eudoxus cnidus bc eric weisstein world scientific biography branch science astronomers branch science mathematicians branch science philosophers nationality greek eudoxus cnidus bc greek philosopher astronomer mathematician accept plato notion rotation planet earth crystalline sphere notice discrepancy observation try adjust plato model postulate crystalline sphere pole set sphere model contain mechanical explanation simply mathematical description problem model hippopede produce superposition motion sphere produce curve retrogression planet observe exhibit differ shape secondly model predict tolerable retrogression jupiter saturn mars venus thirdly model way account observed difference length season finally model fail account variation observed diameter moon change brightness planet correctly interpret indicate distance change eudoxus greek map star eudoxus excel mathematician work ratio form basis book v euclid elements anticipate number way notion algebra absent ancient greek mathematic eudoxus construct geometric proof develop method exhaustion later extend archimede archimede plato additional biography mactutor andrews bonn greek roman science technology bell modern mind ancient bodies zeno eudoxus archimedes ch men mathematics life achievements great mathematicians zeno poincaré new york simon schuster pp eric weisstein