17th Century Mathematics (John Napier, Marin Mersenne, Rene Descartes, Pierre de Fermat, & Blaise Pascal)

1. 17th Century Mathematics
Prepared by:
Geraldine S. Cachero
BSED 3-2

2. John Napier
1550 – 1617
Scottish
• Born in Merchiston Castle,
Edinburgh
• Invented the first system of
logarithms, described in his book
“Mirifici Logarithmorum Canonis
Descriptio” (1614).

3. John Napier
• Improved the decimal notation
and was the first who used and
popularized the decimal point
to separate the whole number
part from the fractional part of
a number

5. John Napier
• Invented the “Napier’s Bones”
~A form of rod by which two numbers can
be multiplied in a mechanical way.

6. Napier’s Bones

7. Napier’s Bones

8. John Napier
• “A Plaine Discovery of the Whole Revelation
of St. John” (1593)
- strongly anti-papal reading
- applied the Sibylline Oracles

10. Father Marin Mersenne
1588 – 1648
French
• Held the earliest-noted
instance of a regular gathering
of mathematicians
• Discovered the Mersenne primes
• Jesuit-educated and a friar of
the Order of Minims

11. René Descartes
1596 – 1650
French
• Born in La Haye en Touraine,
Kingdom of France
• Father of Modern Philosophy
• Published “Discours de la
méthode” (“Discourse on
Method”, 1937), contained
three appendices: La
dioptrique, Les météories,
and La géométrie

12. Descartes: La Géométrie
• Described the Cartesian system
and introduced what has become
known as the standard algebraic
notation
• Invention of the superscript
notation for showing powers or
exponents
• Founded Analytical Geometry or
Cartesian Geometry

13. Cartesian Coordinate System

14. Cartesian Coordinate System

15. Cartesian Coordinate System

16. Cartesian Coordinate System

17. Cartesian Coordinate System

18. Descartes: Discours de la Méthode
• Showed how to use
developments in algebra
since the Renaissance to
investigate the geometry
of curves. Descartes
maintained that an
acceptable curve is one
that can be expressed by
a unique algebraic
equation in x and y.

19. René Descartes
I think,
therefore
I am.

20. Pierre de Fermat
1601 – 1665
French
• Father of modern theory
• Born in Beaumont-de-Lomagne
• Was inspired by Diophantus’
“Arithmetica”

21. Pierre de Fermat
• Little Theorem• Two-Square Theorem
“If p is a prime, then
is divisible by p for any
integer a.”

22. Fermat’s Famous Last Theorem
n > 2

23. Blaise Pascal
1623 – 1662
French
• Born in Clermont-Ferrand
• Formulated one of the basic
theorems in geometry,
known as “Pascal’s Mystic
Hexagon Theorem” described
on his “Essai pour les
coniques” (1639).

24. Pascal’s Mystic Hexagon Theorem

25. Pascal: Pascaline
• In 1642, he invented the first functional
mechanical calculating machine, known as
“Pascaline”, able to perform additions and
subtractions.

26. Pascal’s Triangle
• A convenient tabular
presentation of
binomial coefficient,
where each number
is the sum of the two
numbers directly
above

27. Pascal’s Triangle

28. Pascal: Mathematical Theory of
Probability
• This was the idea of equally probable
outcomes, that the probability of something
occurring could be computed by enumerating
the number of equally likely ways it would
occur, and dividing this by the total number of
possible outcomes of the given situation. This
allowed the use of fractions and ratios in the
calculation of the likelihood of events, and the
operation of multiplication and addition on
these fractional probabilities.

29. Thank You!