Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 330
(r^dr= = . If we assume (=^27t one revolution,this last expression for the area corres-ponding will be -, showing that the space PMA included in the first revo-lution from the pole is equal to one-third the area of the circle, whosei-adius is equal to the radius vector at the end of the… … 322 INTEGRAL CALCULUS. Again, if we take the logarithmic spiral whose equation ist=\og.r and apply it in (1), we shall have ^r^dC ^rdr ^^_\ri J ~2 *^ ~2 4If we estimate the area from the pole where r=0, which makes(7=0, and the whole area is —, that is, the area of the Naperian logarithmic spiral…
Geometry, Analytic · Calculus
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
![An illustration from Works. Popular edition.] 2 series (1886)](https://img.insideoutlibrary.com/img/200/bl-bl_003191336_9-307-1.webp)