months are lengthened
and one shortened to shift from the 355 day lunar calendar to the 365
day solar calendar. Basically the odd months have 31 days and the even
months have 30 days, but February has 29 days in normal years and 30
days in leap years. Leap year day is between 25 & 26 February – so
there were two 25ths. Since the 25th was sexto calendas Martias (the
sixth day before 1 Mar), a leap year was known as a bissextile year.
However, other sources say the repeated day was 23 Feb or 24 Feb.
Some sources say Caesar lengthened Quintilis and named it for himself,
but Quintilis already had 31 days and was later named Julius by the
Senate in -45 (or -46), or after his death in -44. The priests
misinterpreted the rules for leap years – because they counted to four
inclusively and hence inserted leap years every third year! This was
sorted out by Augustus who found out that -8 started three days late. He
cancelled the next three leap years, so the next leap year was in +8, so
the Julian system ran consistently from +5. He may or may not have
adjusted the lengths of some months. Whoever did it, a day was
MEDIEVAL - p. 7
-44
-39
-8
removed from February to lengthen August, so the bissextile day
became the 24th of Feb. The seven day week was taken over from the
Jews in the 4C, qv. A source says that an eight-day week was used
before then. Another source says the weeks alternated between 7 and 8
days. From about 1300 until 1752, the beginning of the year had shifted
to 26 (or 25??) March, at least in England, for reasons unknown to me.
Death of Julius Caesar.
Gaius Asinius Pollo founds the first public library in Rome.
Augustus orders a census. Most probable year of birth of Christ. Augustus
observes that this year starts 3 days late and cancels the next three leap
years. Cf -46, +8. At some time, Augustus changed the name of
Sextilius to Augustus – the motion of the Senate is preserved. Further,
a day is added to Augustus by changing the number of days in later
months and stealing a day from February.
0
This year does not exist! See 525. This led to the 2000th anniversary of Virgil
being celebrated a year early!
14
1C
Death of Augustus.
Waterwheels in Europe, Egypt, Asia Minor, China, but they are not extensively
developed until about 1000. However, cf 5C.
Buddhism introduced to China.
Nicomachus of Gerasa.
Silk Road carries Chinese Silk to Roman Syria.
Roman trading post in India.
Cai Lun = Ts'ai Lun invents papermaking in China, using mulberry bark with
other fibres.
Roman Empire at height.
Theon of Smyrna.
Hadrian establishes a library at Athens.
Ptolemy: Almagest uses Hypsicles' and Hipparchus' 360 degrees for a
circumference, taking the radius as 60. Introduces minutes and
seconds, establishing the use of decimals for whole numbers and
sexagesimals for fractions. Includes a table of chords with 30'
intervals (equivalent to angles at 15' intervals), accurate to five
decimals. He describes the astrolabe and its construction. He estimates
π = 3;8,30 = 3 17/120 = 3.14166. He knows sin (a + b) (equivalent
to Ptolemy's theorem on cyclic quadrilaterals), sin a/2 and the law of
sines. Establishes the Ptolemaic System of astronomy. He extends and
amends Hipparchus' star catalogue to 1028 stars. He asserts that angle
trisection cannot be done 'by geometrical methods'.
His Geography introduces latitude and longitude and assumes the earth's
circumference is 18,000 miles, thereby encouraging Columbus's 1492
voyage. He draws his 0o of longitude through the Canaries – the
furthest west land known. He gives latitude and longitude of some
8000 places. In other works, he explains and uses orthographic and
stereographic projections. There is a traditional map of the world
ascribed to Ptolemy, though the oldest extant versions are 12C or 13C –
a version was produced by Maximos Planudes, c1300, based on
Ptolemy's data. He is often considered the first to try to derive Euclid's
Fifth Postulate from the other postulates, but see Aristotle (-384/-322).
He nearly discovers the law of refraction.
Hadrian's Wall built across northern England.
Heron.
Treadle in use on looms.
Marcus Aurelius sends embassy to China.
Epidemic in Roman world (possibly measles or smallpox).
Septimius Severus captures Byzantium for Rome.
Diophantos.
Epidemic in Roman world (possibly measles or smallpox or malaria). This and
the 165-180 epidemic kill off about half of the population and start the
64
100
0-200
0-200
c105
100-200
125
c125
c85-c165
136
150
Mid 2C
166
165-180
196
250
251-266
MEDIEVAL - p. 8
263
267
286
303
312
313
c320
320
early 4C
324
325
325
326
4C
4C
c390
391
394
399-414
400
405
407
410 & 455
415
431
decline of Rome.
Liu Hui: Jiu Zhang Suan Shu Zhu (Annotation on the Nine Chapters on
the Mathematical Art). Already the origin of the Jiu Zhang Suan
Shu was obscure, but Liu says much knowledge, including this book,
was lost in the burning of the books (-213) and was re-edited during the
Han by Marquis Zhang (= Chang Ts'ang) (c-150) and Geng Shouchang
(= Keng Shou-ch'ang) (c-60). Modern scholars are not convinced and
one asserts that internal evidence dates it between -50 and +100. Liu's
edition is essentially the version preserved to the present.
Liu's 'method of circle division' estimates
3.141024 < π < 3.142704 by use of a 192-gon, but he uses
157/50 = 3.14 for practical work. Using a 3072-gon, he may have
estimated π = 3.14160, but some historians feel this was done by Zu
(c480). He uses decimal fractions. He gives a limit argument for the
volume of a tetrahedron. He attempts to find the volume of a sphere,
but only succeeds in relating it to the volume of the intersection of two
cylinders. Cf c500.
Liu extends the material on right triangles by adding a tenth
chapter of nine complicated surveying problems involving distance to
an inaccessible point – e.g. determine the height of an island in the sea
by measurements on the mainland – done by a kind of prototrigonometry. [English version in Historia Math. 13:2 (1986) 99-117.]
The diagrams and commentary were soon lost and this chapter became a
separate work in the 7C, known as Hai Dao Suan Jing = Hai Tao
Suan Ching (Sea Island Mathematical Manual).
Hadrian's library at Athens destroyed by the Heruli.
Division of Roman Empire.
Armenia is first country to adopt Christianity.
Constantine embraces Christianity and wins the Emperorship.
Constantine's Edict of Milan tolerates Christianity in the Empire.
Communal monasticism and religious orders are introduced by St. Pachomius
– cf c520.
Pappus.
Seven-day week introduced. (This is based on the first chapter of Genesis,
which was written about -1000 in order to justify the Jewish seven day
week.)
Constantine decrees the Christian sabbath to be Sunday instead of the former
Saturday which had been used due to its earlier Jewish use.
Council of Nicaea fixes dates of the vernal equinox and of Easter.
Iamblichus.
Constantine founds his city of New Rome, soon called Constantinople, on the
site of Byzantium. Formally dedicated on 11 May 330. First Aghia
Sophia built about 326-360.
Indian Siddhantas begin the use of sines instead of chords. Cosines are also
used. The other functions seem to arisen with the Arabs.
Invention of the stirrup, which rapidly progresses to Europe by the 7C.
Theon of Alexandria, editor of Euclid, father of Hypatia. His edition of Euclid
was the only one known until 1808 when a 10C MS of an earlier edition
was found. However, they are very similar. Theon also writes the first
known treatise on the astrolabe.
Theodosius makes Christianity the state religion and bans paganism, ordering
the destruction of pagan temples. (389?)
Theodosius stops Olympiads.
Fa-hien travels to India. On his return he translates Indian works.
Sun Tzu.
St. Mesrob Mashtots creates the Armenian alphabet of 36 letter.
Roman legions withdraw from Britain.
Rome sacked by Goths
Death of Hypatia, daughter of Theon, at Alexandria.
Patriarch Nestorius of Constantinople is declared a heretic by the Council of
Ephesus. His followers, the Nestorian Christians, are driven into Asia
MEDIEVAL - p. 9
440
5C
5C
460
468
476
c480
499
c500
c500
505
510
early 6C
c520
525
527-565
5-12C
529
532
533
and eventually reach China where they found a church in 638. En route,
they had a school at Edessa (modern Urfa, Turkey) which was closed in
489 and they established a university at Jundi-shapur [= Jundai Shapur
= Gondeshapur, modern Shahabad, south of Dezful, near Ahvaz, Iran]
in the Sassanian kingdom of Chosroes in the 6C. Cf 531-579.
A source says this was the first year that Christmas was celebrated on 25 Dec.
First description of sugar manufacture, in India. Sugar cane came from
Malaya. Another source says it was brought to Greece in the time of
Alexander and commonly used in Greek medicine, but that crystallised
sugar was first prepared in the 7C, with the Persians doing it in the 8C.
Watermills for grinding grain are widespread – examples are known from
Athens to northern England. Cf 1C, whose source said they weren't
common until c1000.
Proclus.
Zhang Qiujian = Chang Ch'iu Chien: Zhang Qiujian Suan Jing = Chang
Ch'iu Chien Suan Ching (Zhang Qiujian's Mathematical Manual =
Chang Ch'iu Chien's Mathematical Manual). 92 problems.
Introduces 100 fowls problem.
Fall of Rome.
Zu Chongzhi = Tsu Ch'ung-chih (430-501), also known as Wenyuan, estimates
π by 22/7 and by 355/113.
Aryabhata I: Aryabhatiya uses a complicated decimal positional systems with
letters for digits. He uses sines and gives a simple table of them.
Chess invented, probably in northwest India.
Zu Geng formulates Cavalieri's Principle and uses it to find the volume of a
sphere by finding the volume of the intersection of two cylinders and
using Liu Hui's result (cf 263).
Varahamihira II. First clear statements of sin a/2 and sin2 a + cos2 a.
Boethius.
Conversion of Clovis, king of the Franks, to Christianity.
St. Benedict (of Nursia) (c480-c543) promulgates his Rule for communal
monasticism at Monte Cassino and 13 other Benedictine monasteries
that he founds. Cf c320.
(or 552 or 532 or c531?) Dionysius Exiguus suggests the Christian Era, i.e. the
division between BC & AD, but omits a year 0 and determines or
adopts the birth of Christ as 25 Dec 1 AD, with the Annunciation and
Incarnation on 25 Mar 1 AD, which would be the first day of the
Christian Era. (One source claims these were in 1 BC.) The lack of the
year 0 often leads to confusion – in 1930, the 2000th birthday of Virgil
was celebrated a year early!
Reign of Justinian.
There was a religious university, Sri Mahavihara Arya Bhikshu Sanghasya, at
Nalanda (Nālandā), near Patna, Bihar. At its height, it had 2000
teachers and 10,000 students, from as far away as Korea. It had an
observatory and astronomy was seriously studied. It seems likely that
Aryabhata (Āryabhaţa) I was head of this university, c500. Xuan Zang,
a Chinese Buddhist monk, travelled to India and studied at Nalanda in
629-647, then carried 600 Buddhist texts back to China. Legend says
the library had 9,000,000 volumes and it burned for six months after the
Afghan invasion in 1199.
Justinian closes the academies at Athens, including Plato's. Some scholars,
including Simplicius, migrate to Persia, Baghdad, etc.
Aghia Sophia burnt down in a riot. Justinian has a new one built in 532-537 by
two mathematicians: Anthemios of Tralles, a professor of solid
geometry with no known building experience, and Isidorus of Miletus,
best known as a commentator on Euclid, but also author of a treatise on
vaulting.
Justinian, Emperor at Constantinople, attempts to regain control of Italy but
fails.
MEDIEVAL - p. 10
542
542
c550
6C
6C
552-565
531-579
560
595
597
560-636
c600
606
615
616
622
628
c629
632
636
636
638
638
640
642
Silkworms and silk technology smuggled out of China to the Byzantine
Empire. This leads to the end of the Silk Road.
An epidemic kills over half the population of Constantinople.
Chess reaches Persia.
Cosmas of Alexandria's Christian Topography refutes the 'false and heathen'
notion that the earth is a sphere and shows it is flat with Jerusalem at
the centre.
Heavy plough in use by the Slavs. This changes the method of agriculture to
strip fields ploughed to produce a ridge and furrow pattern.
Turks dominate Central Asia.
Reign of the Sassanian king Chosroes. He gathered together a library of Greek
and Indian manuscripts at Ctesiphon and had them translated into
Persian. Nestorians establish a university at Jundi-Shapur (modern
Shahabad, south of Dezful, near Ahvaz, Iran) in the Sassanian empire of
Chosroes. Cf 431. The texts and the university were rapidly taken up
by the Arabs after their conquest of the Sassanian Empire in 642-651.
The Persians had preferred the Indian astronomy, so the first Arabic
astronomy was non-Ptolemaic.
Eutocius: commentaries on Archimedes and Apollonius.
Earliest extant tablet with Hindu numerals.
St. Augustine lands in England to evangelise.
Isidore of Seville, encyclopedist and doctor of the Church, preserves much
ancient knowledge. Said to be the first to distinguish astronomy and
astrology.
Chess reaches Persia.
The Pope is believed to have ordered every church to have a sundial.
Arab ambassadors to China.
Persians under Chosroes destroy Jerusalem and capture Alexandria. They are
expelled by Heraclius, the Byzantine Emperor, c628.
16 Jul: Hegira of Mohammed (570-632). Beginning of Moslem calendar, of
355 or 356 days, averaging 354 days 9 hours. However, for
agricultural purposes, a solar calendar was often used, e.g. as devised by
Omar Khayyam in 1079, qv. Modern Moslems use the Gregorian
calendar, subtracting 622 from the year AD to produce the year AH
solar. E.g. 1976 AD was 1354 AH solar, but 1396 AH lunar. Islam
also influences time-keeping and geography/cartography as the times of
prayer are prescribed astronomically and the direction of prayer (the
Qiblah) is to be toward Mecca. Though Mohammed's followers
initially devoted themselves to conquest and conversion, Mohammed
made many statements emphasising scholarship: Seek knowledge from
the cradle to the grave though it be in China; The seeking of knowledge
is obligatory upon every Muslim; etc.
Brahmagupta uses an idea of instantaneous motion in computing the orbit of
Mars (cf 1150).
Bhaskara I's Laghu-Bhaskariya uses a positional decimal system, with letters
representing digits and a zero.
Death of Mohammed. Beginning of the Omayyad Dynasty, cf 660. The
Omayyads were an aristocratic Mecca family that had initially opposed
Mohammed.
Arabs capture Damascus and Syria.
Roman priest goes to China.
Caliph Omar (= Umar) I captures Jerusalem, Palestine and Syria.
Nestorians found a church in China. Jundi-Shapur conquered by Arabs.
Cf 642, 651.
Caliph Umar I interprets Mohammed's phrase: "The number of months in the
sight of God is 12" as requiring a year of 12 lunar months. Hence the
Muslim year is about 354 days long.
(or 640) Fall of Alexandria to Arabs. Library burnt (though it had already
been burnt several times by Julius Caesar (-48), by Theodosius (389)
and by Christian fanatics (several times in the previous two centuries).)
End of Greek tradition, though the language continues in use until
MEDIEVAL - p. 11
c1340. Alexandria eventually declines to a fishing village of 4000
people.
642
Arabs conquer Persia. Cf 638, 651.
651?? or 634-651?? Arabs learn about sugar cane and transport it throughout the Arabic
world, including Sicily and Spain in the 9 & 10C.
644
First mention of windmills. Other sources say they were first used in 6C
France, while others say they came to Europe via the Crusades. Perhaps
developed from Tibetan wind-powered prayer cylinders, but the
developments of this had vertical axles, reaching Afghanistan in early
10C and China in late 13C. Ibne-Mucane, an Arabic writer in Portugal,
mentions windmills in the 10C. The first European example of this type
is c1440. The horizontal axle windmill seems to be an independent
European invention, c12C. The post mill, which has the entire mill
suspended from a post so it can turn into the wind, was invented in 15C
Netherlands. Another source says windmills first appeared in the
Netherlands in mid 13C, possibly derived from Persian examples.
649
Arabs conquer Cyprus.
651
End of Sassanian Empire in Persia. Cf 638, 642. Jundi-shapur is the leading
university and becomes a major centre for transmission of classical and
oriental learning to the Arabs.
7C
St. Carthach founded a university at Lismore, Co. Waterford, Ireland, but it
was destroyed by Viking raids in 978.
656
Followers of Ali, Mohammed's son-in-law, assassinate Uthman, the 3rd Caliph
after Mohammed, leading to civil war. Ali becomes Caliph? Cf 661.
660
Omayyad dynasty established at Damascus. Ends in c750.
661
Assassination of the fourth Caliph, Ali. Cf 656. His followers split from the
main body of Islam to become the Shi'ites.
662
Earliest written reference to Hindu numerals outside India, by the Syrian Abbot
Severus Sebocht of Nisibus, Bishop of Kennesrin, in his Syriac
translation of Theon of Alexandria's treatise on the astrolabe.
668
Greek Fire invented by Callinicus (or Kallinikos) of Heliopolis (in Syria). This
begins the development of more and more explosive mixtures,
culminating in gunpowder.
672
Arabs conquer Rhodes.
673
Arabs first besiege Constantinople but are driven off.
675-735
Venerable Bede (now St. Bede) points out the error in the Julian Calendar and
suggests adding 3 days per 400 years. He describes dating using the
Christian era of Dionysius, but Gibbon says it did not become popular
until the 10C. Steel (cf -1) says he started his years in September,
leading to later confusion – cf late 10C. Bede variously used 1, 24 and
29 Sep corresponding to a tax cycle, the autumnal equinox and
Michaelmas.
c685
Khalid ibn Yazid (c660-704), an Ommayad prince at Damascus, is the first
Muslim noble to become interested in scientific books in other
languages, particularly on alchemy. He brings some Greeks from Egypt
and has them translate from Greek and Coptic into Arabic.
c694
Stirrup adopted by the Arabs.
711
Arabs conquer north India (Sind, modern Pakistan) and Samarkand.
711
Apr: Tariq ibn Ziyad (= Tarik bin Ziyad), Governor of Tangier, leads a force of
several thousand and invades Spain, landing at the rock, Gibraltar (Jebl
at-Tariq) named for him. On 19 Jul 711, he annihilates the Visigothic
King Roderic and all his leadership at Jerez de la Frontera and/or
Guadalete and/or near Medina Sidonia, allowing the Arabs to capture
Córdoba and Toledo by the end of the year and to overrun the entire
peninsula by 714 and to advance into France. The capital is briefly at
Sevilla, but moved to Córdoba in 716.
717-718
Arabs besiege Constantinople but fail. The general success of the Arabs leads
to Iconoclasm and the wholesale destruction of icons in the Byzantine
Empire during 726-780 & 831-843.
c715
The fifth Omayyad caliph, Abdul Malik, makes Arabic the official language,
displacing Greek and Persian.
MEDIEVAL - p. 12
722
724
725
732
c750
c750
8C
8C
8C
751
754-775
762
768-814
Spanish Christian Visigoths, under Pelayo, defeat Arabs at Covadonga,
beginning the 770 year War of Reconquest.
Yi Xing (= Zhang Sui = I-Hsing = Yi-hsing) directs the first field
measurements to establish the earth's circumference. He gets
c46,500 km, compared to the true value of 40,032 km. He uses second
order differences on unequal intervals. He may have learned sines from
an Indian source. In 721-727, he prepares the Ta Yen Li = T'ai-yen
calendar. He is said to have built or used a waterclock.
Leo III, the Isaurian, makes first decree against icons. He also abolishes the
university at Constantinople. (I haven't seen any earlier mention of this
university.) Cf c1050.
Oct: Arabs defeated by Charles Martel at Battle of Tours (or Poitiers) – height
of Islamic expansion via Spain. Franks adopt stirrup.
