The Bequest of the Greeks

2-square achievements algebra Almagest altitude ancient angle Archimedes arithmetic called century chapter chord classical geometry conjecture construction continued fraction convergents cube curve determine divisor Egyptian Elements equal equation Euclid Euclid's Elements Euclidean algorithm exist fact Fermat Fibonacci Figure follows formula golden section golden-section greatest common divisor Greece Greek mathematics hence Hero Hipparchus Hippias Hippocratean Hippocrates historians hypotenuse infinite inscribed integers irrational Kepler lemma mathe mathematics maticians matics matter means methods Miletus modern nonquadrable number theory occult odd integer Pappus period plane polygon positive integers primitive triple problem proof proposition pseudomath Ptolemy pyramid Pythagoras Pythagorean theorem Pythagorean triples quadratic quadratrix question radius rational number rational triangle reason rectangle rectilinear relation relatively prime right triangle segment sides solid solution solved spectrum squaring the circle straightedge and compass symbols Thales tion transcendental trisection ΙΟ