Early Modern Period (Renaissance)
(1450 A.D. – 1700 A.D.)
A. Trigonometry and Logarithms
• Publication of precise trigonometry tables, improvement of
surveying methods using trigonometry, and mathematical
analysis of trigonometric relationships. (approx. 1530 – 1600)
• Logarithms introduced by Napier in 1614 as a calculation aid.
This advances science in a manner similar to the introduction of
the computer.
B. Symbolic Algebra and Analytic Geometry
• Development of symbolic algebra, principally by the French
mathematicians Viete and Descartes
• The Cartesian coordinate system and analytic geometry developed by Rene Descartes and Pierre Fermat (1630-1640).
C. Creation of the Calculus
• Calculus co-invented by Isaac Newton and Gottfried Leibniz.
Major ideas of the calculus expanded and refined by others,
especially the Bernoulli family and Leonhard Euler. (approx.
1660 – 1750).
• A powerful tool to solve scientific and engineering problems, it
opened the door to a scientific and mathematical revolution.
The Renaissance (reborn") was a cultural movement that spanned the
period roughly from the 14th to the 17th century, beginning in Italy in the
Late Middle Ages and later spreading to the rest of Europe.
The changes of the Renaissance were not uniformly experienced across
Europe .
Although the Renaissance saw revolutions in many intellectual
pursuits, as well as social and political upheaval, it is perhaps
best known for its artistic developments and the contributions of
such polymaths as Leonardo da Vinci and Michelangelo, who
inspired the term "Renaissance man".
A New World View
A new "world view" was created - the way one looked at and
answered basic questions:
What are humans?
What is the purpose of life?
Why am I here?
Italy was the birthplace of the Renaissance for many
reasons. First of all, since Italy was the center of
ancient Roman history, it was natural for the
Renaissance to start there.
Some things such as architectural remains, antique
statues, coins and inscriptions reminded Italians of
the glory of the Roman Empire.
Secondly, Italy was different from the rest of Europe
in another way. Italian cities had survived the Middle
Ages and cities like Florence, Milan, Venice, and
Genoa all grew into wealthy, prosperous cities of
manufacturing and trade. Rome and Naples also
contributed to the Renaissance cultural recovery.
Wealthy Italian merchants encouraged the cultural
rebirth by applying political and economic leadership.
They also had great attitudes that helped shape the
Italian Renaissance.
These merchants suggested education and individual
achievements and they spent quite a bit of money on
the arts.
A New Conception of the World
Skepticism (Şüphecilik). Humans began to have a
questioning attitude and challenged tradition and
authority.
Secularism (Laiklik). They believed life on earth
was more important than the afterlife. There was
greater emphasis on this life and less on the afterlife
and on God - the world is to be enjoyed.
During the early Renaissance, Florence was a very
important city. It came to symbolize the Italian
Renaissance.
Florence was very much like ancient Athens because
it produced a great number of talented poets, artists,
architects, scholars, and scientists in a short period
of time.
Humanism was an intellectual movement that was at
the heart of the Italian Renaissance. It put an
emphasis on man, his intellect, and his life on earth.
It also stated that the Church shouldn't rule certain
matters and it rediscovered ancient items, thoughts,
and beliefs. Humanist scholars hoped to use their
wisdom to increase their understanding of their own
times.
Galileo Galilei
(1564-1642)
Galileo was born in Pisa, Italy on
February 15, 1564.
His father, was a musician.
Galileo was the first of six
(though some people believe
seven) children.
His family belonged to the
nobility (asalet) but was not
rich. In the early 1570's, he and
his family moved to Florence.
In 1581, Galileo began studying
at the University of Pisa .
At the University of Pisa, Galileo learned the physics
of the Ancient Greek scientist, Aristotle. However,
Galileo questioned the Aristotelian approach to
physics. Aristotelians believed that heavier objects
fall faster through a medium than lighter ones.
Galileo eventually disproved this idea by asserting
that all objects, regardless of their density, fall at the
same rate in a vacuum. To determine this, Galileo
performed various experiments in which he dropped
objects from a certain height. In one of his early
experiments, he rolled balls down gently sloping
inclined plane and then determined their positions
after equal time intervals. He wrote down his
discoveries about motion in his book, De Motu, which
means "On Motion."
In 1592, Galileo was appointed professor of
mathematics at the University of Padua. While
teaching there, he frequently visited a place called
the Arsenal, where Venetian ships were docked and
loaded. During his visits to the Arsenal, he became
fascinated by nautical technologies, such as the
sector and shipbuilding.
A year later, he patented a model for a pump. His
pump was a device that raised water by using only
one horse.
Galileo's belief in the Copernican System (Güneş
merkezli evren) eventually got him into trouble with
the Catholic Church (dünya merkezli evren).
A committee of consultants declared to the
Inquisition (soruşturma) that the Copernican
proposition that the Sun is the center of the universe
was a heresy (sapkınlık). Because Galileo supported
the Copernican system, he was warned that he
should not defend Copernican theories. In 1633,
Galileo was found guilty of heresy for his Dialogue,
and was sent to his home near Florence where he
was to be under house arrest for the remainder of his
life. In 1638, the Inquisition allowed Galileo to move
to his home in Florence, so that he could be closer to
his doctors.
By that time he was totally blind. In 1642, Galileo
died at his home outside Florence.
SEE VIDEO 1
John Napier
1550-1617
In his Mirifici Logarithmorum
Canonis descriptio (1614) (A
Description of the Wonderful
Canon of Logarithms) the
Scottish John Napier introduced
the concept of logarithms as an
aid to calculation.
Napier’s Logarithms
Napier’s concept of a logarithm is
not the one used today. Soon after
Napier’s book was published the
English mathematician Henry
Briggs collaborated with him to
develop the modern base 10
logarithm.
Tables of this logarithm and
instructions for their use were
given in Briggs’ book
Arithmetica Logarithmica
(1624).
A page from this work is shown on
the left.
Henry Briggs and the Development of
Logarithms
Gottfried Leibniz
1646 - 1716
Leibniz and Newton independently
developed the calculus during the same
time period. Although Newton’s version
of the calculus led him to his great
discoveries, Leibniz’s concepts and his
style of notation form the basis of
modern calculus.
A diagram from Leibniz's
famous 1684 article in the
journal Acta eruditorum.
Leibniz’s Calculus
Newton: 1643 – 1727
Leibniz: 1646 - 1716
Newton and Leibniz