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  1. Presentation 2 August 23, 2012

  2. Galileo Galilei (1564-1642) Associated with:Birth of modern science

  3. Ostilio Ricci, Puple of Tartaglia, lecturing on Euclid Geometry • Study of geometry • Studied the works of Archimedes • Lectured at the University of Pisa • A public demonstration at the Leaning Tower to show that bodies of the same material but different weights fall with equal speed.

  4. Question • Galileo dropped weights from the Leaning Tower of Pisa and concluded that objects of different weights still travel ( when dropped ) at the same speed • Did he use Inductive or deductive reasoning for this experiment?

  5. Telescope • From a Dutch spectacle-maker • To make distant objects appear close • Make one for himself • First to use it to look at sky and publish findings • Four satellites revolving about jupiter • Disproof earth is center of all astronomical motions • Aristotelian view • SidereusNuncius ( The Starry Messenger)

  6. SidereusNuncius (The Starry Messenger) • 29 page booklet • Existence of unknown stars • Nature of the Milky Way • Rugged surface of the moon • Dialogue • Conversation between 3 to discuss Copernicanism(for and against) • Church denounced him

  7. Nicolaus Copernicus • Modern Notation • Johann Widmann • First print of the plus and minus signs • Vander Hoecke • First to use in writing algebraic expressions • Robert Recorde • Introduced symbol = (denote equality) • Thomas Harriot • Multiplication with a Dot • > and < sign • William Oughtred • Used cross sign X • ChristoffRudolff • Square root sign 

  8. Robert RecordeThe Whetstone of Witte 1577 • A captain marshalls his army in a square formation. When the square is of one size, he has 284 men to many. But when he rearranges them in a square one man more on a side then before, he lacks 25 men. How many men does he have?

  9. Francois Vieta (1540-1603) • Frenchmen • Perfecting algebraic symbolism • Use letters of the alphabet as symbols for quantities (known and unknown) • Vowels for unknown quantities (Variables) • Consonants represent numbers assumed to be given. • A quadratus, A cubus, … different powers of quantitiy A. • ( all this changes with Descartes)

  10. Vieta solved the quadratic equation x2 + ax = b by substituting x = y – a/2. This produces a quadratic in y in which the first-degree term is missing. • Use Vieta’s method to solve the quadratic equation: x2 + 8x = 9

  11. Rene’ Descartes • To solve the equation x2 + ax = b2geometrically, Rene’ Descartes would have used the method as described • Draw a line segment AB of length b and at A erect a perpendicular AC of length a/c. With C as center, construct a circle at point D and E. Prove that the length of the segment BE is the value of x that satisfies x2 + ax = b2

  12. Johannes kepler (1571-1630) • German, sickly child • Michael Mastlin (Copernicus) • Preparing a yearly almanac (meteorological predictions) • Predictions came true in 1595 • 3 laws of planetary motion