17th Century MathematicsPrepared by:Geraldine S. CacheroBSED 3-2

John Napier1550 – 1617Scottish• Born in Merchiston Castle, Edinburgh

• Invented the first system of logarithms, described in his book “Mirifici Logarithmorum Canonis Descriptio” (1614).

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

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

Napier’s Bones

Napier’s Bones

John Napier • “A Plaine Discovery of the Whole Revelation of St. John” (1593)

- strongly anti-papal reading - applied the Sibylline Oracles

According to Napier:The WORLD will END on…

1688 or 1700

Father Marin Mersenne1588 – 1648French

• 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

René Descartes1596 – 1650French• 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

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

Cartesian Coordinate System

Cartesian Coordinate System

Cartesian Coordinate System

Cartesian Coordinate System

Cartesian Coordinate System

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.

René DescartesI think, therefore I am.

Pierre de Fermat1601 – 1665French

• Father of modern theory• Born in Beaumont-de-Lomagne

• Was inspired by Diophantus’ “Arithmetica”

Pierre de Fermat• Little Theorem• Two-Square Theorem“If p is a prime, then

is divisible by p for any integer a.”

Fermat’s Famous Last Theorem“It is impossible to write a cube as a sum of two cubes, a fourth power as a sum of two fourth powers, and, in general, any power beyond the second as a sum of two similar powers. For this, I have discovered a truly wonderful proof, but the margin is too small to contain it.”

n > 2

Blaise Pascal1623 – 1662French• 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).

Pascal’s Mystic Hexagon Theorem

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

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

Pascal’s Triangle

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.

Thank You!