Abbasid dynasty at Baghdad (but cf 762). The Abbasids were descended from
the Prophet's uncle Abbas and were supported by the Shi'ites, descended
from Ali, the Prophet's cousin who had married Fatima, the Prophet's
daughter. However, once in power, the Abbasids turned against the
Shi'ites. One Omayyad, Abd ar-Rahman (or Abdel Rahman), escapes
the massacres, reaches Spain and establishes the dynasty at Córdoba in
756. They found a university there, possibly in the 8C – cf c970.
Earliest known printed work, a sutra from Korea. Cf 770.
Luitprand, a monk at Chartres, is said to have invented the hourglass. Cf 807,
but most sources say it was invented in the 12C or 13C.
Iron becomes common in ordinary armour and tools.
Ismailis split off from the Shi'ites.
Arabs conquer Tashkent. Battle of Talas: Arabs defeat Chinese and dominate
Central Asia. Arab commander Ziyad ibn Salih captures Chinese
papermakers and introduces papermaking at Samarkand. (This is
narrated by ‘Abd al-Malik al-Tha‘alibi, an 11C historian.) Papermaking
then diffuses to the West.
Reign of al-Mansur, the second Abbasid caliph. He sends embassies to the
Byzantine Emperor to request a copy of Euclid.
30 Jul: Construction of Baghdad begins, founded by al-Mansur, on a c-2500
site. (Cf c750)
Reign of Charlemagne (c742-814), Holy Roman Emperor from 800.
Development of feudalism and of warfare by mounted knights. This is
dependent on several technological innovations during the 6-12C and
leads to a northward shift of Europe's centre of civilization. Among
these innovations are: introduction of the stirrup (early 8C); greatly
increased use of iron; use of the heavy plough, enabling agriculture on
the heavier and more fertile soils of northern Europe (see 6C); a
consequent shift of field use and crops (late 8C onward), including use
of legumes, yielding considerably more crops and, particularly, more
protein, resulting in a substantial increase of population of both people
and horses (and of their health), with much forest land being cleared for
cultivation (the change in agriculture is mirrored in Charlemagne's
attempt to rename the months in terms of the new activities during
them); the horseshoe (late 9C-early 10C – previously cloth had been
used); the horse collar and harness (8-9C), which made horses the
principal power source (a horse with a collar harness can exert 4 to 5
times as much force as with a primitive yoke harness; this makes him as
strong as an ox, but he is 50% faster and has more endurance so he can
work 20% longer per day; overall a horse is about 25% cheaper and can
do the work of two oxen; also horses could be linked in single file,
giving greater power), though farming was not dominated by the horse
until the 11C; improved horses, necessary for knightly combat and for
farm work; development of horse-drawn four wheel wagons (early
12C); consolidation of hamlets into larger and larger villages because
farmers could use horses to reach fields further away; expanded use of
water and wind power. Charlemagne pushes back the Arabs to the
Pyrenees and gains a bit of Catalonia.
MEDIEVAL - p. 13
770
771
Late 8C
775?
721-815
735-804
786-809
c791
794
799 & 800
8-9C
800
800
802
802
Though Charlemagne never learned to write more than his name,
he was fluent in Latin and thoroughly committed to improving
education in his realm. He persuaded Alcuin to come to Aachen and
supervise education in the realm. He was especially interested in
having a correct calendar, which led to a medieval preoccupation with it
- cf 799 & 800, 809.
First block printing, in Japan, to produce 1,000,000 Buddhist prayer papers. Cf
c750.
Brahmagupta's work brought to Baghdad by a Hindu scholar, Kankah (or
Kanaka or Mankah?). A Surya Siddhanta was translated into Arabic
by al-Farazi and an Indian by order of Caliph al-Mansur (Caliph in 754775) and known as Zij al-Sindhind (The Great Sindhind). (Al-Biruni
gives the date 771, but not the name of the Hindu. Others give the date
as 766 or 773. Al-Biruni mentions another embassy from India in 778.)
The Arabs had not yet adopted the Hindu numerals and used the Greek
alphabetic numerals.
Printing in China.
Arabs begin translating Indian and Greek works, but see 771. The leading
figures are Yaqub ibn Tariq (Jacob ben Tarik) (??-796) and Muhammad
ibn Ibrahim al-Farazi. One source says ibn Tariq started a school in
777.
Jabir ibn Hayyan (variously denominated: al-Azdi, al-Kufi, al-Tusi or al-Sufi;
Geber (in Latin)), leading chemist, said to be the inventor of distillation,
but he also compiled astronomical tables and wrote on Euclid, the
Almagest, magic squares and mirrors.
Alcuin of York. He supervises the revival of learning in Charlemagne's
empire. Thought to be the author of Propositiones ad acuendos
juvenes, the earliest known appearance of many problems, including
the earliest examples of real combinatorial problems – the river crossing
problems and the desert crossing problem.
Caliphate of Harun al-Rashid (c766-809). He starts Khizanat al-Hikma
(Library of Wisdom). Extensive translation and study of Greek and
Indian works. Euclid translated by al-Hajjaj ibn Matar. The University
at Jundi-Shapur is still active, is tolerated (even encouraged) by the
Caliphs and plays a major role in translation of Greek works into
Arabic.
Messehalla (= Messahalla = Māshā’allāh), a famous Jewish astrologer in
Baghdad, composes a treatise on the astrolabe. The Arabic is lost and
only a Latin translation survives. Chaucer's 1391 treatise is based on
this. Messehalla had assisted an astrologer in the surveying preliminary
to establishing Baghdad. He also wrote on the armillary sphere, etc.
Papermaking established in Baghdad and soon displaces papyrus and
parchment for official records. Ibn Khaldun, the 14C historian, says the
vizier al-Fadl ibn Yahya introduced paper when there was a shortage of
other writing materials. Ibn Yahya came from Balkh in the north of
Afghanistan and hence would have known of paper there. There is
Egyptian paper from c800.
Due to confusion, a saltus lunae was omitted at the Frankish court in 797. This
was necessary to align the 19-year Metonic cycle with the solar cycle
and its omission would lead to lack of agreement with other calendars.
Dionysius and Victorius put the saltus in Sep while Bede and Alcuin
had it in Jan. Charlemagne and his advisers decided to put it in Mar and
the years of 799 and 800 began in March in Aachen, Paderborn and
Heristal. Cf 809.
Development of horse harness completed in northern Europe.
Christmas: Charlemagne crowned Holy Roman Emperor by the Pope at St.
Peter's, Rome.
Harun al-Rashid sends embassy to China.
Earliest Byzantine reference to chess.
Harun al-Rashid sends present of an (white?) elephant (or in 801) and a
waterclock (or in 807) to Charlemagne.
MEDIEVAL - p. 14
807
809
813
813-833
814
820
c820
820?
c825
c825
825
827
c830
840
Charlemagne orders a 12-hour hourglass. Cf 8C, 13C.
A Frankish synod was called to resolve the problems of the saltus and the date
of New Year that arose in 799 & 800. This decided to start the year on
1 Jan and put the saltus in Jan, but it's not clear how far this reform
extended.
Charlemagne orders usage of the common language (lingua romana rustica)
instead of Latin (lingua latina) in sermons.
Caliphate of al-Mamun (786-833), son of Harun al-Rashid. He establishes Beit
al-Hikma (House of Wisdom) at Baghdad, under the Nestorian Hunayn
ibn Ishaq al-Ibadi (809/810-877). This has a library and an observatory.
Al-Mamun asks the Byzantine Emperor for a copy of all the books in
the Byzantine Empire!! A 10C story is that Aristotle appeared to alMamun in a dream and assured him there was no conflict between
reason and revelation. Al-Mamun even made observations in the
observatory. Al-Hajjaj makes a second translation of Euclid.
Death of Charlemagne. His son, Louis the Pious, is weak and divides the Holy
Roman Empire among his three sons in 838-843.
Αl-Khowarizmi (= al-Khwarizmi = Abu Jafar Muhammad ibn Musa
al-Khuwarizmi) (c780-850) is invited to the Beit al-Hikma as
astronomer and then librarian. He was ordered to produce a new
translation of the Indian Siddhanta. He exposits Hindu numerals and
algebra. His The Book of Addition and Subtraction According to
the Hindu Calculations made the Hindu system available to the Arabic
world – only one copy, in Latin translation (Algorithmi de Numero
Indorum), survives - it was discovered at Cambridge in 1857. It is
thought to have been translated in the 12C by Adelhard of Bath or
Robert of Chester. (A second Latin version has just recently been
found.) His Kitab al-jabr wa l-muqabala (The Book of Restoring
and Balancing) does algebra in words and then geometrically. Much
of the book concerns problems of inheritance. He uses signed numbers
but rejects negative roots. The book's title leads to the word 'algebra'.
The author's name leads to the word 'algorithm'. He works at the Beit
al-Hikma and assists in measuring the degree – cf c825. He produces
astronomical and trigonometrical tables with sines and tangents. Uses
'casting out nines'.
Alhasan ibn Musa ibn Schaker is first to give the construction of an ellipse by a
string and two foci. Cf c-200, c320 & 410-485 in Greek Chronology.
Abd-al-Hamid (al-Turk) exposits algebra very similarly to al-Khowarizmi.
First European grindstone, with a crank.
Al-Mamum sends out expeditions to measure the distance of a degree. The
Compendium of al-Farghani (Alfraganus) includes the results, stated as
56 ⅔ miles of 4000 cubits. (Al-Biruni says 56 miles was also
obtained, but he uses 56 ⅔.) Depending on which cubit was used, this
would be 112.9 or 109.4 km, giving earth circumferences of 40,637
or 39,372 km compared with the correct values of 111.14 km and
40,010 km. By the time of Columbus, the size of the Arabic mile was
lost and he assumed it was the Italian nautical mile, giving him a degree
of 91.5 km and a earth circumference of 30,185 km or 18,756 mi,
comparable to Ptolemy's value. Al-Mamun's astronomers also
determine the angle of the ecliptic is 23o 33'.
University of Pavia founded - ?? [Helen Waddell; Medieval Latin Lyrics;
(1929), 4th ed, (1933); Penguin, 1952, p. 339] says the University
celebrated its eleventh centenary in 1925. But cf 11C.
Arabs occupy Sicily.
Habash al-Hasib al-Marwazi (= Habash al-Hāsib [the Hs should have dots or
cedillas? under them]) at Baghdad computes tables of sin and tan at 1o
intervals to 3 sexagesimal places. He computes a table of cotangents.
Perhaps the first to use tangents and cotangents. He develops a
convergent iterative process for solving Kepler's equation:
x + b sin x = a.
Al-Farghani (Alfraganus): Compendium (or Elements?) summarises
MEDIEVAL - p. 15
c840
c840
842
850
850
9C
859
830-910
836-901
c860
863
868
c870
874
876
867-902
888
c890
c890
c890
c850-930
9-10C
900
c900
858-929
Ptolemy's Almagest.
Al-Adli, first known great chess player. Cf c880-946.
Pacificus, archdeacon of Verona ( -844) invents the nocturnal, a dial which
gives the time at night by use of the date and the position of the stars
near the Pole Star. He is also said to have invented the escapement and
the use of weights to drive a clock.
End of Iconoclasm in Byzantium.
Mahavira.
Pacificus, archdeacon of Verona, is said to have invented the escapement and
the use of weights to drive a clock.
First mention of an explosive substance, in a Chinese text.
University of Karueein (= Qarawiyyan), near Fez, Morocco, founded – it is
claimed to be the oldest extant university in the world.
Ishaq ibn Hunayn, son of Hunayn ibn Ishaq, makes third translation of Euclid,
later edited by Thabit ibn Qurra, and translates the Almagest.
(or 826-901) Thabit ibn Qurra (Thābit ibn Qurra) – works at the Beit al-Hikma
in Baghdad. He translates or edits Euclid, Archimedes, Apollonius,
Ptolemy, etc. He investigates the parallel postulate, using the Saccheri
quadrilateral. He also finds some areas under curves, a la Archimedes.
He gives a dissection proof of the Theorem of Pythagoras and his
generalization to non-right triangles. He gives a complex rule to
produce amicable numbers, but apparently could not find any – cf
c1300.
An Imperial Academy is refounded at Istanbul under Leo the Mathematician.
Cyril and Methodius bring Christianity to Moravia and create the Cyrillic
alphabet for Slavic languages.
11 May: earliest extant printed text with a date – the Diamond Sutra, nearly
5 m long, made by a Mr. Wang in honour of his parents. It is in the
British Library – see 1907.
Beni (or Banu) Musa (Sons of Moses) – three brothers – translate Greek works
at the Beit al-Hikma. They measure a degree on the meridian and
determine the earth's circumference as 39,000 km. They give the first?
description of windmills (cf 644). Their Kitab al-Hiyal (Book of
Ingenious Devices) describes 83 kinds of trick vessels, as well as
fountains, etc.
Earliest surviving dated (Egyptian??) paper.
Oldest surviving inscription using 0, at Gwalior in India.
Saffarid dynasty in Persia, cuts off contact between Arabs and India.
Sep: Oldest extant copy of Euclid's Elements completed by Stephanus clericus
at Constantinople and sold to Arethas of Patrae, later Bishop of
Caesarea. Used and annotated for 5 centuries, it is now in the Bodleian
Library, Oxford.
The Anglo-Saxon Chronicle is the earliest history of a European country in a
vernacular language. Its preparation was probably ordered by King
Alfred (849-999). Copies were sent to various monasteries which made
additions, in one case up to 1154.
Qusta ibn Luqa translates Diophantos's Arithmetica.
Rudrata = Rudraţa: Kāvyālaʼnkāra – first Knight's Paths on a chessboard.
Abu Kamil. His Algebra is the second oldest Arabic example to survive. He
extends and clarifies al-Khowarizmi, integrating more of Greek ideas
into algebra.
First known horseshoes, in Siberia and Byzantium. By the end of the 10C, they
are mentioned as habitual for those going on journeys.
Sridhara.
Gunpowder developed by the Chinese and used in war.
Al-Battani (Albategnius), from Harran. Gives a new result on spherical
triangles. His astronomy was the main vehicle for bringing Indian
astronomy to the west as De Motu Stellarum, emphasising the use of
sines instead of chords. Computes table of sin at ½o intervals to 3
sexagesimal places. One source says he used prosthaphaeresis.
MEDIEVAL - p. 16
860-932
909
c880-946
912
915
927/8
929
932
909-946
952-953
10C
10C
940-998
969
969
c970
Cf: 1005, 1514, c1585, 1540-1603, 1546-1601.
Rhazes = Abu Bakr Muhammed ibn Zakariyya. His main work is in medicine,
but his encyclopedia of medicine, El Háwi, includes philosophy,
astronomy and mathematics.
Fatimid dynasty established in Tunisia, then Egypt. They claimed descent
from Fatima, the daughter of Mohammed. In 969, they conquer Egypt
and set up their own Caliph in opposition to the Abbasid Caliph in
Baghdad. Dynasty ends in 1171.
As-Suli, second known great chess player. Cf c840.
Norsemen, under Rollo, settle in Normandy and adopt Christianity. Some of
them move to the Mediterranean and take over Sicily and southern Italy.
El-Masudi visits India and China.
Earliest surviving dated astrolabe, made by Basţūlus, 315 AH, though the
object was known in classical times.
Abd ar-Rahman III declares himself Caliph at Córdoba.
Manjula states that the rate of change is zero at an extremum. See Bhaskara II
(1150) & Oresme (1323-1382).
Ibrahim ibn Sina, a grandson of Thabit ibn Qurra, gives an easy derivation of
the area under a parabola, writes on sundials and On Drawing the
Three Conic Sections.
Abu al-Hasan Ahmad ibn Ibrahim al-Uqlidisi (the Euclidean) (Abu’l-Hasan-alUqlidīsī). His Kitab al-Fusul fi al Hisab al-Hindi (The Book of
Chapters on Hindu Arithmetic), composed in Damascus, is the oldest
surviving Arabic arithmetic text. It exposits decimal fractions,
generally attributed to al-Kashi in the 15C, using a decimal point – a
source says he used ' . He says scholars now use pen and paper and he
gives algorithms for use on paper.
Papermaking at Damascus and Cairo. By c1000, papyrus was no longer in use.
Ibne-Mucane, an Arabic writer in Portugal, mentions windmills.
Abu Wafa (= Abu’l-Wefa = abu’l-Wafa = Abū al-Wafā’) Muhammed ibn
Muhammed ibn Yahya al-Buzjani, in Baghdad, develops plane and
spherical trigonometry. He lectures on construction with ruler and fixed
compass. Gives first clear statement of sin 2a. Probable first proof of
sine theorem for spherical triangles – but the priority of discovery of
this result was disputed between him and Abu Nasr Mansur and
al-Khujandi. Introduces secant and cosecant. He constructs tables of
sines and tangents at 15' intervals – the earliest known table of tangents.
He first translates Diophantos into Arabic. Wrote a lost work on
finding roots. The first to consider tessellations of the sphere.
Emperor Mu-tsung is reported to have played cards with his wives – the
earliest reference to playing cards. However, it is evident that these
were the 'domino' cards still in use in China. Cf 1120. However, I have
a modern reference which says that cards were already known in the
Tang (618-906).
Cairo conquered and refounded by the Fatimids (cf 909) – there had been cities
on or near the site for about 3000 years. The fourth Fatimid caliph,
al-Muizz (ruled 953-975), was a patron of learning and founded
Al-Azhar mosque/library/university in 970. The library had 40 rooms
of books including 16,000 on the 'sciences of the ancients'. (I've heard
this dated at c875??) The patronage was continued by his successors alAziz (ruled 975-996), al-Hakim (ruled 996-1021, cf 1005) and the next
one.
Al-Hakam II (reigned 961-976) creates a library at Córdoba with 400,000
books – the catalogue was 44 volumes. Córdoba was the greatest city in
Europe with 500,000 (or 100,000 or 1,000,000) people – only
Constantinople, Baghdad and Xian were comparable. The library was
destroyed in the civil wars of 1009-1031. There was a university,
claimed to have been founded in the 8C, though other sources say 10C,
probably referring to the library.
Maslama ibn Ahmad al-Majriti (or al-Magriti), based in Madrid, is a leading
MEDIEVAL - p. 17
c980
late 10C
c987
989
Late 10C
Late 10C
10-11C
c1000
c1000
c1000
c1000
c980
1005
1005
c965-1039
scholar of this period, making a commentary on Ptolemy's
Planisphaerium and a treatise on the astrolabe. His alchemical work,
The Sage's Step is notable for (the first ?) description of a quantitative
chemical experiment.
Gerbert (930-1003) (Pope Sylvester II in 999-1003). Studied at Córdoba.
Attempts to introduce counters with Arabic numerals to use on a
counting board. He rediscovered Boethius' work on geometry. He also
makes a pendulum escapement and is said to have invented the striking
clock.
Steel (cf -1) says New Year shifted to 25 Mar due to increasing veneration of
the Virgin Mary, but that the New Year was moved ahead from Bede's
September date, effectively losing a year! However, not all places
adopted this count – Florence did, but Pisa moved its New Year back.
Hence the date we would now consider to be 25 Mar 1001 would be
consider the beginning of 1000 in Florence, but the beginning of 1001
in Pisa. England used the (incorrect) Florentine style until 1752, when
the New Year was moved back to 1 Jan, but this still means we are one
year ahead, i.e. the year 2000 ought to be numbered 2001!
Abu’l-Faraj Muhammad ibn Ishaq, also known as Ibn Abi Ya‘qub Al-Nadim
al-Warraq ('the stationer') (??-995), in Baghdad, compiles his Kitab alFihrist al-Ulum, a massive bibliography of books which is our only
knowledge of many lost books.
