Elements of analytical geometry and the differential and integral calculus (1856)
Robinson, Horatio N. (Horatio Nelson), 1806-1867 · Cincinnati : J. Ernst · leaf 227
and x y\ the co-ordinate of the par-ticular point touching the ellipse. Thus we may find the equations for the tangent lines to allknown curves. Examples like this serve toimpress upon the minds of learn-ers the connection between thisanalysis and analytical geometry. (Art. .31.) We shall now… … THEORY OF CURVES. 219 Put PF^K and FP=2k. Then ^^=/(-+/0=y+(|>+^^^^^ And PM=^f{x+^h)= y+^|^2A+^g)J^+ <fec. Whence PM--y=OM=(il\h+(^l1\]!l.+ ^q. (1) \dx/ \dx^/l,2 And PM—y=J}^M=ffl)2h+f—^Y-^+ &c. (2) \dx/ \dx^/l.2 Because MN=2M0, NS=20M\ That is, NS=2 OJf=-^2^+^!^-^+ &c. (3)c^a; ^dx^…
Geometry, Analytic · Calculus
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