the works of archimedes

Apollonius appears applied approximation Archimedes axis base called centre of gravity circle circumscribed complete cone conics conoid construction contained cylinder described diameter difference distance divided draw drawn ellipse equal equation Euclid expressed fact figure fluid follows fractions geometrical given gives greater Greek height Hence hyperbola inscribed Join latter lemma length less magnitude manner means Measurement meet method obtain original Pappus parabola paraboloid parallel particular passing perpendicular placed plane polygon portion position possible problem produced proof Prop proportional proposition proved pyramid radius ratio rectangle referred remaining represented respectively result right angles root says sector segment side similar Similarly solid solution solved sphere spheroid spiral square straight line Suppose surface tangent term touch triangle vertex volume whence τὸ τοῦ τῶν