(or 987) The ambassadors of Prince Vladimir of Kiev are so impressed with
the services in Aghia Sophia that Russia adopts Orthodox Christianity,
bringing Russia into Europe.
Abu Sahl al-Kuhi studies centres of gravity and shows how to construct a
regular heptagon by constructing two conic sections.
Abu Nasr Mansur develops use of tangents and cotangents.
Wood block printing is common is China.
Mariner's compass used at Amalfi. In Amalfi, they say Flavio Gioia perfected
it. [G. L'E. Turner, p. 129] says 12C.
Waterwheels and watermills begin to flourish and are used for many purposes.
But cf 5C which says these were common at that time.
Kushyar ibn Labban (971-1029): Principles of Hindu Reckoning exposits
calculation of a 'dust board'. Mentions casting out nines. Includes a
calculation of cube root in decimal system. Computes table of sin at 1'
intervals to 3 sexagesimal places.
Abu Mansur al-Baghdadi (= above at late 10C??) uses decimal fractions, using
a notation like Kushyar ibn Labban.
Gerbert (930-1003) (Pope Sylvester II in 999-1003). Studied at Córdoba.
Attempts to introduce counters with Arabic numerals to use on a
counting board. He also makes a pendulum escapement and is said to
have invented the striking clock.
First printed paper money, in China. (910?? Another source says it was tried
out in 812 and became general by 970.)
Fatimid ruler al-Hakim (ruled 996-1021) founds Dar al-Hikma (House of
Wisdom) in Cairo. This has a library and an observatory. In 1043 a
traveller reports it had 6,500 books on astronomy, geometry and
philosophy. It lasts to the end of the Fatimid dynasty in 1171.
The leading scholar at the Dar al-Hikma was Ibn Yunus (= Ibn Yūnus)
( -1009) who introduced(?) prosthaphaeresis – i.e. multiplication by use
of: cos A cos B = ½[cos(A+B) + cos (A-B)], or the analogous formula
for sin A sin B. But cf 858-929. He founds (or directs) an observatory
at Cairo, presumably that just mentioned. He also noted the regularity
of the pendulum. His book on astronomy, Zij-ul-Albar-al-Hakimi,
displaced the Almagest.
(or c965-1040) Ibn-al-Haitam (= Ibn al-Haitham = Abu ‘Ali ibn al-Hasan Ibn
al-Haytham = Alhazen). Book on Optics has Alhazen's problem,
which leads to a quartic which he solves by intersecting a hyperbola and
a circle. Works on isoperimetry. He shows that light travels from the
MEDIEVAL - p. 18
973-1048
1010
c1010
980-1037
c1025
11C
11C
11C
1009-1031
1041-1048
1044
11C
c1050
object to the eye – as also shown by ibn-Sina and al-Biruni. Recognizes
atmospheric refraction. Discovers spherical aberration and is first to
describe the camera obscura. Optics was translated into Latin and
influenced Roger Bacon and Witelo. He studies the parallel postulate,
using something like the Saccheri quadrilateral. He expresses doubts
about the Ptolemaic system. His Book of the Balance of Wisdom,
1121/1122, carefully discusses many physical properties.
Abu‘l-Rayhan Al-Biruni (= ’Abû-alraihân [the h should have a dot under it]
Muhammad ibn ’Ahmad [the h should have a dot under it] Albêrûnî).
His India (c1030) includes extensive description of Indian mathematics
and astronomy. He determines the year as 365.240278 days and π as
3.1417482 and as 4800/1527 = 3 73/509 = 3.14341 84676, stating that
it is irrational. He describes the common Arabic technique of 'levelling'
to multiply sexagesimals by converting to decimal. He measures the
dip of the horizon from a mountain top to determine the size of the
earth, getting 55.8875 miles per degree. Cf. 825. Computes tables of
sin at 15' intervals and tan at 1o intervals to 4 sexagesimal places. His
Maqālīd ‘ilm al-hay’ah (Keys to the Science of Astronomy) is the
first separate book on spherical trigonometry. He also produces Kitāb
fī isti‘āb al-wujūh al-mumkinah fī şan‘at al-aşţurlāb (A Book of
Detailed Treatment of All Possible Ways of Making an Astrolabe).
Born in the region of Khowarizm. Based at Ghazna, in modern
Afghanistan.
Earliest European mention of chess – the Count of Urgel (in Spain) leaves his
rock crystal chess set to a convent. By 1200, the game has spread over
most of Europe, reaching as far as Iceland, the Baltic and Bohemia.
Al-Karkhi (= Abu Bakr al-Karagi (al-Karaji)) ( -c1024) of Karkh, a suburb of
Baghdad. His book, known as Al-Fakhri, develops algebra, beginning
some syncopation and giving some of the rules of signs and of
exponents. (The laws of exponents were first? given by Archimedes.)
He gave a proof, now lost, that x3 + y3 = z3 has no integral solutions.
Abu Ali Hussein ibn Abdallah ibn Sina (Avicenna). In one of his writings, he
refers to a boy being sent to a "certain vegetable seller who used Indian
arithmetic" to learn from him. This seems to refer to himself! He wrote
on physics and astronomy, making (the first ?) suggestion that the speed
of light was finite, and invented a kind of vernier.
Al-Nasawi, from Nasa, Khurasan, writes Kitab al-Mugni fil-Hisab al-Hindi
(The Satisfying Book on Indian Arithmetic) and uses decimal
fractions, getting 17 = 4.12, though he then converts the result to
sexagesimal.
False dice, with two ones, were made. (Late 12C?)
Al-Muradi, writing in Spain, describes mechanical devices including complex
gearing used for power transmission.
Invention of tide mills.
Civil wars fragment the Omayyad Caliphate of Córdoba. (Another source says
this started when caliph al-Mansur died in 1002.) The library of
al-Hakam II is destroyed. Later Moorish Spain is intermittently
dominated by Berber dynasties at Sevilla (Seville), which succeeds
Córdoba as the greatest city in Europe. But general disorganization
leads to the Christian reconquest, completed in 1492.
Bi Sheng invents block character printing, using fired clay types set in wax on
a wood tray.
Earliest extant formula for gunpowder, in Zeng Gongliang's Wu Jing Zong
Yao (= Wu Ching Tsung Yao. But there is also a Syriac text of 1011C which gives seven recipes for gunpowder.
Earliest known playing card, from Turfan, western China.
Constantine X Monomachus refounds the University at Constantinople. Cf
725.
MEDIEVAL - p. 19
11C
University of Pavia founded. (However, this contradicts assertions that Padua
(1221) is the second oldest Italian university. Also cf 825.)
11C
‘Ali ibn Khalaf of Toledo devises the lamina for astrolabes which eliminates
the need for different plates for different latitudes. By the end of the
century, Ibn az-Zarqālī of Toledo (or Córdoba) develops the saphaea
Azarchelis, a version of the astrolabe not needing a rete, hence reducing
it to just one plate. He built a waterclock.
1054
16 Jul: Schism between Roman and Orthodox churches.
1055
Seljuk Turks conquer Baghdad and later push into western Turkey after the
battle of Manzikert in 1071. They also conquer Jerusalem and much of
Palestine, where their intransigent rule leads to the Crusades.
1056
First known Spanish papermill, at Jativa.
1061
First known mention of chess in Italy – an Italian cardinal castigates one of his
Florentine bishops: "Was it right ... to sport away thy evenings amidst
the vanity of chess, ... with the pollution of a sacrilegious game?" and
sends a complaint to Pope Alexander II.
1065
University of Baghdad founded by the 'prime minister' Nizam-ul-mulk.
1066
Normans, under William the Bastard, conquer England. And all that.
Late 11C
First mention of a flywheel.
1079
Omar Khayyam and others produce the Jalalian or Malik-Shah Calendar, cf at
c1044-1123/4.
1080
Shen Kuo gives four ways to pivot a compass needle, one of which shows the
magnetic declination – see 1492. Older works have claimed that the
earliest Chinese record of a compass is 1297 and that the European
appearance of the compass is independent of the Chinese appearance.
The latter assertion may be correct.
1081-1085
Abū ‘Āmir Yūsuf ibn Ahmad [the h should have a dot under it] ibn Hūd, alMu’taman, is King of Saragossa. His Kitāb al-Istikmāl attempts to
present all known mathematics. Several portions of it were identified in
1985. It includes Ceva's Theorem (named after Giovanni Ceva who
independently found it in 1678), results on cross ratios, a major
simplification of two problems of ibn al-Haytham (independently
discovered in 1942!).
1083
Liu Hui's Sea Island Mathematical Manual (263) printed in China.
1085
Alphons VI captures Toledo from Moors. Toledo becomes the centre for
translations from Arabic MSS. Cf c1125.
1086
Domesday Book records 5624 watermills in England.
1088
University of Bologna founded – the first university in Europe. (Some of the
Moorish schools in Spain could certainly be considered as universities,
though I don't think any survived through the Reconquest – see c750,
c970, 1009-1031, 1096, 1492.)
1088
Su Sung builds an astronomical waterclock at the Observatory at Kaifeng,
using a 3.5 m diameter escapement wheel. It is described in a book of
1172. A model is in the Science Museum, London.
1091
Normans conquer Sicily from Arabs.
1095
Urban II calls for First Crusade. (1096?)
1095
El Cid conquers Valencia from the Moors.
1096
School of Salerno flourishes from 1096 to 1270. It may well predate Bologna,
but is generally not counted as a university, probably because it was
basically only a medical school.
1099
First Crusade conquers Jerusalem and establishes a Frankish Kingdom of
Jerusalem.
c1100
Legend says Godfrey de Bouillon (c1060-1100) brought chess to Europe when
he returned from the First Crusade. However, he died on the Crusade
and his life became the subject of romantic legends.
c1044-1123/24
Omar Khayyam (Abul-Fath Umar ibn Ibrahim al-Khayyami). His Algebra
considers and classifies cubics, giving geometrical solutions via conics,
but avoids negatives. He mentions a method that may have been the
binomial theorem for use in finding roots – this was described in
another work, now lost. Studies the parallel postulate of Euclid, using
MEDIEVAL - p. 20
the quadrilateral of ibn al-Haytham and Saccheri in a different way,
possibly the first to recognise the three cases dependent on whether an
angle is obtuse, right or acute. He is part of a group of eight who, in
1079, produce the Jalalian or Malik-Shah Calendar with 8 leap years in
a 33 year cycle, giving a year of 365.24242 days. "Ah, but my
calculations, people say, / Have squared the year to human compass,
eh? / If so by striking out / Unborn tomorrow and dead yesterday." He
asserts that values like 2 and π are actually numbers, rather just
ratios of magnitudes as in Greek thought. See also Nasir Eddin, 12011274.
c1100
1102
1109
1116
1118
1120
1120
1120
c1125
Early 12C
1128
c1130
1132
1137
1133-1144
The use of a magnetic needle for geomancy is recorded in China in 1040-1044,
1089-1093, 1116. It is used for navigation in 1119 and 1122.
Papermaking introduced to Sicily.
William of Champeaux lectures on logic at Paris – usually taken as the
beginning of the University, though others date it to Abélard's teaching
in 1208. The Sorbonne was established in 1253 (qv).
Chinese using the magnetic compass for navigation, possibly already by late
11C.
Saragossa falls to the Christians. A source says cannon were used by the
Moors, but cf 13C.
Plato of Tivoli (fl. 1116-1138), at Barcelona, translates Arabic works, mostly
on astronomy. Assisted by Abraham ben Hiyya, he also translates from
Hebrew.
Walcher, Prior of Malvern (England), produces a Latin translation of an
astronomical work by Pedro Alphonsi, an Arabic-speaking Spanish Jew
who had converted to Christianity and visited England.
Emperor Suen-ho has playing cards made for his wives – probably the Chinese
'domino' cards. Cf 969. This comes from a Chinese encyclopedia of
1678. They are also recorded in 12C Arabia (I've forgotten this source –
it may refer to the following facts). There is a fragment of a 12C or 13C
card and an almost complete early 15C deck from Egypt? (it is from the
Mameluke era and now in the Topkapi Museum) which show that the
52 card deck came to Europe from Egypt (or thereabouts). Indian cards
and games are such that it is conjectured that cards originated in Persia
or central Asia and that the Arabic/Egyptian and Indian forms are
derived from a common ancestor rather than one from the other.
However, a Chinese origin seems more likely from the evidence. John
Scarne says there is an 11C card from Chinese Turkestan, cf 11C.
Archbishop Raymond I of Toledo (in office 1125-1152) establishes a school of
translators. His successor Rodrigo Jimenez de Rada (archbishop in
1170-1247 (??)) continued supporting the school.
Al-Jazari's Compendium of the Theory and Practice of the Mechanical
Arts describes watermills and windmills, clocks, musical automata, etc.
First use of a crank in a mechanism. May have known of a speed
governor.
Chinese invade Turkestan.
Adelard of Bath (fl. 1116-1142) – first translator of al-Khowarizmi's
Arithmetic and of Euclid's Elements, from Arabic into Latin, at
Toledo. Cf c1270, 1482. His translation of an astronomical work
introduced the sine and tangent to the Latin world. He was tutor to
Henry II and the first known Englishman to study Arabic.
First guns – with bamboo barrels.
Medical school founded at Montpellier, sometimes claimed to be Europe's first,
but Salerno seems to be earlier – cf 1096. Montpellier is certainly the
oldest extant medical school in Europe. Montpellier becomes a
university in 1287. But another source says the Faculty of Medicine,
and hence the University, was founded by Cardinal Conrad, the Papal
Legate, on 17 Aug 1221. But the source adds that medicine had been
studied at Montpellier in rabbinic schools going back to the 11C.
First lectures at Oxford – beginning of the University, which had existed in
MEDIEVAL - p. 21
1139
c1140
1092-1167
1144
1145
12C
1150
c1150
1150s
1126-1198
1157
c1160
1162
1167
1135-1204
1170
1171
1172
c1175
1176
1176
1096-1270
Late 12C
some form from at least 1096.
Second Lateran Council prohibits the use of crossbows.
Al-Idrisi (1100- ), a Muslim geographer at the court of Roger II in Palermo,
writes a systematic geography of the world, called the Book of Roger.
He relates that a Moroccan sailor was blown off course in the Atlantic
and returned telling of a fertile land inhabited by naked savages –
America??
Ibn Ezra. His works include a poem about chess.
Arabs recapture Edessa (modern Urfa, Turkey), beginning the expulsion of the
Crusaders.
Robert of Chester spends 1141-1147 in Spain, with some time at Toledo. He
makes the first translation of al-Khowarizmi's Algebra in 1145. (This
may be a confusion with al-Khowarizmi's Arithmetic - ??check. Cf
c1130.) The translation begins "Dicit Algoritmi", whence the word
algorithm. His 1144 translation Book of the Composition of Alchemy
is the first Latin work on alchemy. He also computed astronomical
tables for London and a treatise on the astrolabe, introducing the term
'sine' as the translation of the Arabic 'jaib'.
The Arab geographer Edrisi (c1099-1154) is the first (outside China?) to
mention polarity of a magnet.
Bhaskara II: Lilavati & Bijaganita. He uses the idea of differentiation to find
velocities of planets fairly generally (cf 628). He determines the rates of
change of sin x and cos x and repeats Manjula's observation (932). In
his Golādhyāya, he uses a form of integration to determine the area of a
circle and the area and volume of a sphere, though he does not have the
notion of the limit or sum of the series involved. See also Manjula
(932) and Oresme (1323-1382).
John of Seville (= Johannis Hispalensis) (fl. 1135-1153 at Toledo). A Jew who
had converted to Christianity, he translated from Arabic to Castilian.
An associate, Domingo Gundisalvo, translated the Castilian to Latin.
Papermaking introduced to Western Europe, in Italy, at Fabriano (1150 (more
likely 1276??)) and at Xativa (or Jativa), Spain (1154 or 1151 or 1056,
qv).
Abu el Walid Muhammad Ibn Rushd (= Averroes).
First modern bank established at Venice.
Almagest translated from Greek into Latin, in Sicily.
Birth of Temujian, later known as Genghis Khan.
English students at Paris migrate to Oxford and expand the University. First
indications of a general university at Oxford.
Moses ben Maimon = Maimonides: Treatise on the Terminology of Logic.
He asserts that π cannot be known precisely (apparently meaning it is
irrational) and gives 3 1/7 as an approximate value.
Earliest known use of a form of the word 'engineer', at Durham.
Saladin (= Salah al-Din) deposes last Fatimid Caliph in Egypt and founds
Ayyubid dynasty.
Al-Samaw’al ben Yahya ben Yahuda al-Maghribi (d. 1180) uses decimal
fractions. His The Shining Book on Calculations has the rules of
signs and rules of exponents.
Gerard of Cremona (1114-1187), at the College of Translators in Toledo,
translates 76 books from Arabic, including Ptolemy's Almagest and
Euclid's Elements. One of the first to use the word 'sinus' for half the
chord.
Ayyubid dynasty in Egypt and Syria. Ends in 1250.
Rabbits reach England and become common in the 13C. They were an
important new source of meat.
Height of the School of Salerno, one of the first universities in Christian
Europe (cf 1096), particularly noted for medicine. Michael Scot was a
student, c1175 – he translated Aristotle.
Alexander of Neckam: De naturis rerum describes mariner's compass. By
1225, it was in common use as far as Iceland. He also describes
weaving and the use of the treadle therein. By the 13C, treadles are
MEDIEVAL - p. 22
1180
1187
c1190
1193
12-13C
c1200
c1200
c1200
c1200
1200
1202
1202
1204
1206-1227
1209
1206-1279
1212
1214
Early 13C
1215
1220
1220
c1221
1221?
1221
commonly used for looms and lathes. Pedal keyboards provided for
organs by c1418.
Glass windows first used.
Saladin recovers Jerusalem and most of Palestine for Arabs, destroying the
Christian army at the Horns of Hattin.
Magnetic needles being used as compasses in Italy.
Eustanthius ( -1193), Archbishop of Thessalonica, says dice should have
opposite sides adding to 7 to prevent cheating. This is mentioned by
Cardan.
Arabs increasingly use incendiary devices based on forms of gunpowder in the
Crusades.
Windmills began working in Holland and Britain. (Perhaps mid 13C?)
Jacques de Vitry's history of the Crusades, Historia Orientalis, describes
mariner's compass.
Development of the rudder for ships.
A source says the first written descriptions of magnifying lenses begin to
appear in 1200.
University of Paris chartered.
Leonardo of Pisa (called Fibonacci from the 19C) (c1170-c1240 or
c1180-c1250): Liber Abaci popularizes the use of Hindu-Arabic
numerals by a systematic exposition and then uses them to solve almost
every known type of problem. He treats negatives as debts. He
estimates 3.1410 < π < 3.1427 or π = 864/275 = 3.141818 by use of a
96-gon. When the Liber Abaci was published in 1857, it comprised
459 pages of A4 size.
Fourth Crusade launched. Venetians, under Doge Enrico Dandolo, pervert it to
the restoration of their favourite to the Emperorship of Constantinople.
13 Apr: Fourth Crusade sacks Constantinople. Contemporary accounts say the
Byzantines would rather have been conquered by the Moslems, for the
Crusaders "used Christians worse than the Arabs used the Latins, for
they at least respected women." Latin emperors rule Byzantium until
1261.
Genghis Khan becomes Great Khan and leads Mongol invasions.
After a town vs gown riot at Oxford, the surviving students move to
Cambridge, expanding the University, which seems to have existed for
some time previously.
Mongols conquer China.
Moors decisively defeated by Pere (Peter) the Catholic, of Catalunya and
Aragon, at Las Navas de Tolosa. By 1266, the Reconquest has taken all
of Spain except Granada which becomes a vassal state until 1492.
