The History of a Lemma from Archimedes to Newton

In this work, we identify some traces of the history Archimedes’ straight line, a lemma introduced by Archimedes within solution prop. II 4 On Sphere and Cylinder, in which it is asked to cut sphere with plane order obtain two spherical segments such that their ratio equal given ratio. course solving proposition method analysis, assuming what required, as specified method, path along one goes search final point, from required comes, expressed referred line or square problem. The Syracusan mathematician promised later give lemma, but he did not keep his promise. was taken up again Eutocius Ascalon towards end Hellenistic period, had considerable resonance among Arab mathematicians, who traced specific research around it, finally finding attention Latin tradition Newton first part analytic method.