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2.1 |
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3.1 |
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Next time: More on Greek mathematics and the distinction between geometry and arithmetic- measurement without numbers!
- Video: The Emergence of Greek mathematics [Euclid from BBC Uppen University] VIDEO3173 (26 min.)
- After the video: Euclid's proof of the pythagorean theorem (on-line) Proposition 47 . Note the key aspects of the argument related to statements that triangles with equal bases between the same parallel lines would be equal. This follows from Proposition 35.
Next time: More on Euclid. Why did the work avoid measurements and numbers? What is the theory of proportions? How was it used? Areas and proportions.
On
the Equilibrium of Planes 6-7: weights balance in inverse proportion to
the distances from the fulcrum.
Method
Prop 1: Finding the area of a parabolic section by balancing.
Method Prop 2: More balacing to compare
the volumes of a sphere, circumscribed cylinder, and inscribed cone (with a
great circle of the sphere as base)
Compare with Euclid:bookXII/propXII10.html and Archimedes On the Sphere and Cylinder.
On Conoids and Spheroids 1: a basic proportion theorem