be the locus of the point K. Let that curve meet the plane of the circle in L. In PA take PH equal to PD, and erect the perpendicular HI meeting that curve in I; and the attraction of the corpuſcle P towards the circle will be as the area AHIL drawn into the altitude AP. Q. E. I.
For let there be taken in AE a very ſmall line Ee. Join Pe, and in PE, PA taka PC equal to Pe. And becauſe the force with which any point E of the annulus deſcribed about the centre A with the interval AE in the aforeſaid plane, attracts to it ſelf the body P, is ſuppoſed to be as FK; and therefore the force with which that point attracts the body P towards A is as and the force with which the whole annulus attracts the body P towards A, is as the annulus and conjunctly; and that annulus alſo is as the rectangle under the radius AE and the breadth Ee, and this rectangle (becauſe PE and AE, Ee and CE are proportional) is equal to the rectangle PE x CE or PE x Ff; the force with which that annulus attracts the body P towards A, will be as Pe x Ff and conjunctly; that is as the content under Ff x FK x AP, or as the area FKkf drawn into AP. And therefore the ſum of the forces with which all the annuli, in the circle deſcribed about the centre A with the interval AD, attract the body P towards A, is as the whole area AHIKL drawn into AP. Q. E. D.