University of Oxford chartered and students return after 5 year hiatus – cf
1209. The oldest colleges date from the 13C – Balliol, Merton and
University all claim to be the oldest.
Alfonso VIII founds first Spanish university at Palencia.
University of Salamanca founded. Its statutes were promulgated by the
antipope Benedict XIII in the early 15C. Columbus came here in 14841486, to try to persuade the University about his plans.
(or 1225) Leonardo of Pisa (called Fibonacci from the 19C) (c1170-c1240):
Liber Quadratorum (Book of Squares) is probably the first western
book in the field of number theory. He first(?) proves that the product
of two sums of two squares is again a sum of two squares.
Leonardo of Pisa (called Fibonacci from the 19C) (c1170-c1240): Practica
Geometriae introduces 'sinus rectus arcus' and 'sinus versus arcus'.
Mongols conquer Persia and establish capital at Tabriz. In 1223, they make a
foray into Russia under Subotai, reaching the Volga in 1225.
Montpellier University founded – ?? See 1137.
Sep: University of Padua founded when Bishop Jordanus of Padua invites
William of Gascogne, professor of Decretals at Bologna, to come to
Padua. William invites Peter the Spaniard to follow him and Peter
does. An alternate story is that a group of Bolognese professors left
MEDIEVAL - p. 23
Bologna due to political discord and went to Padua. Albertus Magnus
was here in 1222 or 1223. Padua is usually considered the second
oldest Italian university, though Salerno was earlier and Pavia is
claimed to have been founded in the 11C. In 1360, it was given the
right to confer degrees in theology, previously only permitted to Paris,
then Bologna.
1224
University of Naples founded by Emperor Frederick II of Sicily.
1225
Jordanus de Nemore: De Arithmetica gives Pascal triangle for use in
computing powers of binomials. He is first to prove that stereographic
projection preserves circles. An edition by Lefèvre d'Etaples was
printed in Paris in 1496.
1225
Fibonacci: Flos estimates a root of x3 + 2x2 + 10x = 20 in sexagesimal as
1; 22, 7, 42, 33, 4, 40 and attempts to show it cannot be constructed
with ruler and compass.
First half of 13C
The University of Turin is founded by Cardinal Guala Bisshieri at nearby
Vercelli, but this ceases in 1372. In the early 15C, Prince Ludovico de
Savoia Acaia re-establishes the university in Turin and this is confirmed
by a Papal bull of 1404 and an Imperial diploma of 1412. Over the next
decades, it moves several times to nearby cities, sometimes to escape
the plague.
1227/8
Foundation of the school/university al-Mustansiriyyah at Baghdad.
1229
Emperor Frederick secures Jerusalem by diplomacy.
1230 or 1231 Explosive grenades or bombs or rockets in use in east Asia. Said to have been
a great aid to Kubla Khan's army (but Kubla Khan did not become Great
Khan until 1260 – ??). Another source quotes a chronicle of 1232
saying the Mongols made a covered passage of ox-skins to advance to
the foot of the walls of the town of Kai Kung Fu and undermine the
walls, but the defenders lowered "heaven-shaking thunder" which blew
to pieces both the men and the passage. Beside this, they had 'arrows of
flying fire which suddenly flew forwards and scattered fire for ten paces
around'.
1231
University of Cambridge chartered.
1236
Córdoba captured by the Spanish.
Early 13C
John of Holywood (= Sacrobosco) (c1213-1256). His Spherics is the standard
text on spherical astronomy for four centuries. In his influential
Algorismus, he attributes the Hindu-Arabic numeral system to the
Arabs.
1236-1242
Mongols under Subotai conquer Russia, including parts of Poland and Hungary
but withdraw from Budapest in 1242 when news of the Great Khan's
death reaches them.
1238
Granada becomes an independent kingdom. After 1266, it is the only Islamic
kingdom left in Spain, though a vassal to the Spanish king. About this
time, the flight of Jews from Spain takes four camel loads of
manuscripts to Paris, containing the works of and commentaries on
Aristotle, translated from Greek to Arabic to Latin. The study of
Aristotle was initially prohibited but Aquinas (c1225-1274) managed to
reconcile Aristotle and the Church.
1192-1280
Albert, Count of Bollstädt of Swabia, known as Albertus Magnus. Thomas
Aquinas studied with him. He gives a recipe for gunpowder using
proportion 6 : 2 : 1 for saltpetre : charcoal : sulphur and describes its
use for firecrackers and rockets – cf Bacon, c1260.
c1240
Ottoman Turks first appear in western Anatolia.
1243
Mongols conquer Armenia and Seljuk Turks.
1245
The Pope sends the Franciscan John of Plano Carpini to convert the Mongols.
He reaches the Mongol capital in the steppes but only stays four months
before returning with the first knowledge of the Mongols.
1246
Spanish reconquer Sevilla, the greatest city in western Europe.
1247
Qin Jiushao = Ch'in Chiu Shao, also known as Daogu: Shu Shu Jiu Zhang =
Shu Shu Chiu Chang (Mathematical Treatise in Nine Sections).
Gives general solution of Chinese remainder problem (i.e. permitting
MEDIEVAL - p. 24
1248
1248
c1225-1274
1249
1250
13C
13C
1252
1253
1255
1258
1201-1274
moduli which are not relatively prime). Although this must have been
used for calendrical computations at least as far back as 462, Qin's work
is the first to describe the method. Extends the work of Jia Xian
(c1030) and Liu Yi (c1200) into Horner's method for general
polynomials, with coefficients that can be negative or decimal. First
Chinese use of 0 for zero. Solves
x10 + 15x8 + 72x6 - 864x4 -11664x2 - 34992 = 0. One problem has 180
solutions. Has formula for the area of a triangle in terms of its sides,
but much different than Heron's.
Li Ye = Li Yeh, originally named Li Zhi: Ce Yuan Hai Jing = Ts'e Yuan Hai
Ching (Sea Mirror of Circle Measurements).
Sevilla (Seville), the greatest city in Europe, is captured by the Spanish under
(St.) Ferdinand III of Castile.
St. Thomas Aquinas.
Faro recovered from the Moors, completing the reconquest of Portugal.
Mameluk dynasty in Egypt and Syria, succeeding the Ayyubids established by
Saladin. Ends in 1517.
Cannon are claimed or clearly described in Arabic battles of 1204, 1248, 1260,
1274, 1303, etc. However, other sources claim these are just throwing
of Greek Fire and that cannons are first clearly used in 1324, cf. Cf
1118.
Invention of the hourglass in Europe. Turner says 12C. Cf 8C, 807 for a much
earlier date, though the later date is indicated by 1309-1313, 1337-1339.
The Franciscan William of Rubruck travels as far as the Mongol capital in
Mongolia. (= Guillaume de Rubruquis or Rubriquis, 1230 or 12531255 ??)
The Sorbonne is founded in Paris as a theological college by Robert de
Sorbonne (or Sorbon or Cerbon), chaplain to St. Louis. At the time,
there were already about a dozen colleges in Paris, but these seem to
have vanished and the Sorbonne is considered the oldest part of the
University. Any master could start his own college once he had
permission from the Bishop's Chancellor. By the end of the 14C, there
were some 40 colleges; by the end of the 15C, there were about 50 and
John Evelyn records 65 colleges in the late 17C. In 1349, there were
502 professors; in 1403, there were 909. However, it is not clear when
the multiplicity of colleges really came together as a university – the
word already occurs in statutes of 1215. The four main faculties were
formed in the early 12C and the students and staff had formed
themselves into four national groupings: French, Picards, Normans and
English by this time. By 1245, these groups were meeting to elect a
Rector, who superseded the Chancellor as head of the University and
eventually became a kind of sovereign over the Left Bank which had
10,000 students. As at Oxford and Cambridge, the privileges of
students led to many conflicts, often bloody and sometimes lethal. By
the Revolution, only ten colleges remained.
Nicolo and Maffeo Polo reach Beijing.
Mongols under Hulagu Khan (brother of Kublai Khan) capture Baghdad. It is
recorded that there were 36 libraries in Baghdad at the time. End of
Abbasid Caliphate.
Nasir Eddin (= al-Din) al-Tusi (= Naşīr al-Dīn (= Nasiruddin) al-Ţūsī). Builds
an observatory at Maragha (= Maragheh or Maraghah in Iran, near
modern Tabriz) in 1259. Writes the first systematic treatise on
trigonometry, The Transversal Figure, marking its emergence as a
separate discipline. It has little immediate influence, but later
influences Regiomontanus (1464). First clear statement of the law of
sines. Nasir's edition of Euclid was printed in Arabic in 1594 and later.
In it he discusses the difficulties of the parallel postulate, following
Omar Khayyam (c1044-1123/4). He shows (as did Khayyam) that the
parallel postulate is equivalent to triangles having angles totalling 180
MEDIEVAL - p. 25
1260
1260
c1260
1261
1261
1264
c1266
13C
13C
Late 13C
1269
c1270
c1270
1271-1295
1247-1275
c1275
c1275
1276
degrees, though this seems to have been realised as early as Aristotle (384/-322). Wallis translated this discussion in 1651 and it later inspired
Saccheri. Nasir Eddin also follows Omar in treating the positive reals
as numbers. Introduces Tusi couple to clarify Ptolemaic system. Ibn alShattir (fl. 1350, d. 1375) improves this, qv. (Not to be confused with
Sharaf al-Din al-Tusi.) Refers to Pascal's triangle.
Mongols under Hulagu Khan take over Damascus but are turned back from
Egypt by the Mameluks at ‘Ayn Jalut in Galilee and the death of the
Great Khan.
Kublai Khan, grandson of Genghis, becomes Great Khan, ruling until 1294.
Roger Bacon (1214-c1292). In a letter to Pope Clement IV in 1263 (or c1267),
he points out the error in the Julian calendar and suggests calendar
reform, as eventually carried out in 1582. He is often associated with
the introduction of gunpowder, the mariner's compass and spectacles, if
not the telescope. He certainly described gunpowder as an explosive
mixture in 1242 or 1267, and he may be the first to mention the use of
saltpetre in it and how to prepare the saltpetre, but there is no indication
of use of gunpowder in a gun, only in fire-crackers and perhaps rockets.
He gave the recipe in a coded form which states: 7 parts salpetre; 5
parts charcoal; 5 parts sulphur – this gives a very poor gunpowder (the
standard ratio is 15 : 3 : 2). He did suggest enclosing it to increase the
effect. Bacon seems to have no connection with the compass. He gives
only a vague description of using two lenses to produce an enlarged
image to improve sight.
25 Jul: Michael VIII Paleologus recaptures Constantinople from the Latins and
re-establishes the Byzantine Empire.
Yang Hui: Xiang Jie 'Jiu Zhang' Suanfa (Zuan Lei) = Hsiang Chieh Chiu
Chang Suan Fa (Tsuan Lei) (Detailed Analysis of the Mathematical
Rules in the "Nine Chapters" (and Their Reclassification)).
Includes Pascal triangle up to 6th powers, attributed to Jia Xian (c1030).
Only part of this has survived.
Kublai Khan founds Peking as Mongol capital.
Christians conquer all of Spain except for Granada, which remains
semi-independent as a tributary of Castilla until 1492.
Canary Islands rediscovered by a ship blown off course (or 1334?).
Probable beginnings of double-entry bookkeeping.
Numerous travellers between Europe, Middle East, India and China.
Peter the Stranger of Maricourt: Epistola de magnete describes the marine
compass but it remains generally unknown until 1520 – though another
source says it was developed by c1250 – cf. late 12C. Thought to have
been in general use on Arabic and Chinese ships by the early 13C. The
Epistola was the beginning of serious study of magnetism.
Roger Bacon studied at Paris in the late 1230s under Petrus Peregrinus, said to
be the author of one of the first treatises on the magnet. Are these the
same person?
Campanus Novariensis edits Adelard's c1130 translation of Euclid's Elements.
(He is often forenamed Johannes, but this first appeared in the 16C
with no known evidence.) It was his edition that was the first printed
Euclid in 1475.
First geometry text written in a French language – Le Practike de geometrie,
an anonymous text in the dialect of Picardy.
Marco Polo travels to China.
Apex of Chinese mathematics in late Sung.
Jacobus de Cessolis's sermon based on chess is one of the first works on chess.
It was one of the first books published by Caxton in 1475.
Nicholas de Nicolaï (attrib.): Bonus Socius collection of chess problems.
First papermaking in Italy, at Fabriano, though a little had been made in Genoa
in the early 13C. The use of water power made their paper cheaper than
North African or Egyptian, though it took some time to be as good.
MEDIEVAL - p. 26
1277
c1280
c1280
c1280
1280
1279-1368
c1260-1310
1283
1284
c1285
1287
1290
1290
1290
c1290?
1291
1291
1292
1294?
1295
1299
1299
c1300
c1300
Venetians learn art of glass blowing from Syria.
Spinning wheel appears in Europe – believed to have come from India.
First mechanical clocks, in England, then in Europe. Previously there had been
many waterclocks and the oldest surviving picture of one is from c1250.
A guild of clockmakers is mentioned in Cologne in 1183 and in 1220,
they occupied a street, the Urlogingasse. In 1271, Robert the
Englishman wrote a treatise on the state of clockmaking and the
attempts to make a purely mechanical clock.
Invention of spectacles – convex lenses to correct long sight. A source says by
1290. Cf c1200, c1285.
Al-Hasan al-Rammah's Book of Horsemanship for the Holy War first
describes purification of saltpetre, gives 70 recipes for gunpowder and
describes rockets and torpedoes.
Mongol empire covers China, Central Asia, Iraq, Iran and most of Russia.
Maximos (or Maximus) Planudes: Arithmetic after the Indian method. He
also draws the oldest extant map of the world based on Ptolemy.
The Spanish Treatise on Chess-Play (= Libro de Acedrex, Dados e Tablas)
(the Alfonso MS) produced for Alfonso (or Alphonso) X, "The Wise"
(Alfonso El Sabio), of Castile and Leon (reigned 1252-1284, based in
Sevilla (Seville)). First clear mention of backgammon – though this
may date back much further, there is no earlier clear description.
Mentions many other board games. Cf 1292.
Peterhouse, the oldest Cambridge college, is founded by Hugo de Balsham,
Bishop of Ely (an earlier, unsuccessful, foundation had been made by
him in 1280, but was a mixture of a lay and a clerical group).
Bernard de Gordon gives first? mention of spectacles in his Lilium Medicinae.
Cf c1280.
School of Montpellier becomes a university. (Or 1290??) Cf 1221, 1137.
University of Coimbra founded in Lisbon, moving to Coimbra in 1306. It
moved again, becoming permanently settled in Coimbra in 1537.
Edward I ordered the erection of a tower with a clock and striking bell at
Westminster. It became known as Great Tom of Westminster.
Edward I expels Jews from England. They are not allowed back until the 17C.
Oldest extant gun with metal barrel, in China. (Or c1280 or 1332?, qv.)
Genoese defeat Moroccans and open the Strait of Gibraltar to Christian
shipping.
Mameluks of Egypt capture Acre and all remaining Crusader lands in Asia,
effectively ending the Crusades.
Alphonsine Tables – astronomical tables computed in Toledo for King
Alphonso (or Alfonso) X, "The Wise", of Castile and Leon – cf 1283.
Gives year as 365.242546 days. Edited by Jehuda ben Salomon Kohen
of Toledo. First printed in 1483. Two sources date this as c1272 –
??CHECK. They are not superseded until the Prutenic Tables of 1551.
Death of Kublai Khan. Mongol empire fragments.
Majorcan pilots are using the mariner's astrolabe, but it is not developed for
common use until c1484.
A 'fun house' with distorting mirrors and mechanical practical jokes was built
at Hesdin in Artois. The Dukes of Burgundy maintained it at least until
the late 15C.
The Chronicle of Sandro di Pipozzo, of Venice, mentions cards. Possibly the
first mention of cards in Europe – however, one source says Sandro's
writing is lost and only known through an 18C reference. I have a
source that says cards were mentioned in 1275 and that they are
mentioned in German MSS of 1286 to 1384. Cf 1329, 1367, 1371,
1377, 1379, 1392.
Invention of the mechanical escapement for weight driven clocks, in Northern
Europe.
Kamal al-Din al-Farasi (or al-Farisi) studies ibn al-Haytham's Optics and gives
the first explanation of rainbows. Theodoric of Freiberg gives the same
explanation at about the same time. Al-Farasi states and proves the
MEDIEVAL - p. 27
c1300
c1300
1301
1302
1303
1303
1303
1308
1309-1313
1309
1312
c1320
1321
1322-1356
1324
Early 14C
1326
1326
1328
1329
1330
c1330
c1330
existence part of the Fundamental Theorem of Arithmetic.
Al-Banna (1256-1321) discovers the second known pair of amicable numbers:
17296 and 18416, apparently using Thabit ibn Qurra's rule, cf 836-901.
The Book of Fires for the Burning of Enemies, attributed to Marcus
Graecus, repeats Albertus Magnus's recipes and uses of gunpowder. Cf
1192-1280.
First use of a gun (where?) – by 1326 they were in regular use.
Boniface VIII attempts to impose Papal control over Christian kings. Philip IV
of France sent messengers who conveyed his disapproval so forcefully
that the Pope died a few days later and the Papacy was moved to
Avignon.
The University of Rome was established by Pope Boniface VIII, though it
claims some origin in -63.
Zhu Shijie = Chu Shih-Chieh: Siyuan Yujian = Si Yuan Yu Jien (Precious
Mirror of the Four Elements = Jade Mirror of the Four
Unknowns). Gives Pascal's triangle up to 8th powers. Describes it as
'the old method'. Has general concept and use of finite differences. He
sums quadratics, cubics, quartics and quintics and has several general
formulas. He uses fourth differences to sum 33 + 43 + ... + n3 and
gives the equivalent of Newton's Interpolation Formula. The 'four
elements' are four unknowns so he can deal with systems of polynomial
equations with up to four unknowns. He includes the Sea Island
problems (see 263).
Mameluks defeat Mongols at Marj al-Suffar, south of Damascus. End of
Mongol threat to the Middle East.
The University of PERUGIA, Umbria, was founded by a papal bull of Clement
V.
A poem of Francesco da Barberino is earliest reference to a hourglass (with
sand).
The Papacy moves to Avignon, leading to the Great Schism in 1378, qv.
Rockets filled with gunpowder used by the Chinese against the Tartars.
Dante's Paradiso, XXXIII, 133-136, mentions circle squaring or measuring
('misurar lo cerchio').
Levi ben Gerson (c1288-c1345) writes (in Hebrew) on Greek and Arabic
trigonometry, emphasising the sine function rather than the chord
function. In 1328, he describes Jacob's Staff, later called the cross-staff,
a device for measuring angles used by navigators and surveyors.
Sir John Mandeville's Travels, a mixture of fact, earlier traveller's stories and
sheer fiction, claims he got to China and visited the lost Tribes of Israel.
It was the most popular travel book of its time, though it's not clear if
the author ever left England! Clearly asserts the world is round.
First(?) use of a cannon at the Muslim siege of Huescar.
Yusuf I builds a university in Granada. Though much altered, the building still
exists as the Palacio Madraza, opposite the Capilla Real, though it is not
in much use. After the Christian conquest of the city in 1492, some
80,000 books from the University were burned by Fernando and Isabel
in the Plaza Nueva.
Artillery was being manufactured at Florence.
First picture of a cannon – an English miniature showing it shooting an arrow!
Glenys Crocker [The Gunpowder Industry; Shire Album 160, (1986);
2nd ed., 1999, p. 3] reproduces this and gives the date 1326. Other
sources give 1325 and 1327.
Paolo Gherardi: Liber di Ragioni is first algebra in a vernacular language and
the western work to study cubic equations. He gives some incorrect
solutions which were widely copied over the next two centuries.
