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history-page20 - rests on fFteen postulates and six...

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Postulate 4 tacitly assumes congruence. Russell: That without further conditions a triangle can be moved without any alteration in its structure is “a tissue of non- sense”. Do “intersecting” arcs have a point in common? Russell: “The value of . . . [Euclid’s] work as a masterpiece of logic has been . . . exaggerated.” David Hilbert’s Grundlagen der Geometrie cleared things up. Euclidean geometry
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Unformatted text preview: rests on fFteen postulates and six primitive terms. • Others Successors • Archimedes ◦ Computed the area and volume of a sphere rigorously: unique in ancient world. ⋆ Proof for the area of a sphere ◦ Volume of circumscribed cylinder = volume of sphere + volume of a cone inscribed in the cylinder. ◦ How were the results stated? • Appolonius: Conics...
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