Geometry played a key role in the scientific revolution according to the document. Figures like Galileo, Kepler and Descartes used geometry as a tool to understand and model nature. They viewed the natural world as behaving according to geometric rules and principles. Geometry allowed them to separate complex motions into simpler components and derive laws of mechanics. It became the paradigm for the new rational, mathematical physics of the 17th and 18th centuries.

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3. Galileo Kepler and Galileo Descrided geometry was the key to understanding nature. Galileo Strand of renaissance Achimedean pratical mathematicians epitemic ambition.

4. 16 th century Guidobaldo del’mante’s Liber Mechanicorum (1577) had pretty much completed a geometrical description of simple statics and the compounding of the 5 simple machines. Archimedean mechanical stydy was the problem of motion, of projectile motion. This is the sort of forced, artificial motion that Aristotle’s physics had left outside rigorous and certain science.

5. Last half of the 16 th century It seemed commonly agreed amongst a small sector of artillered, applied mathematicians and academics that there ought to be laws of projectile motion.

6. For Galileo Geometry was a tool. ( special tool, tool that allowed true and certain calculations.) Geometry, geometric analysis and geometric models allowed for the separation and unpacking of this complicated compouding into its unfelted ‘prefect’ component parts.

7. Descartes The third key figure in the scientific revolution . Showed something of an inheritance from that Archimedean mechanics as well as the Aristotelian answer to it.

8. He postulated that matter came in ultimate small corpuscles of various sizes that filled all space, and that all material phenomena were caused by nothing more than the compounded and complex motions of corpuscles. These corpuscles had no properties whatsoever except that they occupied space, and then when hit by something, moved off according to simple billiard-ball mechanics until it was hit by something else. With such an austere ontology, Descartes was able to derive linear inertia25 in about three lines of reasoning.

9. DUALIST ONTOLOGICAL POSITION Non-material Phenomena Like emotions or thoughts or other phenomena of the spirit. Which have no material qualities or effects whatsoever. An idea his no weight or volume, and cannot move a pencil.

10. 2. Material Phenomena Which are ultimately derived from nothing more than the motions of ultimate, inert material particles. They only obey the laws of a geometrical mechanics.

11. GEOMETRY AS SCIENCE Geometry play roles in the new physics of Kepler, Galileo and Descartes. The paradigmatic method of understanding nature was not just quantitative, but was through the use of geometry. Nature ultimately behaves in a geometrically describe way: * mechanics * projectile motion * laws of nature

12. The laws of nature are in some sense geometrical and can be demonstrated by geometry. Mechanics was exhibited as the paradigm science, but it had his status because it was paradigmatically geometrical. This is illustrated by Newton * in final section of the Principia * to sum up his grand model that synthesises a mathematic mechanics based on a notion of force

13. * celestial mechanics, based on a completely obscure force called universal gravity. So in effect- celestial dynamics can be derived from geometry alone.

14. The Enlightenment Geometrically demonstrated laws of mechinics to model the physical world. The nominal beginnings of a kind of physical- mathematical thinking that was to become the paradigm of the new physics of the Eighteenth century, called at the time Rational Mechanics. (Newton’s laws of gravity). The laws of physics could be demonstrated geometrically without ontological commitment.

15. A More Public Face Natural philosophy and its applications came out of the ivory towers and noblemen’s courts. A new status for a mathematical natural philosopher. Geometry was the finest way to train the mind, the most perfect training in reasoning and clear thinking.

16. Geometry was: The symbol of ordered and reasoned knowledge. A training in geometry was the surest buttress against any sliding backwards into superstition, ill founded beliefs about the world. The anti-rationalist occult natural philosophical heresies of the late renaissance.

17. The geometrical good governance of the universe. The infinitesimal calculus (geometry-of-the-infinite) was seen as the greatest triumph of the importance of the study of geometry. The teaching of this geometry of the infinite was the ultimate exercise of the limits of the mind’s capacity to reason and reason abstractly. Geometry has occupied any number of different social, intellectual, philosophical, and scientific positions over the ages.

18. THE END… Geometry is a role in our understanding of the world. The status of geometry is what we make it to be. It seems that one of the most fundamental of human scientific intuitions is that the physical world is ultimately geometrical. Study geometry is in some sense to uncover some kind of ultimate essence of the physical world.

19. Geometry sits in: social intellectual Instituitional context