Bishop of Würzburg prohibits card games.
Thomas Bradwardine.
Richard of Wallingford begins the first great astronomical clock, at St. Albans
Abbey. Completed c1356. The first clock to be clearly described.
Immanuel Bonfils of Tarascon develops use of exponents. Not published until
1937. He also proposes decimal fractions. (c1370??)
MEDIEVAL - p. 28
c1330
1331
1331
1332
c1333
1335
1325-1354
1338
1338-1453
1337-1339
1340
1342
1343
1344
1346
1346
1347
1346-1350
1348
Mid 14C
Mid 14C
14C
1348
Bishop Richard Aungerville of Durham establishes a lending library at Durham
College, Oxford, (now Trinity College), claimed to be the first in
Britain, though it was probably not a public library. Cf 1608, 1653,
1691, 1701, 1705.
Cannons probably in use at the battle of Cividale, Italy.
The University of Cahors was founded in 1331 by Pope John XXII.
Oldest extant cannon with a metal (bronze) barrel made in China (or c1290?) –
now in Chinese History Museum, Beijing.
Black Death (= bubonic plague) breaks out in China and travels west.
Mechanical clock, with striking mechanism, set up at St. Gothard Church,
Milan. The earliest mechanical clock of which we have definite
knowledge.
Ibn Batuta (1304-1369), an Islamic jurist, travels from Tangier to Mecca and
then to Iraq, Iran, Turkey, Russia, Afghanistan, India, Arabia, Africa,
Sumatra, China and back to Tangier, then to Spain and Mali, covering
75,000 miles. His four volume Rihla is one of the leading sources of
information for this period.
Description of a cannon in use at Rouen.
Hundred Year's War.
Ambrogio (or Pietro) Lorenzetti's fresco, Allegory of Good Government, in the
Palazzo Pubblico in Siena, has the earliest known depiction of an
hourglass (sandglass).
Double entry book-keeping in use in Genoa. By 1350s or 1400 it is in common
use in Italy.
Peter of Alexandria translates Levi ben Gerson (1321).
The University of Pisa was chartered by Pope Clement VI.
Maestro Dardi of Pisa: Aliabraa argibra gives first correct algebraic solutions
of cubics. These only work for special forms, mainly those that can be
reduced to the cube of a linear term equal to a constant, but succeeding
authors ignored the specified restrictions.
Gunpowder first manufactured in Britain, on Hounslow Heath.
Battle of Crécy (Crecy) – first use of cannon in the West, or by the English.
Oct: Italian merchant ships return from Black Sea to Sicily bearing plague
sufferers.
Black Death (= bubonic plague) sweeps across Europe from the Mediterranean,
killing a third to a half of the population, perhaps 25,000,000 people. A
source says that Florence lost 2/3 of its population, some 18,000 people,
in summer 1348. In central Europe, the plague was often blamed on the
Jews and this led to major persecutions. The plague reached England in
Aug 1348 and over 1,000 villages were wiped out and were never
resettled. Recurrences of the plague over the next century cause the
population to decline further until c1450 and lead to considerable
changes in medieval society. Florence is said to have lost over 10,000
people in summer 1400. Cf first half of 13C, c1333, 1347, 1381, 1386,
1474.
First papermaking in France, at Troyes. Cf 1390.
Civil adoption of 24 equal hours for the day, beginning in Italy. However, the
Italians start their 24 hour day at sunset, while most other countries use
the common 2 x 12 hour day.
Ottoman Turks rise to power in Turkey, under Osman, founder of the Osmanli
dynasty, establishing a capital at Bursa in 1326 and Adrianople
(= Edirne) in 1363.
Colour printing and bronze type in use in China. Cf 1403.
The Charles University (Univerzity Karlovy or Universitas Karolina) was
founded in 1348 by Charles IV of Bohemia, later Holy Roman Emperor.
In 1383, a site was acquired – the Karolinum at Železná 9 – but it was
remodelled in the Baroque style in 1718 [Hayman, p. 68]. It is claimed
to be the oldest university building still functioning in Europe, but very
little survived Nazi demolition in 1945, most notably (or only) the 14C
Gothic oriel window on the SE side, facing the Estates Theatre
(Stavovské divadlo). Only some central offices and a few departments
MEDIEVAL - p. 29
are on this site. The reforming movement of Jan Hus led to a rift
between the Hussite Czechs and the Catholic Germans in the early 15C.
In 1409, Hus persuaded Wenceslas IV to issue the Decree of Kutná
Hora, which changed the constitution of the University to favour the
Czechs. Some 2000 students and many professors then emigrated and
founded the University of Leipzig. In 1882, the University was divided
into German and Czech parts.
1348
University of Florence founded, opening on 6 Nov 1349. (1321??)
1350
Berthold Schwarz, a Franciscan, is said to have invented gunpowder – there is
a statue commemorating him in the Rathausplatz of Freiburg im
Breisgau [MGG-Germany, p. 137].
1350
A source says German monks developed the first alarm clocks to wake them
for prayers.
14C
Drawloom reaches West from China.
14C
Italians invent word 'millione'. A source says 1370.
c1350
Ibn al-Shattir, in Damascus, improves Nasir al-Din's improvements to Ptolemy,
getting close to a Copernican view. Copernicus apparently knew of this
work.
c1350
Richard Swineshead (= Suicet, Suiseth, etc.) sums 1/2 + 2/4 + 3/8 + 4/16 + ....
1352
A fresco by Tomaso da Modena in the Chapter House of the Seminary of S.
Niccolo, Treviso, Veneto, seems to show a monk using a magnifying
glass which exhibits the Aristotelian conception that rays emanated
from the eye. Cf 1592.
1352
A source says the earliest portrait showing spectacles being worn is of Cardinal
Ugone. [Could this be the Treviso fresco?]
1356
Narayana (Pandita) (Nārāyaņa Paņdita [the d should have a dot under it]):
Ganita-kaumudi (Gaņitakaumadī). He was the founder of the Kerala
school of mathematics which continues for several centuries, including:
Madhava, Paramesvara, Nilakantha, Samkara, Jyesthadeva. They
develop the ideas of the calculus given by Bhaskara II (1150),
particularly obtaining various series with reasonable usage of limiting
arguments and summations. It is an interesting and unsolved question
whether these Indian results ever became known in Europe – it is
known that the Jesuit mathematical and astronomical scholar, Matteo
Ricci (1552-1610), spent several years in south India at the beginning of
the 17C, but no relevant reports of his are known. One source says he
had stated the binomial theorem for positive integral exponent.
1358
Hanseatic League formed, linking over 200 towns of northern Germany into a
trade alliance which dominated northern Europe for several centuries.
Capital at Lübeck.
1359
Technique of salting herring developed in Europe.
c1360
Karl IV, Holy Roman Emperor, sets up the system of seven Electors
(Kurfürsten).
1318?-1374? Paolo dell'Abbaco. Writes first treatise on bookkeeping using the
Hindu-Arabic numerals.
1323-1382
Oresme (published 1868) uses fractional exponents and recognises that the rate
of change is zero at an extremum. (See also Manjula (932) & Bhaskara
II (1150).) First(?) to graph equations and give the equation of a line.
First(?) person to propose a Date Line – which assumes the earth is
round. First(?) to show the harmonic series diverges. First writer of
scientific works in French.
1335-1347
First mechanical clocks: Milan, 1335; Modena(?), 1343; Padua, 1344;
Monza, 1347; Paris, 1370.
1364
Jagiellonian University of Cracow (Krakow) founded. It was re-established in
1400 by a member of the Jagiello family and subsequently renamed.
1364
Jacopo di'Dondi ( -1359), a professor at the University of Padua, and his son
Giovanni build an Atraraum, one of the first astronomical clocks, here
in 1348-1364 (or 1344-1364 or 1364-1381, one source claims it was
present in 1343). The clock tower was greatly damaged in the early
MEDIEVAL - p. 30
15C and the tower and the clock were reconstructed in 1427-1434 from
the original plans and the new clock was started on 16 Jun 1434. This
tower and clock are extant (as of 1910), to the north of the Cathedral,
though the clock was repaired in 1529 and slightly altered in 1688 and
1838. Dondi was later renamed Jacopo dell'Orologio. He was buried
near the Baptistery and an inscription can be seen there. Giovanni
published a treatise on clocks in 1365. There is a modern facsimile of
the clock in the Science Museum, London.
1365
University of Vienna founded, though it is said not to have achieved full status
until it had a Faculty of Theology in 1385. This is the oldest Germanspeaking university.
1356-1377
Earliest dated cannons, in China.
1367
City of Berne prohibits card games.
1367
University of Pécs founded.
1370
The Tour de L'Horologe on the Quai de l'Horologe, Paris, is asserted to contain
the oldest public clock in the world, dating from 1370. [Don Lemon;
Everybody's Scrap Book of Curious Facts; Saxon, London, 1890,
p. 38] says the first clock resembling a modern clock was made by
Henry Vick for Charles V of France in 1370. Legend says that Charles
was unhappy with the IV for four and said it ought to be IIII and this
has been followed ever since. Another source says the tower is restored
and 'partially old' and that the clock "commemorates the oldest clock in
Paris, constructed by the German Henri Vic, and erected by Charles V."
Nothing of the original clock remains. The leaflet for the Conciergerie
says the tower was built by John the Good in the 14C, but the present
clock dates from 1585.
1371
Playing cards mentioned in a Catalan document in Spain, where cards are
called 'naip'. This is claimed to be the first mention in Europe, but cf
1299, 1329, 1367, 1377, 1379, 1392.
c1375
Antonio de' Mazzinghi is first vernacular author to use two unknowns with
different names: cose and quantità. He also is happy to use surd
coefficients rather than squaring to eliminate them and uses a negative
root of a quadratic.
c1375
Introduction of artificial nitre beds for producing saltpetre, in central Europe.
1377
First description of playing cards in Europe, in a Swiss MS by John of
Rheinfelden, describing a deck of 52 cards – the original MS is lost and
the oldest version is a 1429 copy. Within a short time, they are
widespread in Europe, but they are not mentioned in several lists of
games of the previous decade, though there are records of them in
Venice (1299), Würzburg (1329), Berne (1367) and Spain (1371). They
are also not mentioned in the general literature before this time, even by
authors such as Petrarch, Boccaccio and Chaucer with an interest in
games. A Paris ordinance regulating gaming in 1369 makes no mention
of cards, but the equivalent ordinance of 1377 mentions them. By 1380,
cards are recorded in Florence, Basel, Regensburg, Brabant, Paris and
Barcelona, and several of the records describe cards as new or having
arrived this year. Cf 1379, 1392, 1398.
1377
Ibn Khaldun clearly describes cannon in his account of a siege of 1274.
1378
Non-French Cardinals elect a Pope in Rome while French Cardinals elect one
in Avignon. This Great Schism lasts 40 years and at the end there are
three Popes.
1379
The arrival of playing cards is recorded in Viterbo. The Duke of Brabant's
accounts show the purchase of cards.
1380
Rockets used in a battle between Venice and Genoa.
1381
Wat Tyler's Rebellion in England, caused by social disruptions produced by the
Black Death (plague) – cf 1346-1350.
1386 (or 1385)
University of Heidelberg founded by Rupprecht I – first German
university. To escape the plague, it moves 19 times!
1388
University of Cologne founded. It was closed by the French in 1798 and did
not reopen until 1919.
1389
(or 1409??) University of Leipzig founded, apparently the third university in
MEDIEVAL - p. 31
1390
1391
1392
1392
c1395
1396
1397
1398
c1400
1401
1402
1403
1405
1406
1409
1413?
1411
1414
1415
1419
1419
c1420
1422
1420s
1423
1423
c1425
1425
1426
1427
1428
Germany, after Heidelberg (1386) and Köln (1388). The 1409 date is
based on the fact that in 1409, the constitution of the Charles University
in Prague was changed to favour the Hussite Czechs and some 2000
students and many professors then emigrated and founded the
University of Leipzig.
First German paper mill, established by Ulman Stromer at Nuremberg. This is
said to be the first papermill north of the Alps, but cf 1348.
Geoffrey Chaucer's treatise on The Astrolabe is the first scientific work in
English. It is based on Messehalla's work of c791 and was written for
his 10-year old son Lewis. There is also a MS The Equatorie of the
Planetis thought to be by him and possibly even in his own hand.
Three packs of cards made for Charles VI of France.
University of Erfurt founded. It closes in 1816.
Anonymous Florentine MSS use x = y - p/3 to transform between cubics with
no linear term and cubics with no quadratic term, using problems where
the latter form has an easy solution by trial and error.
Earliest European pound lock for a canal, near Bruges.
Turks capture Athens and Greece. First Turkish siege of Constantinople.
First record of gypsies in Europe. They are said to have introduced cards, but
cards were known a generation earlier.
Madhava finds infinite series for trigonometric functions.
Tamerlane besieges and captures Baghdad.
Tamerlane defeats Ottomans but he dies later in the year. This relieves the
siege of Constantinople. Tamerlane's conquests temporarily disrupt
trade routes and spark off the Age of Discovery.
Type foundry set up in Korea, casting bronze type in sand moulds. Cf 14C.
Metal screws in use.
Earliest known illustration of a clock in a MS in the Bibliothèque Nationale,
Paris.
University of Aix(-en-Provence) founded. With the growth of Marseilles in
the 19C, the University declined and now has only Law and Letters.
Fillipo Brunelleschi (1377?-1446) invents perspective.
University of St. Andrews founded. This was confirmed by bulls from the
antipope Benedict XIII!
Poggio Bracciolini initiates collecting and copying of MSS at Rome.
Portuguese capture Ceuta in Morocco, marking the beginning of European
expansion, especially when it was realised that Ceuta did not open up a
route through the Mediterranean.
University of Rostock founded, first university in the Baltic region.
Portuguese discover Madeira. They settle it in the following year. This opens
the Age of Discovery.
Invention of the compound crank, in the form of the carpenter's brace, by some
Flemish artisan.
Second Turkish siege of Constantinople.
Development of corned (i.e. grained) gunpowder, making it much more
efficient.
Earliest known example of block printing in Europe.
S. Bernardino of Siena (1380-1440) preaches against playing cards.
Masaccio (Tommaso di Giovanni) (1401-c1428) is first painter to use
perspective effectively. Donatello (Donato dei Bardi) (1386-1466)
applies perspective in sculpture.
University of Louvain founded – first in the Netherlands, now Belgium –
cf 1575.
It is claimed that the first student to fail out of a university was a Paul Nicolas
who was refused his degree in PARIS in 1426, despite his taking legal
action.
Azores discovered by the Portuguese.
Ulugh Beg (1394-1449), grandson of Tamerlane, builds school in 1417 and
observatory in 1428 at Samarkand, based on the 1259 Maragha
observatory of Nasir Eddin. By this time, Persian is beginning to
MEDIEVAL - p. 32
?-1429
1405-1433
c1430
1435
1436
1394-1460
1397-1475
1440
1440-1450
1446
1447
c1450
15C
Mid 15C
supplant Arabic as the scientific language in this area.
(or ( -c1436)) Jamshid Ghiyath al-Din al-Kashi (= Ghiyāth al-Dīn Jamshid
Masud al-Kāshānī = Gamšid b. Mas‘ūd al-Kāšī). Astronomer to Ulugh
Beg in Samarkand from 1406. In his Miftāh al-hisāb [each h should
have a dot or a cedilla? under it] (The Calculators' Key or Key to
Arithmetic) of 1427, he 'invents' decimal fractions (but cf 953 etc.),
developing them carefully, e.g. multiplying them. In this he also
computes volumes of domes by approximate integration. In 1424, his
Risala al-Muhitiya (= Al-Ricala al-Muhitiyyah) ((The AllEmbracing) Treatise on the Circumference) gives 2π as
6.28318 53071 79586 5, by using a polygon of 3 x 228 = 805,306,368
sides, making careful allowance for rounding errors. He actually does
his work in sexagesimals, obtaining 6; 16, 59, 28, 34, 51, 46, 15, 50.
He gives this also in decimals as 6.28318 53071 79586 5. Gives an
algorithm for fifth roots. Mentions binomial coefficients and states the
addition rule: BC(n,k) = BC(n-1,k) + BC (n-1,k-1). Develops an
iterative process for solving the cubic involved in trisection to obtain
sin 1o to 10 sexagesimal places as
0; 1, 2, 49, 43, 11, 14, 44, 16, 26, 17 = .01745 24064 37283 51037.
(sin 1o = .01745 24064 37283 51282, so his result is correct to 17
decimal places.
Zheng He = Cheng Ho, a Muslim Chinese admiral, leads seven expeditions to
the East Indies and Indian Ocean, reaching the east coast of Africa and
making maps. One of Zheng's expeditions had 60 ships and 27,000
men, with the largest ships being nine masted and 140 m long.
(Columbus's Santa Maria was 24 m long and Da Gama's ships were 32
m long.)
First extant European spring-driven clock, built for Philip the Good, Duke of
Burgundy. Even if the works are not original, there were others by the
1440s. This clock includes the earliest fusee.
Leon Battista Alberti (1404-1472): De Pictura, 1435, and Della Pittura, 1436
– first book on perspective. Despite its great influence, it was not
printed until 1540.
Council of Basle. Nicholas of Cusa proposes reform of the Julian calendar.
Prince Henry the Navigator, sponsors first voyages of exploration.
Paolo Uccello. May have written a book on perspective.
Ulugh Beg (or his observatory) computes tables of sin and tan at 1' intervals to
5 sexagesimal places.
Development of printing by Gutenberg and Fust in Mainz (or Strasbourg) using
lead moveable type. Initially Gutenberg thought of printing as a method
of producing the equivalents of manuscripts at a fraction of the cost. He
used some 290 types for his famous Bible in order to simulate
manuscript characters. Dating of early printing establishments is:
Mainz, 1454; Strasbourg, 1460; Bamberg, 1461; Venice, 1461;
Padua, 1461; Vienna, 1462; Nuremberg, 1470; Naples, 1471 or 1473;
Buda(pest), 1473; Reggio, in Hebrew, 1475; London, 1476. By 1500,
more books had been printed than had been hand copied in the previous
1000 years! More than 35,000 titles were printed by 1500. Cf. 1482,
1500. Gutenberg may have been preceded by Laurens Janszoon Coster
(c1370-1440) in Haarlem, but Coster's work was much simpler.
Venice founds public schools for the teaching of humanities. In 1449, public
lectures in philosophy, geometry and arithmetic are being given by
Paolo della Pergola. Cf 1490.
Dante's Divine Comedy, (Purgatorio, C.VI) describes a dice game called zara
and discusses possible and favourable chances – perhaps the first
systematic discussion of a game of chance.
Tarot cards added to the deck of cards. Tarot is first mentioned by St. Anthony
in 1457. They do not seem to be used for divination until c1781.
The post mill, which has the entire mill suspended from a post so it can turn
into the wind, is invented in 15C Netherlands.
Marine compasses begin to be used in Europe.
MEDIEVAL - p. 33
1401-1464
Nicholas of Cusa. Criticizes the Ptolemaic system, suggesting the earth rotated
on its axis and revolved about the sun. Cf 1436.
1450
University of Glasgow founded.
c1452
Leon Battista Alberti (1404-1472): De re aedificatoria emphasises the role of
mathematics in architecture.
1453
The first English person of note to be killed by a handgun is the Earl of
Shrewsbury. Another source says the 4th Earl of Salisbury was the first
European to use cannon in battle, in 1428 (but see 1338, 1346), and also
the first soldier to be killed by a cannon in Europe. (?? needs
confirmation.)
1453
29 May: Fall of Constantinople to Ottoman Turks. Cannon are a decisive
weapon. Byzantine scholars and Greek manuscripts travel to the west.
