252 Mathematical Elements Book IV.

Radius, the Quantity found is to be added ; thatis, increases the Gravity, which obtains everywhere between the Quadrature, and 35 Deg. l6Min. from it.

1308 These Forces , whatever is the Figure of the Moon’sOrbit , are exacts determin’d ; for they are com-pared with the Addition of Gravity in the Qua-dratures, supposing the Moon in the Quadratureto be at the same distance from the Earth, atwhich it really is in the Place which is considers;

*1291 but this Addition is difcover’d in every Cafe*.

1289 Tho’ it be foreign to the Purpose of this Worky to give a Computation of the Moon’s Motion,I thought it necessary to explain in a few Wordswhat is the Method whereby to discover the For-ces that govern the Moon ; because the moreexactly we know the Forces, the more easilyshall conceive their general Effect.

Now to examine the Moon’s Motion, we mustsingly consider its several Irregularities ; whichto do without Confusion, we must remove severalIrregularities, and conceive the Moon as movingin a Circle about the Earth, in which Curve it j s

* 241 plain that it can be retain’d by Gravity* J this

1308 Motion is disturb’d by the Action of the Sun,

1309 and the Orbit is more convex in the Quadratures thfttin the Syzygies. The Convexity of a Curve, whicha Body describes by a central Force, is so muchthe greater,as the central Force does more strong-ly every iMoment turn the Body out of the way »it is also the greater the more slowly the Bodymoves, because the central Force acting the Jong-er , has a greater Effect in inflecting the way°*the Body. From contrary Causes the Convexityof the Curve is diminifh’d ; both concur in increa-

*1303 st n § Convexity of the Orbit in the Quadra-

*1304 tures*, and diminishing it in the Syzygies*.

prom