Newton's Principia, sections I, II, III, with notes and illustrations. Also a collection of problems (1863)
Newton, Isaac, Sir, 1642-1727, Frost, Percival, 1817-1898 · Cambridge, London, Macmillan and Co · leaf 81
. If SY be the perpendicular on the tangent PY at P in acurve, Y will trace out a curve, and if YZ be a tangent to the locuso/Y, SZ perpendicular to it, SY2 = SP.SZ. Let P be a point near P, SY perpendicular on PP, SZperpendicular on Y Y. Since angles SYP, SYP are right angles, a semicircle onSP… … but, ultimately, as P moves up to P, PPY becomes the tangentat P, and FYZthat at Y to its locus, also 8Y=8Y; .-. SZ. 8P= 8Y*. V. 1. In the curve in which the abscissa varies as the cube ofthe ordiuate, shew that the sub tangent is three times the abscissa. 2. If PY SL tangent to an ellipse at P…
Mechanics · Celestial mechanics
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