The Birth of Mathematics in the Age of Plato

Academy analysis ancient angles anthyphairesis antiquity applied Archimedes Archytas Aristotle Aristoxenus arithmetic astronomy axioms axis calendar celestial century chapter circle Cnidus commensurable constellations construction cube curves Cyzicus definition demonstration described ecliptic Elem Elements epimore Epinomis equal equation equimultiples Euclid Euclid's Elements Eudemus Eudoxus Eudoxus of Cnidus fact fifth figures fixed stars fourth fraction geometry golden section greater Greek harmony Hippocrates of Chios ideas incommensurable intervals irrational later latitude lemma length less magnitudes mathe mathematicians maticians mean medial Menaechmus method modern movements multiple numbers observation Octaeteris perfect number Phaenomena Philip of Opus Philolaus philosopher planet Plato poles polygon principles problem proof Prop proved pupils pyramid Pythagorean quoted ratio reality rectangle relations rotation segments solids solution Speusippus square numbers straight line Theaetetus theorems theory of proportion Theudius things third sphere Timaeus tion treatise triangles truth unequal universe Xenocrates zodiac