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Archimedes: Engineer and Mathematician

Archimedes: Engineer and Mathematician. Levers: “Move the World” Buoyancy and density Optics. Aristotle: “The Philosopher” (384 – 322 B.C.). Matter on earth made of Empedocles’ elements: Sublunary (below the moon) Matter in the Heavens made of the fifth element: Quintessence

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Archimedes: Engineer and Mathematician

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  1. Archimedes: Engineer and Mathematician Levers: “Move the World” Buoyancy and density Optics

  2. Aristotle: “The Philosopher” (384 – 322 B.C.) Matter on earth made of Empedocles’ elements: Sublunary (below the moon) Matter in the Heavens made of the fifth element: Quintessence All objects on earth made of mixtures of the elements

  3. How do objects move? Anthropomorphic approach Things go where they “want” to go Example: Heavy things, lots of earth, move down faster than light things, with air or fire Gaia hypothesis

  4. Aristotle’s Forces For the most part, see last slide (anthropomorphic): natural motion Violent motion: making something go where it doesn’t want to go Ultimately natural motion wins out

  5. And what is natural motion? For sublunary objects, the natural motion is to move in a straight line until stopped. Motive force keeps natural motion from immediately taking over Nature abhors a vacuum For heavenly bodies, natural motion is perfect circular motion

  6. What about those heavenly bodies? All heavenly bodies are perfect spheres, the perfect shape They move on concentric spheres, centered on the Earth: Geocentric theory Need lots of spheres (56) to get it right

  7. Aristotle: Philosophy or Science? All of his ideas based on reason: no experiments All together a “reasonable” world view based on limited observations Authoritative

  8. Eratosthenes and Aristarchus Note Archimedes though Earth was round. Circumference measured by Eratosthenes in 3rd century B.C. Aristarchus postulated a sun–centered, Heliocentric system

  9. Why did we need all those spheres in slide 6? Retrograde motion Ptolemy (85 – 165 A.D.) Deferents, epicycles, and subepicycles (like a spirograph) 76 curves necessary

  10. Problems, as always Should all things really fall at the same rate? Ockham’s Razor (1300) Too many spheres (curves)? Motive Force?

  11. Starting to solve those problems. Middle ages (Dark ages) most of ancient learning is lost 13th century – Universities Leonardo daVinci and the Renaissance Late 1400’s, “lost” knowledge rediscovered.

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