An Elementary Treatise On the Differential Calculus, With Applications And Numerous Examples;
The book An Elementary Treatise On the Differential Calculus, With Applications And Numerous Examples; was written by author Joseph F Edwards Here you can read free online of An Elementary Treatise On the Differential Calculus, With Applications And Numerous Examples; book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is An Elementary Treatise On the Differential Calculus, With Applications And Numerous Examples; a good or bad book?
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4. Show that the inverse of a conic with regard to the focus is a Lima- 5on (Equation r=a + 6 cos ff), which becomes a cardioide if the conic be a parabola. 5. Show that the Equation of the inverse of a conic with regard to the centre is of the form r^=A+B coa29, which becomes a Lemniscate of Bernoulli if the conic be a rectangular hyperbola. 174 CHAPTER Vn. 229. Tangents to Curve and Inverse inclined to Radius Tector at Supplementary Angles If P, P' be two contiguous points on a curve, and Q, ...Q' the inverse points, then, since OP . OQ=OP' . OQ', the points P, P', ■Q', Q are coney clic ; and since the angles OPT and OQT are therefore supplementary, it follows that in the limit when P' Fig. 29. ultimately coincides with P and Q' with Q, the tangents at P and Q make supplementary angles with OPQ. The ultimate ratio of corresponding elementary arcs, viz., OP OP . OQ k^y "OQ ds_^PP'_jOP ds'—^^QQ'~-^^OQ'" OQ^ r'2 fc2 230. It follows from the preceding article that when two curves intersect, their inverses intersect at the same angle ; and as particular cases, if two curves touch, their inverses touch, and if the original curves cut orthogonally their inverses cut orthogonally.
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