Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 341
rchimedes, and it issaid that he requested them to be engraved on his tomb. For another example, we require the volume generated by the revo-lution of a cycloid on its base. The differential of any revoloid is jty^dx. For the cycloid we have dx=—J^ ^ (Art. 48.) J2ry—y^ Whence J ^y-dx=J-^£M=.^=^… … These integrals require no con-stant, for when we make 2/=0 thevolume will be 0, as it ought to be. If we make y=2r, the corres-ponding volume will be half thevolume sought, and (4) will be-come rt. fhis value put in (3) will give ■Tir. And this substituted in (2) will give r y^dy ^^nr^ J^iry—y^…
Geometry, Analytic · Calculus
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
![An illustration from Libro primo [-quinto] d'architettvra ... (1566)](https://img.insideoutlibrary.com/img/200/ia-libroprimoquinto00serl-14-29.webp)