1455
Gutenberg's Bible.
1456
Cape Verde Islands rediscovered after being lost since the expedition of Hanno
the Carthaginian, c-480.
1456
Ottomans capture Athens and besiege Belgrade. János Hunyadi's lifting of the
siege of Belgrade halts the Ottoman advance for 80 years – cf 1526.
1457
First mention of tarot cards, by St. Anthony.
1460
Printing in Strasbourg.
1460
The University of Basel (= Basle = Bâle), first in Switzerland, was founded.
1461
Printing in Bamberg.
1461
Nicolas Jensen comes from Mainz to Venice and sets up the first Italian
printing press. (A source says 1469 is more likely.) By 1500, there
were 268 printers in Venice and they had produced over 2,000,000
books. Cf. 1500.
1461
Lorenzo and Cristoforo Canozii da Lendinara start printing in Padua with a
reprint of the Gutenberg Bible.
1462
Printing in Vienna.
1463
First known use of house numbers, on the Pont Notre-Dame in Paris.
1463
The University of Bourges was founded by Louis XI in 1463. It was a major
university for about a century, but it was a casualty of the Wars of
Religion.
1464
Johannes Müller (1436-1476), called Regiomontanus after his native city of
Königsberg: De triangulis establishes trigonometry as a separate
branch of mathematics. Comparable to al-Tusi's work (c1250). He
only uses sines and cosines. Not published until 1533. He is said to
have made an artificial eagle which flew. Cf 1471, 1474.
c1465
Georg von Peurbach.
1467
A local guide book states that the Academia Istropolitana, the first Slovakian
university, was opened in Jul 1467 in Jirásek's Street, Bratislava.
1469
Ferdinand of Aragon marries Isabel of Castile, uniting most of non-muslim
Spain, leading to the eventual expulsion of the Moors of Granada in
1492 and the unification of Spain.
1470
Johann Sensenschmitt establishes printing in Nuremberg.
c1470
Al-Misri (c1423-1494), at Al-Azhar, Cairo, gives 47o 50' / 1o 25'
= 33; 45, 52, 56, 28, 14, 7, 3, 31, 45, 52, ....
c1470
Louis XI (king from 1461 to 1483) invites printers from Mainz to set up at the
Sorbonne in Paris.
1471
Johann Müller, known as Regiomontanus (1436-1476) moves to Nürnberg in
1471 and sets up an observatory, using instruments of his own design,
assisted by Bernhard Walther – this seems to be the first observatory in
Europe. Cf 1464, 1474.
1472
The University of Bavaria was founded in Ingolstadt but moved to Landshut in
1800 and then again in 1821 (or 1826) to Munich, where it is now the
University of Munich. However, the original building in
Goldknopfgasse is now used by the Hoheschule.
1471 or 1473 Printing started in Naples by Sixtus Rufingerus, a priest from Strasbourg, or by
Arnold of Brussels.
1473?
Earliest known printed map, using copper engraving, in Italy.
1473
Andreas Hess begins printing in Buda(pest).
1474
Regiomontanus publishes the first almanac. He is called to Rome to assist
MEDIEVAL - p. 34
c1475
1475
1475
1476
1477
1477
1478?
1478
1480
1482
1482
1482
1482
1483
1484
1484
1484
c1487
1487
1488
1489
1490
1491
1491
1492
Sixtus IV with calendar reform, but dies of the plague in 1476.
Anonymous MS Ital. 578 in the Biblioteca Estense, Modena, is first to clearly
view powers in terms of exponents and give general rules for their
multiplication and division. The most complex problem is
64x12 + 32x8 = 16896x4.
Piero della Francesca (1412?-1492): De corporibus regularibus.
First dated printing in Hebrew: Rashi's Commentary on the Pentateuch, at
Reggio.
William Caxton (1422-1491) sets up the first printing press in Britain, at
Westminster Abbey. His first book: Dictes or Sayengis of the
Philosophres appears in 1477. He had previously translated The Game
and Playe of Chesse and had it printed in Bruges in 1474, probably at
the printers where he was learning the trade (though another source says
he learned at Cologne).
University of Tübingen founded by Eberhard the Bearded, Prince of
Württemberg.
University of Uppsala founded.
Piero della Francesca: De prospettiva pingendi. (1485?)
First printed arithmetic, at Treviso, Italy. This has neither author not title and
has been called The Treviso Arithmetic in English. A recent facsimile
uses the last words of the opening sentence as a title: Larte de
labbacho.
Earliest known grindstone with treadle and crank.
First printed arithmetic in Germany, by Ulrich Wagner, and first printed
arithmetic in Spain, by Francesch Sanct Climent.
First printed Euclid, at Venice, based on Campanus's edition (c1270) of
Adelard of Bath's translation of c1130. There are about 200 MS
versions of the Elements, so perhaps 300 or 400 ever existed in
medieval Europe. By 1600, some 70 editions had been printed,
comprising perhaps 20,000 copies!!
Diogo Cao, a Portuguese explorer, reaches the Congo.
Earliest known printed town plan, of Florence by Francesco Rosselli.
First printing of the Alphosine Tables of 1292 (or 1272).
Chuquet: Triparty, not published until 1887. Includes use of zero and
negative exponents, considers negative roots, compares an arithmetic
and a geometric series as a primitive idea of logarithm. The MS was
left to his student Estienne de la Roche who carefully avoided using
most of its new ideas in his books.
Pietro Borghi: Arithmethica, the first great commercial arithmetic text.
The mariner's astrolabe is simplified and developed for shipboard use and
becomes common until displaced by the 1731 sextant.
Leonardo da Vinci (1452-1519) invents and builds swinging gates for canal
locks.
Two Portuguese spies, disguised as Arab merchants, set out from Alexandria to
discover the sources of the spice trade. One, Pêro de Covilhao, makes a
map of the Indian Ocean which eventually gets to Lisbon (though
neither spy got back) where it inspires da Gama's voyage of 1497-1498,
qv.
Bartholomeu Diaz (or Dias) rounds Tempest Cape, renamed the Cape of Good
Hope by King Joao II of Portugal.
Johann Widman: Behende und hubsche Rechnung. First use of + and signs in print, as signs of excess and deficiency.
University of Venice founded (cf 1446), but it was subsidiary to Padua.
Phillipo Calandri: Arithmetica, printed in Florence, is the first arithmetic book
with printed illustrations in the text.
University of Aberdeen (King's College) founded. (Marischal College was
founded in 1593.)
2 Jan: Surrender of Granada, the last Islamic part of Spain, to Fernando and
Isabel. They soon burn 80,000 books from the Islamic university's
library and expel the Jews. Baths are abolished as a heathen
abomination until the 19C.
MEDIEVAL - p. 35
1492
1492
1494
1494
1494
1495
1497
1497
1497-1500
1498
1498
1500
1500
c1500
c1502
12 Oct: Columbus discovers America, though he doesn't reach the mainland
until 1498. During his first voyage, he discovers the declination of the
compass – see 1080.
(A Breton story is that fishermen from Bréhat already were fishing
the Newfoundland banks years before this and that a Breton captain
living in Lisbon told Columbus about the New World in 1484 and
described how they sailed to it.)
Frances Pellos: Le compendion del abaco, written c1460, is published in
Turin. First(?) use of the decimal point.
Portuguese and Castilian kings make the Treaty of Tordesillas which divides
the new worlds between them along the longitude line 370 sea leagues
west of the Cape Verde Islands. This gives Brazil to the Portuguese and
has given rise to suspicion that the Portuguese already knew of its
existence before it was officially discovered by Cabral in 1500, qv.
First English paper mill.
Luca Pacioli (c1445-1517): Summa de Arithmetica, Geometria, Proportioni
et Proportionalità is the first printed description of algebra and the first
in a vulgar tongue and hence was greatly influential. He asserts that
cubics cannot be solved by the methods used for quadratics. He 'solves'
one cubic using the wrong method of Gherardi. He gives some
problems using two unknowns. It first publishes double entry
bookkeeping, in the Venetian form. First printed version of the problem
of points, the inspiration for probability theory. The book also is the
first geometry in Italian.
Aldus Manutius (1449-1515) starts his Aldine press in Venice, devoted to
producing compact and readable books, especially of Greek texts. He
introduced italic type in 1501.
Jun: John Cabot discovers the American mainland, probably Cape Bauld or
Cape Bonavista, Newfoundland.
8 Jul: Vasco da Gama sets out from Lisbon with four ships, around the Cape of
Good Hope. He later reaches Mombasa in Mar 1498 and then Calicut
on the Malabar Coast of India on 18 May 1498. By 1515, the
Portuguese were masters of the Indian Ocean.
A drawing of Leonardo da Vinci seems to be a pendulum escapement for a
clock. In a 1490 drawing, he shows a fusee, a tapering spiral for
compensating for the decline of power in a spring as it unwinds.
Cardinal Cisneros founds Universidad Complutense in Alcala de Henares, near
Madrid, in 1498. (Complutum was the Roman name of the town.) It
becomes famous for producing the Complutensian Polyglot Bible in
1517, the first European polyglot Bible, with texts in Latin, Greek,
Hebrew and Chaldean. The University moved to Madrid in 1836,
where it is still called the Universidad Complutense.
Pacioli/Da Vinci: De Divina Proportione is the first work to give drawings of
many polyhedra – not published until 1509.
Pedro Alvares Cabral, a Portuguese captain on his way around Africa, is blown
off course and discovers Brazil, but cf 1494. Another source says
Brazil was discovered by Vincente Pinzon in 1499. A Portuguese
expedition, including Amerigo Vespucci, goes to Brazil in 1501 (though
some people doubt if Vespucci actually went on this and another source
says he was exploring during 1496-1503, reaching Mexico).
This is the traditional end of the first era of printing. In Italy at least 214
mathematical works were printed between 1472 and 1500. It is
estimated that over 8,000,000 copies of over 35,000 books were
produced in Europe in this period.
Venice establishes first Chair of Navigation.
Nilakantha (Nīlakaņţha Somasutvan) (1444-1545): Aryabhatiya-Bhasya
(Āryabhaţīya-Bhāşya) and Tantrasamgraha (Tantrasamgraha
[the m should have a dot under it]) of 1502. He gives the alternating
series for π/4 usually called Leibniz's (1674), as well as Gregory's
series for tan-1 x (1671). Other series were found by his followers in
MEDIEVAL - p. 36
1502
1502
c1506
1507
1509
1509
1510
1511
1511
1512
1512
1513
1513
1514
1514
1514
1515
1515
1517
1517
1517
1519
1519-1522
1521
1521
1520-1525
1522
1522
1524
1524
1524
Kerala over the next century or so. In his commentary on Aryabhata I,
Nilakantha asserts that no rational value can be found for π. (Some
authors claim he is saying that Aryabhata I meant this.)
(1510?) Peter Henlein (or Hele) builds first spring driven pocket watch at
Nuremberg. Earliest surviving watches date from c1540.
University of Wittenberg founded. In 1817, it was combined with that in
Halle.
Scipione Ferro (or dal Ferro or del Ferro) solves cubic with no x2 term and
with no x term. He tells this to his pupil Fiore (or Fior).
The Portuguese, under Alfonso de Albuquerque, destroy Arab ports in
Zanzibar and East Africa to eliminate competition, then attack and
destroy the Omani fleet and establish bases in Oman in order to
monopolise trade with India.
Luca Pacioli: De divina proportione, with illustrations by Leonardo,
published. Cf 1498.
Luca Pacioli: Euclidis megarensis ..., i.e. The Elements in Latin. This is a
correction of the 1482 publication. Pacioli is believed to have made an
Italian translation, but it is lost.
Charles de Bovelles (Carolus Bovillus) (1479-1553): Liber de perfectis
numeris is probably the first printed work on number theory, but it
claims that 2n - 1 is prime when n is odd!!
Portuguese reach Pacific.
Charles de Bovelles (Carolus Bovillus) (1479-1553): Geometrie en Français
is first geometry text printed in French.
Waldseemüller publishes a theodolite design. Cf 1556.
First printed arithmetic in France (according to Swetz).
Ponce de Leon is first Spaniard to reach American mainland, at Florida.
Balboa crosses Panama and sees the Pacific Ocean.
Johannes Werner reinvents prosthaphaeresis (or perhaps just the formula for
sin A sin B). This is circulated in a manuscript De triangulis
sphaericis and knowledge of it eventually reaches Brahe. It is not
published until the 19C. Werner also suggests measuring the distance
between the moon and a star to determine absolute time and hence
longitude – 'the method of lunar distances'. See 1524.
Portuguese reach China.
Pope Leo X invites astronomers to Rome to reform the calendar. Copernicus
declines since the motions of the sun and moon were not understood!
Hoist run by a waterwheel in the Tyrol.
First printed version of the Almagest, using Gerard of Cremona's 1175
translation, in Venice. (or 1496??)
Ottomans under Selim the Grim conquer Syria and Egypt – end of Mameluk
dynasty. Selim becomes Caliph.
31 Oct: Martin Luther (1483-1546) nails his 95 Theses to the door of the
Schlosskirche in Wittenberg, starting the Reformation. The Lutherans
try to teach all children to read. Luther is excommunicated in 1520 or
1521.
First European polyglot Bible – cf 1498.
First printed arithmetic in Portugal.
Magellan's expedition first circumnavigates the earth. They find their
reckoning off by a day!
Diet of Worms – Luther refuses to recant.
Ottomans capture Belgrade.
Adam Riese writes his texts.
Werner: Libellus restarts study of conics.
Ottomans capture Rhodes.
Michael Stifel relates an arithmetic and a geometric progression as a primitive
logarithm.
Gemma Frisius gives first diagram showing the measurement of a lunar
distance. See 1514.
Giovanni da Verrazano, an Italian working for Francois I of France, explores
MEDIEVAL - p. 37
the coast of North America, discovering New York Bay and Manhattan
Island, but he misses both Chesapeake and Delaware Bays!
1525
Albrecht Dürer's Unterweysung der Messung ... exposits perspective,
bringing the Renaissance to northern Europe. This is also the first
printed work to discuss such geometric topics as higher plane curves
and approximate constructions for the regular heptagon, etc. One
source asserts Dürer studied with Ferro at Bologna. He also invents the
idea of a net of a polyhedron.
c1525
Beginning of watch manufacture in Germany.
1525
Oldest known spring clock, by Jacob Zech of Prague. This uses a fusee.
c1525
Cuthbert Tunstall (1474-1559) was Bishop of Durham in 1522-1529/30.
During his time, the idea of a university at Durham was first proposed.
The idea was revived in 1604 and in 1649-1659, but the opposition of
Oxford and Cambridge prevented it.
1525
Christoff Rudolff's Die Coss publishes radical sign.
1526
Mughal Empire founded in India by Babur.
1526
Suleiman the Magnificent wipes out Hungarian forces at the Battle of Mohács
(= Mohacz), allowing the Ottomans to occupy Budapest and about a
third of Hungary and to gather strength to besiege Vienna – cf 1529.
1526
University of Nuremberg (Nürnberg) founded as a gymnasium by
Melanchthon. In the late 16C, it migrated to Altdorf and became a
university in 1622. The Altdorf campus was supplanted by Erlangen
and was abolished in 1809. It's not clear if Nuremberg and Erlangen are
now or were two branches of the same institution. Nuremberg is
considered the first German science university.
1529
Edict of Worms confirmed by the Pope. Six princes and 14 towns meet at
Speyer to 'protest' against the Edict, leading to the term Protestant.
1529
Suleiman the Magnificent conquers Hungary and besieges Vienna but is driven
back, leaving large supplies of coffee beans!
1529 or 1530 The Collège Royal (des Trois Langues) was founded by François I in Paris as
an antithesis or antagonist to the narrow scholasticism of the University
(= Sorbonne).
1530
Religious meeting at Augsburg fails to reach agreement but Melanchthon
draws up the Confession of Augsburg which becomes the basic charter
of Protestantism.
1530
Gemma Frisius first proposes determining longitude by use of sea-going
clocks. It takes two and a half centuries for such clocks to be
developed. (Another source says this idea first occurs in the fourth ed.
of his De Principiis Astronomiae & Cosmographiae in 1553.) Cf.
1559.
1530
Agricola's De Re Metallica.
c1530
Tartaglia (1500-1557) solves cubic with no x term.
1533
Regiomontanus's De Triangulis is published.
1533
First printed Greek version of Euclid, in Basel.
1534
Luther completes his translation of the Bible, the first literary work in modern
German.
1534
Calvin converts to Protestantism.
1534
Henry VIII breaks with Rome.
1535
Tartaglia solves cubic with no x2 term on night of 12/13 February, in response
to a challenge from Ferro's pupil Antonio Maria Fiore.
1537
First printed arithmetic in England (according to Swetz).
1537
Tartaglia: La Nova Scientia is first publication on ballistics, later developed in
his Quesiti of 1546. He makes the first ballistic experiments. He is the
first to show that the path of a projectile is curved everywhere and the
first to find that a 45o angle gives maximum range.
1538
First printed Greek version of the Almagest, in Basel.
1538
First printing in Arabic – a Koran (Qur'an) printed by Paganino de' Paganini, of
which the only known copy was discovered in 1987.
1539
25 March: Cardano (1501-1576) learns solution of cubic from Tartaglia. He
extends to the general cubic.
1540
First printed version of Alberti's 1435 De Pictura – in Basel.
MEDIEVAL - p. 38
1540
1540
1539-1541
1540
1543
1543
1543
1544
1544
1545
Ferrari solves quartic.
Robert Recorde's Grounde of Artes is first English book to use +, - .
Rhaeticus works with Copernicus to produce De Revolutionibus. In 1540, he
prints the Narratio Prima (First Account), an open letter to his teacher
in Nuremberg, Johannes Schöner, which summarises Copernicus's
theory of the motions of the earth. In 1542, he publishes some of the
early material as a textbook of trigonometry – this includes the first use
of the secant and the introduction of the notion of infinity. In 1543, he
organises the publication of De Revolutionibus.
Society of Jesus (The Jesuits) founded.
Tartaglia publishes Italian translation of Euclid, the first vernacular edition of
Euclid.
Cardano & Ferrari go to Bologna and learn of Ferro's solution.
The dying Copernicus (1473-1543) publishes his De Revolutionibus Orbium
Coelestium. He dedicates it to Pope Paul II (or III) and hopes it will
help to reform the calendar. The first copy reaches Copernicus on his
deathbed. The book is eventually banned as heretical until 1835, but cf
1551.
First printed version of Archimedes' works. (1543??)
University of Königsberg (now Kaliningrad, Russia) founded by Duke
Albrecht of Prussia.
Cardano's Ars Magna publishes solutions of cubic, attributing the case with no
x2 term first to Ferro, later to Tartaglia. He also publishes Ferrari's
solution of the quartic, uses negatives and introduces complexes, which
he calls 'truly sophisticated'. He also asserts that Pacioli had denied the
possibility of solving these, but Pacioli had simply said that known
methods could not do it.
I consider the three entries on Copernicus, Archimedes and Cardano to mark the
beginning of the modern era of mathematics and physics. Similarly
important works, e.g. Vesalius: De Humani Corporis Fabrica (1543),
Agricola (1556), occur in other sciences.
1545
1546
1550
1551
1551
1551
16C
16C
1551
1545-1563
Pedro de Medina: Arte de Navegar
Tartaglia: Quesiti e Inventioni Diverse. Castigates Cardano's betrayal of
confidence.
Maurolycus uses induction to sum n and n2, but doesn't state the principle
clearly. (1575??)
