Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 250
rithmic spiral. From this definition we have at once t=\og.r, f<yr the equation of the logarithmic spiral, in which r representsthe radius vector, and i the measuring arc. (Art. 44.) We can now deduce some of the properties of thespirals by the application of the differentialexpressions for the… … 242 DIFFERENTIAL CALCULUS. In (Chap. V,) we found Sub-tangent AT= , and because r=afy we have dr Or dr=naf~*di.dt_ 1dTnaf-^ r^dt CL^t^^ dt^^ Whence = .= , the sub-tangent, and when dr nat^^ n »=1, as it is in Archimedes* spiral, the value of the sub-tangentis ai^. But in that spiral T=^at, and a=—…
Geometry, Analytic · Calculus
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