Rhaeticus (1514-1576) publishes tables of the six trigonometric functions for
10' intervals, to 7 figures. These are the first printed tables with secant
and cosecant. He then starts on tables with 10" intervals, completed and
printed by his student Otho in 1596, qv. The value of sin 10" implies
π = 3.14159 26523. He and his pupils spent 12 years producing a 15
place table of the sine for 10' intervals, but it was lost until Pitiscus
relocated it and printed it in 1613, qv.
Erasmus Reinhold uses Copernicus's work to compute much improved tables
of planetary orbits, known as the Prutenic Tables, superseding the
Alphonsine Tables of 1292 (or 1272). These paved the way for
adoption of Copernicus's theory and for the calendar reform of 1583 and
the eventual adoption of Copernicus's theory. They were not surpassed
until Kepler's Rudolphine Tables of 1627.
Dee introduces cross-staff to England.
Use of vernacular languages becomes dominant in popular literature, but
treatises continue to be written in Latin.
Ready availability of paper allows the Hindu-Arabic system to become the
most common method.
Martin Cortes: Breve compendio de la sphera y de la arte de navegar.
Council of Trent revives Catholicism, leading to the Counter-Reformation and
the Thirty Years' War (1618-1648). In the Netherlands, fighting starts
in 1568 with a revolt against Spanish rule and the war is called the
Eighty Years' War (1568-1648), leading to the independence of the
MEDIEVAL - p. 39
1555
1556
1556
1556
1557
1558
1558
1559
1559
1559
1509-1575
1561
1564
c1564
1568
1568
1569
1570
1571
1571
1572
1572
1572
1537-1612
1575
1575
Netherlands.
Peace of Augsburg allows German states freedom to choose their religion – but
the Catholics soon attempt to counter this.
Leonard Digges' theodolite design published. Cf 1512.
Tartaglia: General Trattato.
Recorde: The Castle of Knowledge – possibly first English book to approve
of Copernicus.
Robert Recorde's Whetstone of Witte is the first English algebra book and
introduces = .
Jean Trenchant publishes first compound interest tables.
University of Jena founded.
William Cunningham proposes using a watch to determine longitude. It's not
clear if he was familiar with Gemma Frisius's proposal of 1530, though
he mentions watches from Flanders.
The Jesuits found a university at Evora, Portugal, but it is suppressed in 1759.
The Académie de Genève (Geneva) founded.
Federico Commandino translates and comments on Archimedes, Apollonius,
Aristarchus, Hero, Pappus, Ptolemy and especially a translation of
Euclid into Latin in 1572, of which he supervised a translation into
Italian in 1575.
English buy instructions for making nitre beds from a German, Cf c1375.
1562 First German edition of Euclid.
First French edition of Euclid.
Cardano completes Liber de Ludo Aleae (The Book on Games of Chance).
This is the first book on gambling and probability, but it remains
unpublished until 1663, after Pascal and Fermat had created and
developed probability theory much further. Cardano mentions that
opposite sides of a die should add to 7.
First mention of convex lenses used to correct near sight.
Beginning of the Eighty Years' War of independence (1568-1648), the Dutch
version of the Thirty Years' War (1618-1648).
Gerhard Kremer (Gerardus Mercator) (1512-1594) publishes a world map, but
the complete atlas does not appear until 1595.
First English Euclid, translated by Henry Billingsley, with Introduction by John
Dee. Dee outlines the entire field of mathematics as then known. He
refers to 'perspective glasses' – possibly a forerunner of the telescope or
a reference to Digges' device – cf 1571.
Thomas Digges: Pantometria publishes first description of a telescope,
devised by his father Leonard Digges, possibly as early as 1550.
Battle of Lepanto ends Turkish maritime power in the Mediterranean.
Bombelli: L'Algebra. First book so titled. Exposits and improves work of
Tartaglia and Cardano. He develops complexes and fully discusses the
'casus irreducibilis' that Cardano had avoided. Uses continued fractions.
Unpublished MS of further chapters uses negative lengths and even
negative areas. He is also the first to use material from Diophantos.
24 Aug: St. Bartholomew's Day Massacre of c2000 Protestants in Paris. 1573
L. Valentin(e) Otho gives π = 355/113, as done by Zu Chongzhi
(c480). Peurbach (1423-1469) also gives this value.
November: A nova appears, visible in the twilight, in Cassiopeia. Observation
(by Brahe?) finds no detectable parallax, which meant it was part of the
fixed stars where Ptolemaic theory said no changes could take place.
This was one of the first observations leading to the fall of the
Ptolemaic theory – cf 1577. This nova inspired Brahe to take up
astronomy, leading to his De Nova Stella of 1573.
Christopher Clavius. Produced many standard texts. In 1574 he publishes an
edition of Euclid and tries to prove the Fifth Postulate.
Taqi al-Din (= Taqī al-Dīn) establishes an observatory in Istanbul. Though
short-lived (the Caliph ordered it destroyed because he didn't like some
astrological predictions), it may have been the inspiration for Brahe's
observatory.
Cf 1581 for founding of the University of Leyden (= Leiden).
MEDIEVAL - p. 40
1576
Thomas Digges' A Perfit Description of the Caelestiall Orbes, ..., a
supplement in his revision of the book of his father, Leonard Digges,
Prognostication Everlasting. This gives an English translation of
Book I of Copernicus, making it widely known in England. He adds
some of his own notes, particularly that the universe is infinite and
filled with infinitely many stars. Cf Bruno, 1600.
1577
A great comet appears and is studied by Brahe, who shows it is much further
than than the moon, not in the Earth's atmosphere as stated by Aristotle.
This and his observations of 1572 were major factors in the eventual
acceptance of Copernicus's theory.
1540-1603
Francoise Vieta (or Viète). Knows formulas for sin na and cos na. First clear
statement of the law of cosines. Develops spherical trigonometry. In
1579, his Canon Mathematicus Seu ad Triangula exposits plane and
spherical trigonometry, tabulating all six functions to minutes,
advocates decimal fractions (using a , or │ for the decimal point) and
first gives the formula for sin A sin B. In 1593 (1579??), he uses a
polygon of 6 x 216 sides to determine π to 9 places. Finds an infinite
product for 2/π. [F. Rudio first proved that this converged in 1891.]
Develops symbolic algebra, using vowels for unknowns. Shows how to
solve Cardano's irreducible case of the cubic by use of trigonometry.
Popularises use of + and - signs. See 1591.
1579
University of Vilnius founded by Jesuits at the request of the Polish king
Stefan Batory. Closed by the Russians in 1832. Reopened in 1919.
1581
University of Leyden (Leiden) founded – first in Holland – cf 1425. William
(the Silent) of Orange offered the city a reward for its resistance to the
Spanish in 1574 during the Dutch Revolt – either no taxes for ten years
or a university – the city wisely chose the university. It was open to
students of all religions and soon became the leading university of the
world. Another source dates the founding to 1575. Cf 1568.
1581
Seven Dutch provinces form the Republic of the United Provinces,
independent of Spain, but the war of independence (the Eighty Years'
War) continues until 1648.
1582
The University of Würzburg, Bayern, founded.
1582
Clavius completes Aloysius Lilius's (Luigi Lilio's (or Giglio's)) proposal to
reform to the Gregorian Calendar. The year is taken as 365.2425 days
(off by .12 days per 400 years). [One author claims that Copernicus's
data were the basis for the reform – ??] 10 days (5-14 October)
omitted. This corrects back to c325, the date of the Council of Nicaea,
rather than to the time of Caesar, because the Council of Nicaea fixed
the date of Easter. Consequently, the vernal equinox is about 21 or 22
March. The beginning of the year is moved from 25 Mar to 1 Jan.
Various Protestant countries refuse to accept the reform – cf 1583.
Denmark, Netherlands and Protestant German states change in 1700.
Scotland changes in 1600, but England does not adopt it until 1752,
when 11 days have to be omitted. The orthodox countries, including
Russia, do not change until the early 20C and Vietnam changed in 1967,
having to skip 13 days. Some Orthodox countries may still be using the
Julian calendar?? Clavius exposits the ideas in a book in 1603.
1582
Academia de Matematicás founded in Madrid. Cf 1625.
1581 or 1583 Galileo notes constancy of the pendulum, but he doesn't use it for timing
rolling bodies. He makes an attempt at building a pendulum clock in
1640, qv. Mersenne suggests the idea to Huygens, c1640, leading to
Huygens creating the pendulum clock in Dec 1656. (1590?)
1582
Stevin publishes first useful compound interest tables, previously kept secret.
1548-1620
Simon Stevin. He recognizes a + (-b) = a - b, negative roots of quadratics and
that an equation has a root in an interval where it changes sign. He
states Pascal's triangle. In 1586, he determines the law of the inclined
plane and writes the first book on hydrostatics since Archimedes. He
actually did try dropping different weights to see if the heavier fell
faster.
1583
English government consults John Dee about reforming the calendar in view of
MEDIEVAL - p. 41
1583
1583
1585
1585
1585
c1585
1586
1588
1588
1546-1601
c1590
1590
1591
1592
1592
1592
1592
1593
1594
c1594
1595
1595
Gregory's reform of 1582 and he produced a scheme for it, but the
Protestant English decided not to have any truck with a Catholic reform.
Cf 1582, 1752.
University of Edinburgh founded.
T. Fincke introduces terms 'tangens' and 'secans'.
University founded in Franeker, Friesland, Netherlands, but it was closed by
Louis Napoleon in 1811. Descartes was a student in 1629.
Adrien Anthoniszoon estimates π = 355/113, as done by Zu Chongzhi (c480).
Stevin: De Thiende (in Flemish) = La Disme (in French) (a 16 page section of
his book: L'Arithmetique) popularizes decimal fractions, though the
notation is not as good as al-Uqlidisi's of 952. (Rudolff (1530) and
Vieta (1579) also used them earlier.) This book includes the first
translation of Diophantos into a modern language. Stevin uses some
limits. He is the first to express the solution of the quadratic equation
by a single formula.
Joost Bürgi proves Werner's result for sin A sin B and discovers and proves
the formula for cos A cos B. He also develops a clock escapement
which was a forerunner of the pendulum clock.
Blaise de Vigenère's Traicté des Chiffres introduces his cipher and modern
cryptography.
First printed version of Pappus, using Commandino's Latin translation. One of
the problems inspires Descartes to invent analytic geometry.
John Spielmann (or Spilman) starts first major paper-making mills in England,
at Dartford. Supposedly 'foolscap' derives from the watermark of a
jester (Spielmann) which was part of his coat of arms. Cf 1617.
Tycho Brahe. Builds an observatory on the island of Hveen and begins the
modern era of astronomical measurements. Rediscovers? and exploits
prosthaphaeresis, which had probably been communicated from
Werner's work of 1514 and utilised by Brahe's assistant Wittich. He
estimates π = 88/785.
Zacharias Jansen invents compound microscope.
Trinity College Dublin started by the City Council. Chartered by Elizabeth I in
1592 and opened in 1594.
Viète: In Artem Analyticem Isagoge is often considered the beginning of
symbolic algebra. It introduces use of letters for knowns (consonants)
as well as unknowns (vowels).
Galileo first attaches a scale to a thermometer tube.
Abacus still in use by German merchants.
Earliest known depiction of the use of a magnifying glass, by George
Hoefnagel. However, I have seen a 1352 fresco by Tomaso da Modena
in the Chapter House of the Seminary of S. Niccolo, Treviso, Veneto,
which seems to show a monk using a magnifying glass which exhibits
the Aristotelian conception that rays emanated from the eye. Another
source cites a 1352 portrait of Cardinal Ugone wearing spectacles –
possibly a reference to the Treviso fresco?
Jyesthadeva (Jyeşţhadeva): Yuktibhasa (Yuktibhāşā, based on the
Tantrasamgraha of Nilakantha (1502), gives rationale or proof for all
the Keralese calculus results then in use.
Adriaen van Rooman (Adrianus Romanus) extends Vieta's work to 17 places
for π.
Th. Blundeville's Exercises contayning six treatises ... is first English book to
deal with trigonometric tables.
John Davis invents backstaff. He may have been using it on his voyages to
northern Canada in 1585-1587 as his charts are far more accurate than
his predecessors.
Gerhard Kramer (Gerardus Mercator) (1512-1594): Atlas, sive
Cosmographicae ... is the first complete version of his work (cf 1569)
and the first book to be called an 'atlas'.
Pitiscus: Trigonometria is first use of the word and first treatise to consider it
separately from astronomy.
MEDIEVAL - p. 42
1571-1630
1595
1596
1596
1597
1598
1598
1600
1600
1600
1600
1564-1642
1603
1607
1607
1608
1608
1608
1609
1609
1609
1610
1609-1610
Johann(es) Kepler.
9 Jul: during a lecture, Kepler drew a circle circumscribed about a triangle
circumscribed about a circle and realised that the ratio of the radii was
the same as for the orbits of Saturn and Jupiter. This sent him off into
his researches and led to his famous picture of spheres and regular
polyhedra, as exposited in his Mysterium Cosmographicum of 1596
and Harmonices Mundi of 1619.
L. Valentine Otho completes and publishes the trigonometric tables at 10"
intervals started by his master Rhaeticus, cf. 1551, as Opus Palatinum.
Kepler: Mysterium Cosmographicum shows his polyhedral view of the
universe.
Gresham College starts in London.
Philip III of Spain offers a substantial pension to "the discoverer of longitude".
Edict of Nantes gives some toleration of Protestants in France.
William Gilbert: De Magnete begins scientific study of electricity and
magnetism. Often described as the first product of the scientific
method. He notes that a magnetized sphere would rotate under the
influence of a magnetic field and advanced this as an explanation of the
earth's rotation.
Harriot (1560-1621). Shows the stereographic projection is conformal.
Scotland adopts Gregorian calendar.
Giordano Bruno (1547-1600) burned at the stake for supporting the Copernican
theory, etc. He is often credited as being the first to advance the idea
that the universe is infinite and that there are infinitely many worlds, in
his Dell infinito Universo et Mondi of 1584, but Thomas Digges
advanced these ideas in 1576.
Galileo.
Accademia dei Lincei founded in Rome by Prince Federigo Cesi – the first
modern learned society (or 1601?). The word 'lincei' means 'lynx-eyed',
but actually derives from the Greek argonaut Linkeus, the eponym of
the animal. It still exists, but has had several hiatuses in its existence.
Jamestown – first successful British colony in North America.
First mention of a ship's log for measuring its speed, in a description of an East
Indian voyage. The captain threw a log into the water at the bow and
kept pace with it as he walked astern.
Abraham Verhoeven starts first newspaper, in Antwerp.
Telescope invented(?) in Middelburg, Holland by Hans Lippershey. He offered
examples to the States-General of Holland on 21 Oct and applied for a
patent. Jacob Metius of Alkmaar and Hans Jansen and his son
Zacharias of Middelburg, both also claimed the invention within two
weeks of Lippershey's application. It appears that telescopes were
already being sold by a Dutch pedlar at Frankfurt. They were being sold
in Paris in the spring of 1609. The Jansens later claimed (in 1655) to
have invented the microscope about this time, but the earliest definite
mention of it is in 1619, while Galileo's use of a microscope is
described in 1610 and 1614. See also 1570 & 1571.
The first municipal public library in Britain is founded in Norwich. The
original 1772 volumes are still in the city library! Cf c1330, 1653,
1691, 1701, 1705.
May: Galileo hears about telescopes and rapidly builds one, soon surpassing all
previous examples. Thomas Harriot uses a six power telescope on the
moon to make a drawing of it – but this was only marginally better than
using the naked eye.
Kepler: De Motibus stellae Martis and Astronomia Nova give his results on
the orbit of Mars and his first two laws of planetary motion.
Henry Hudson discovers New York Bay and the Hudson River for the Dutch
East India Company.
Ludolph van Ceulen computes π to 35 places.
Galileo discovers moons of Jupiter, mountains on the moon, sunspots and their
movement, and the phases of Venus – the first observational evidence
MEDIEVAL - p. 43
1610
1612
1613
1613
1614
1614
1614
1615
1616
1616
1616
1616
1616
1616
1617
1617
against the Ptolemaic system since it showed that Venus must revolve
about the sun and did not shine by its own light. He first sees three
moons of Jupiter on 7 Jan 1610 'at the first hour of the night'. His first
descriptions of his observations are in a letter of 7 Jan 1610, including
his observation of Jupiter made 'only this evening'. On the 11th, he
realises the stars by Jupiter are moons and on the 13th, he sees a fourth
moon. He publishes his findings in a 24 page pamphlet: Sidereus
Nuncius (The Starry Messenger) in Mar 1610. It is not until the end
of Aug that others, including Kepler and Harriot, confirm his
observations. In Oct-Dec 1610, he detects the phases of Venus.
(Another source says he discovered the phases of Venus and Mercury,
sunspots and the rotation of the sun in 1611.) His pupil Castelli
develops the technique of projecting the telescope onto a screen so the
sun could be observed.
John Wedderburn describes Galileo's use of a microscope, but Galileo did not
develop the idea.
Bachet: Problemes plaisans et delectables ....
Pitiscus relocates the table of 15 place sines at 10' intervals compiled by
Rhaeticus and his students and publishes it in his Thesaurus
Mathematicus.
Martin Weigel, in Germany, invents idea of blasting rock with gunpowder. In
1627, the method is mentioned in Hungary.
Napier: Mirifici Logarithmorum Canonis Descriptio gives tables of
logarithms and instructions on how to use them. He invents the word
logarithm. He doesn't publish how to compute them until seeing that
they were useful. His log of x is what we would denote
107 ln (107/x). At the end, he notes that Briggs had proposed a more
convenient system. Cf. 1616, 1619, 1624.
The University of Groningen founded.
The first university in Westphalia was founded in Paderborn by Bishop
Dietrich IV von Fürstenberg, but it was closed at some point, perhaps
under Napoleon. Several schools were formed into a polytechnic in
1972 and this became the University of Paderborn in 1980.
Briggs and Napier invent logarithms to base 10.
William Schouten discovers Cape Horn – previous navigators had gone
through the Straits of Magellan.
William Harvey announces his theory of the circulation of the blood.
Edward Wright translates Napier into English. He dies before completing it
and his son Samuel and Henry Briggs finish and publish it. An
anonymous appendix, now known to be by William Oughtred,
introduces the  sign for multiplication.
The Church orders Galileo to cease teaching the Copernican system.
Copernicus's De Revolutionibus is placed on the Index of prohibited books.
Galileo proposes using the satellites of Jupiter to determine longitude at sea
and submits the idea for the prize offered by Philip III in 1598. Philip's
advisers said that observing them at sea is not easy and they are only
visible on some nights and under good conditions, so the method was
not sufficiently usable. He later (1637?) submitted the idea to the
States-General of Holland, and in 1638-1639, when two Dutch
merchants brought a letter and a gold chain from the States-General as
thanks for his proposal. Cf c1650.
Napier's Rabdologiæ, seu Numerationes per Virgulas describes his 'Bones',
binary arithmetic and the Promptuary, a multiplying device which has
been called the first mechanical calculator, though it still required
mental carrying. He calculates square roots in binary. Within a few
months an almanac refers to the calculating rods being available.
Though the book appeared just after Napier's death, the 'bones' seem to
have been devised long before and were even somewhat known in the
mathematical community. The term 'Napier's Bones' was already
coined in 1617.
Briggs publishes first part of his table of common logarithms.
MEDIEVAL - p. 44
1617
1618
1619
1619
1620
1620?
1620
1620
1620
1621
1621
1621
1621
1622
1624
1620-1632
1625
c1626
1626
1627
1629
1618-1648
1630
1630
1632
1632
1632
1595-1665
1635
1636
1636
John Spielmann (or Spilman), in England, cf 1588, obtains a monopoly on the
manufacture of the new playing cards, whose invention was attributed
to him, though they were widespread in in 14C Europe.
A revolt in Bohemia starts the Thirty Years' War (1618-1648) which devastates
Germany and much of northern Europe. See 1568 & 1621 for the
Dutch version.
Napier's posthumous Mirifici Logarithmorum Canonis Constructio explains
how to compute logarithms.
Kepler: Harmonices Mundi includes his third law, describes the Archimedean
polyhedra and tessellations and some of their duals and two star
polyhedra.
John Speidell's New Logarithms gives first logarithms to base e.
Gunter's logarithmic scale (1624 or 1623??). See Computing Chronology for
details of the development of the slide rule.
Gunter's Canon Triangulorum ..., the first tables of logarithmic trigonometric
functions, saying he had already been lecturing on logarithms. An
English edition appeared in 1620. He introduces terms 'co.sinus',
'cotangens', ('cosecans' ??) and 'log'.
Francis Bacon: Instauratio Magna (The Great Instauration) is first
philosophical presentation of the scientific method.
Bürgi's publication of logarithms.
Oughtred invents slide rule, first (?) circular, then linear, but doesn't publish it.
He introduces abridged multiplication.
Willebrord Snell (or Snel) computes π to 36 places.
Cornelius Drebbel is reputed to have demonstrated a compound microscope in
London, Paris and Rome. Possibly the first such.
The Dutch War of Independence (the Eighty Years' War, cf 1568) had a
Twelve Years' Truce in 1609-1621, but the beginning of the Thirty
Years' War (cf 1618) leads to renewal of the Dutch war as part of the
larger war.
Thomas Blundeville again proposes using a clock to determine longitude. Cf
1530, 1559.
Briggs publishes table of common logarithms.
Various inventors of various slide rules.
The Reales Estudios del Colegio Imperial is established by the Jesuits in
Madrid to continue the 1582 Academia de Matematicás when it closed.
Willebrord Snell (properly Snel van Roijen) (1596-1626) finds law of
refraction (1621?). Descartes publishes it in 1637.
Girard introduces abbreviations 'tan', 'sec'.
Kepler: Rudolphine Tables supersedes the Prutenic Tables of 1551.
Girard: Invention nouvelle en l'algebre allows negative roots, interprets
negatives as 'retrogressions' and first? conjectures that an n-th degree
equation has n linear factors.
Thirty Years' War devastates much of Europe.
Mersenne.
Oughtred.
Galileo: Dialogo sopra i due Massimi Sistemi del Mondo (Dialogue
concerning the Two Chief World Systems) attempts to present the
Copernican system as a theory but is so obviously biased in favour of it
that Galileo is brought before the Inquisition in 1633. Pope Urban VIII
interprets the book as ridiculing him. The book was placed on the Index
of Prohibited Books and remained there until 1823.
University of Dorpat (now Tartu, Estonia) founded by Gustavus Adolphus,
modelled on Uppsala University. It closed about 1700, but reopened in
1802.
First British chair of Arabic established at Cambridge University by Sir
Thomas Adams.
Fermat.
Cavalieri.
The University of Utrecht founded. It is now the largest in the Netherlands.
A college is founded by the Massachusetts colonial government at Cambridge,
MEDIEVAL - p. 45
1636
1637
1637
1638
1638
1639
1593-1662
1640?
1640?
1641
1643
c1645
1646
1647
1648
1649-1660
17C
1623-1662
c1650
1652
1653
1654
1654
1655
1655-56
1656
1657
Massachusetts. In 1638, a settler from London, named John Harvard,
died and left $2000 (half his estate) and his library to the new college
which was renamed in his honor the following year.
Chair of Arabic established at Oxford University by Archbishop Laud.
First national observatory founded, in Copenhagen, but it later burned down.
Descartes (1596-1650): La Geometrie.
Ottomans conquer Baghdad.
The first printing press in America is set up in Harvard Yard by Stephen Day.
(I have a vague memory that there was an earlier press in South
America – ??)
A source says Galileo's discovery of the pendulum was first published in
L'Usage du Cadran ou de l'Horologe Physique Universelle in Paris
in this year.
Desargues.
Pascal finds his theorem in projective geometry.
Pascal: On the Arithmetic Triangle and Fermat's method of infinite descent
are the first clear uses of induction.
Galileo and his son Vincenzio attempt to make a pendulum clock but he dies
before finishing it. Viviani asserts Galileo described the idea in Jun
1637. In 1658 or 1659, he made a drawing from Vincenzio's
description of their 1649 model.
Torricelli demonstrates pressure of the atmosphere, as predicted by Galileo.
A group at Oxford starts holding regular scientific meetings – the forerunner of
the Royal Society.
University of Breda founded about this time.
A university was founded in Harderwijk, Gelderland, Netherlands, in 1647, but
closed by Louis Napoleon in 1811. Constantijn Huygens received a
doctorate here.
Peace of Westphalia ends Thirty Years War' (1618-1648) and permits both the
Catholic and Protestant religions in Germany. Up to half of the
population had been killed. The main trade routes had come to Venice
and then overland through Germany, but the disruption of the War and
the development of maritime trade around Africa and to the New World
result in Germany and Venice never recovering their prosperity. Part of
the Treaty recognised the independence of the Netherlands, confirmed
by the Peace of Munster.
The Puritans adopt a new calendar after the execution of Charles I, with years
called 'the first year of freedom', ....
Accademia dei Lincei starts Gesta Lynceorum, first proceedings of a scientific
society. Cf 1665.
Pascal.
After c1650, Galileo's method of determining longitude from the moons of
Jupiter is adopted by surveyors on land. Louis XIV, upon seeing a new
and accurate map of France, remarked that he was losing more territory
to his astronomers than to his enemies. Cf 1616.
Collegium Naturae Curiosorum founded at Halle.
Chetham's library founded in Manchester by Humphrey Chetham. It is locally
claimed to be the first free library in Europe. Another source says it
was the only town library 'up to the mid-nineteenth century, that was
entirely free and accessible to the public.' Yet another source says the
first 'free public lending library' was opened in Manchester in 1853 –
presumably a misprint for 1653. But cf c1330, 1608, 1691, 1701, 1705.
Chevalier de Mere asks Pascal for advice on a dice bet. The resulting
correspondence between Pascal and Fermat is considered the foundation
of probability theory.
Otto von Guericke, of Magdeburg, carries out the Magdeburg experiment.
Mar: Huygens discovers the first moon (Titan) of Saturn.
Winter: Huygens explains the peculiar appearance of Saturn as due to rings.
Dec: Huygens invents the pendulum clock.
Huygens: De Ratiociniis in Ludo Aleae, an appendix to a book by van
Schooten, is the first published work on probability.
MEDIEVAL - p. 46
1658
1658
1658
1659
1660
1660-1662
1660-1664
1663
1665
1665
1665
1666
1666
1667
1667
1668
1668
1673
c1673
1674
1675
1675
1676
1678
1678
J. Newton uses 'cosinus'.
Christmas Day: Huygens starts his pendulum clock – however they were
already being made for him in 1657. The first example was constructed
by Salomon Coster of The Hague in 1657 and Huygens presented it to
the States General. The oldest known example, from 1657, is in the
Museum Boerhaave, Leiden, and [Museum Boerhaave, p. 10] says this
is Coster's first example. Huygens gave Coster the sole right to make
the clocks on 16 Jun 1657 [Museum Boerhaave, p. 11]. [Museum
Boerhaave, p. 52] says these clocks were accurate to 10 sec per day. He
published his invention in a booklet, Horologium in 1658. Within a
few years they were being produced throughout Europe. Apparently he
was anticipated by Johann Philipp Treffler, a clockmaker in Augsburg.
Cf 1673.
Hooke describes the balance spring and seems to have made some watches
using it. Cf 1675.
Huygens publishes first maps of Mars.
Marcello Malpighi observes capillaries, completing the evidence for Harvey's
theory of the circulation of the blood.
Royal Society founded.
Huygens tests his clocks at sea but finds them undependable.
James Gregory proposes reflecting telescope but doesn't build one.
5 Jan: Journal des Sçavans, first scientific journal in the vernacular, founded
by D. de Sallo, starts.
Philosophical Transactions. It is the oldest surviving scientific journal. Cf
17C.
Great Plague in London and Britain, kills perhaps 100,000 people in London.
Universities close. Newton retires to Woolsthorpe and develops most
of his main ideas.
Great Fire of London. Wren is diverted from mathematics to architecture.
Académie des Sciences founded, but doesn't seem to start publishing a journal
until 1729, when the Histoire begins summarising the proceedings from
1666.
James Gregory's Vera Circuli et Hyperbolae Quadratura gives first series
expansions for trigonometric functions and proves π is irrational.
However, several of these series had been found by Nilakantha
(1444-1545) and his followers in Kerala. It is an interesting and
unsolved question whether these Indian results ever became known in
Europe.
Paris Observatory founded.
Newton builds first reflecting telescope, using a different system than
Gregory's proposal.
The University of Lund, Sweden, founded.
Huygens: Horologium Oscillatorium published in Paris giving his clock
designs, particularly his invention of cycloidal cheeks.
Antony van Leeuwenhoek (1632-1723) develops microscope to magnify by
300 (or 270) and discovers micro-organisms. (1683??)
J. Moore uses 'cos' and 'cot'.
Royal Observatory founded at Greenwich.
Huygens develops a watch, using a balance spring, and obtains a French patent
– but cf 1658.
Hooke: A Description of Helioscopes ... describes his invention of the balance
spring watch. c1675, he also invents the anchor or recoil escapement,
which makes the pendulum clock much more usable and accurate and is
still in common use. The first examples are produced by W. Clement in
London in 1676. But there is a 1671 turret clock by Clement, using this
escapement, in the Science Museum and the idea has been attributed to
him. The helioscope probably inspired Hadley to invent the octant.
Hooke states Hooke's Law anagrammatically. I don't know when he explicated
it.
University of Padua awards the first degree to a woman, Elena Lucrezia
Cornaro (= Corner) Piscopia. The fact that she was a descendent of
MEDIEVAL - p. 47
1660-1700
1682
1683
1685
1690
1691
1693
1699
1700
1701
1701
1705
1707
c1712
1714
1714
1715
early 1700s
1721
Doges of Venice may well have had something to do with the award –
the next woman to get a degree was over fifty years later at Bologna.
Minute hands begin to appear on clocks. By 1700, they are fairly common.
Second hands start appearing and are common in early 18C.
Acta Eruditorum founded in Leipzig.
Turks again besiege Vienna and are driven back by Prince Eugen of Savoy and
King Jan Sobieski of Poland. They are driven back to Belgrade. High
point of Ottoman Turkish expansion. In 1699 and 1702, they are forced
to pull back and cede large areas to Austria and Russia.
Edict of Nantes (see 1598) revoked. Many Huguenots emigrate from France
taking technical skills to England, Germany and America.
First printing press in Ireland, at Belfast.
Innerpeffray Library founded by David Drummond, claimed to be the first free
public library in Britain – but cf 1608, 1653 and also 1701, 1705.
The University of Halle founded.
Abraham Sharp computes 72 decimal places of π using a series of
Gregory/Leibniz.
Protestant German states, Netherlands, Denmark adopt Gregorian calendar.
Joachim Bouvet, a Jesuit missionary, describes the binary ordering of the Yi
Jing hexagrams (see c1060) to Leibniz about 1690, reviving Leibniz's
interest in binary which he had developed c1672, but not published.
Public library founded in Reigate, Surrey, and is still extant. Cf c1330, 1608,
1653, 1691, 1705.
Narcissus Marsh founds Marsh's Library, Dublin, the first public library in
Ireland. Cf 1608, 1653, 1691, 1701.
Admiral Sir Clowdisley Shovell runs four ships aground in the Isles of Scilly,
losing about 2000 lives, including his own, due to not knowing their
longitude (though other sources say his crew had celebrated a famous
victory rather too extensively). A more detailed version says they had
been in storm for some days and were not even clear as to their latitude,
believing they were near Ushant, the island at the end of Brittany.
First numbering of houses in England gives numbers to staircases in Lincoln's
Inn and other Inns of Court. The first street to be numbered is New
Burlington Street, in Jun 1764 and numbers start becoming common
from 1767.
8 Jul: Parliament passes An Act for providing a Publick Reward for such
Person or Persons as shall Discover the Longitude at Sea (The
Longitude Act). This offered: £10,000 for a solution of the problem of
finding longitude at sea to within 1o (about 60 miles) at the end of a six
week voyage to the West Indies; £15,000 for a solution within 40' and
£20,000 for a solution within 30'. (The £ was worth about 100 times
its current value. Skilled labourers, such as carpenters, earned about
£16 per year.) The Act established the Board of Longitude which
contained the Astronomer Royal, the PRS, the first Lord of the
Admiralty, the Speaker of the House of Commons and the Savilian,
Lucasian and Plumian professors at Oxford and Cambridge as exofficio members. The Board continued until 1828 and distributed over
£100,000 in grants.
Jeremy Thacker, of Beverley, East Yorkshire, first uses the word 'chronometer',
somewhat facetiously, in describing his clock which had two innovative
features – it was sealed in a vacuum chamber and it had a mechanism to
keep it going while it was wound, but it still could err by six seconds
per day.
Graham invents 'dead-beat' escapement, which much improves Hooke's anchor
escapement, making pendulum clocks accurate to a few seconds per
week. This was the most accurate method for nearly two centuries. The
first ones go the Greenwich Observatory.
René de Reaumur observes wasps making their nests from wood and has the
idea of making paper from wood pulp.
Graham devises the first temperature compensating pendulum, attaching a
MEDIEVAL - p. 48
1725
1729
1731
1735
1737
1739
1741
1744
1748
1752
c1755
1757
1755-1759
1759
1761
1762
1767
1773
c1790
1793
small vessel of mercury to a pendulum.
Graham invents the cylinder escapement for balance spring watches.
Bradley discovers of the Aberration of Light, the first observational proof of
the revolution of the Earth.
John Hadley invents the octant, later developed into the marine sextant. Hooke
had suggested an octant in 1666. Newton had exhibited such an
instrument in 1699 but had not developed it. An American, Thomas
Godfrey, developed a quadrant in 1730 and the Royal Society gave him
£200 in recognition of his priority. The sextant rapidly displaces the
mariner's astrolabe. Good observers differ by only a minute in
measuring the sun's meridian altitude.
John Harrison builds the first marine chronometer, H1. It is tested on a voyage
to Lisbon aboard the Centurion in 1736 and it shows that the navigators
were off by 60 miles on the return voyage. It takes until 1759 to get one
which really works and is compact.
The University of Göttingen was founded by George II of England, who was
also Elector of Hannover. (or 1733??)
Harrison completes his H2, but it is not tested at sea because of the war with
Spain.
Captain George Anson attempts to make a landfall by sailing along a parallel,
but heads the wrong way due to having lost his longitude.
Consequently many of his crew perish from scurvy.
Euler's Theoria Motuum Planetarum is the first work to systematically use
the abbreviations: sin, cos, tang, cot, sec, cosec.
Euler advocates fixing radius as 1 for trigonometric ratios.
Britain adopts Gregorian Calendar – see 1582. 11 days dropped: 3-13 Sep.
Beginning of year changes from 25 Mar to 1 Jan. It is often claimed
that this accounts for the peculiar dates of the British fiscal year, from 6
Apr to 5 Apr, but there were several further shifts of the fiscal year – see
my History of the Calendar for details. There was considerable popular
resistance and even some rioting! Hogarth's engraving 'The Election'
includes a poster "Give us our Eleven Days".
Mudge invents detached lever escapement for balance spring watches. In the
late 19C, it becomes the standard version.
Harrison completes his H3, introducing bimetallic strips and ball bearings.
Harrison builds his fourth chronometer, H4, the first small one. It only lost 5
seconds in a 62 day voyage and is considered the most important
watch ever made.
Kastner first defines trigonometric functions as numbers rather than lengths.
Maskelyne tests the method of lunar distances on a voyage to St. Helena to
observe the transit of Venus and finds he can always determine
longitude to within a degree. This leads to the The Nautical Almanac
being started in 1767.
Harrison claims the Longitude Prize, but it takes 11 years and the intervention
of the King before it is awarded.
The Nautical Almanac is started, providing tables of lunar distances for
determining longitude.
Harrison finally is awarded the Longitude Prize of £20,000.
First wrist watches, by Jaquet-Droz and Leschot of Geneva.
As part of the Revolution and the adoption of the metric system (adopted on 1
Aug 1793), France adopts a year of 12 30-day months with 5 or 6
holidays at the end. This was devised by Gilbert Romme. The calendar
started on 22 Sep and the months were named by the poet Fabre
d'Eglantine: Vendémiaire, Brumaire, Frimaire, Nivôse, Pluviôse,
Ventôse, Germinal, Floréal, Prairial, Messidor, Thermidor, Fructidor.
There was a 10-day week, with day names Primidi, Duodi, Tridi,
Quartidi, Quintidi, Sextidi, Septidi, Octidi, Nonidi, Decadi. The system
was very unpopular and was abolished by Napoleon on 1 Jan 1806. The
French also tried to decimalize time with 10 hours of 100 minutes and
angles with 100 centigrades in a right angle.
MEDIEVAL - p. 49
1828
1838
1838-1840
1847
1869
c1870
1880
1883
1883-1884
19-20C
1963
1970s
1967
Greece becomes independent.
De Morgan coins the term 'mathematical induction' in an article in the Penny
Cyclopedia on Induction in mathematics.
Bessel (1838), Henderson (1839) and Struve (1840) observe stellar parallax,
demonstrating the revolution of the Earth and getting a measure of the
size of the universe.
General Post Office adopts London Time throughout UK.
Charles F. Dowd proposes time zones in the US and Sandford Fleming
independently campaigns in Canada. Both the US and Canada correlate
with the Greenwich Meridian.
J. T. Thomson & Thomas Muir both invent radian measure and devise the
word. However the idea appears to have been previously known under
various names – 'unit of circular measure', 'radial angle'. Thomson and
Muir discussed the idea and various names and Muir consulted with
Alexander John Ellis. The word first appears in print in an 1873
examination paper set by Thomson in Belfast. Ellis used radial angle in
an 1874 book. William Garrett used radian in an 1877 book. [This
surprises me – how was the derivative of sin x determined before
radians were used??] [Math. Gaz. 76 (no. 475) (Mar 1992) 100-101.]
Another source says the radian was invented in 1897.
Greenwich Mean Time adopted as standard throughout Britain.
Noon, 18 Nov 1883: Standard Time adopted in the US on the initiative of the
American Railway Association.
The Rome and Washington Conferences for the Purpose of Fixing a
Prime-Meridian and a Universal Day propose and adopt the Greenwich
Meridian and the basic idea of time zones, which implies the acceptance
of the International Date Line. The vote was 22 to 1 with 2 abstentions.
It was estimated that 90% of sea charts in use were already based on
Greenwich. The Philippines, having been colonized from the New
World, had to skip a day to conform with its Asian neighbours, but I
don't know when this happened. Alaska had already made changes in
1867, qv.
Gregorian calendar adopted by Japan (1873), St. Kilda (in the Outer Hebrides,
1912), China (1912), Turkey (1916), Russia (1917), Yugoslavia and
Roumania (1919), Greece (1923). The Greek and Russian Orthodox
churches have still not adopted it and are now 13 days behind. I believe
some countries have not yet adopted it!! Since Russia adopted it after
the Revolution, it turns out that the October Revolution was actually in
November!
Time signals become internationally coordinated.
Atomic clocks replace astronomical observations as the basis of time-keeping
and the earth is found to be running a bit slow, leading to the occasional
introduction of 'leap-seconds' at the end of the year – currently one or
two per year. 1995 had one leap second.
Vietnam adopts Gregorian calendar.