2$o Mathematical Elements Book IV*

an equal Force towards the Syzygy /, with thatwith which at F it is impell’d towards the Syzy-gy L.

1303 Hence it follows, that in the Motion of the Moonfrom the Syzygy to the Quadrature, between L andB, as also between / and A, the Gravity of the Moontowards the Earth is continually increas'd, and the

1304 Moon is continually retarded in its Motion ; but itithe Motion from the Quadrature to the Syzygy, be-tween B and /, as also between A and L, everyMoment the Moon’s Gravity is diminijh’d, and H sMotion in its Orbit is accelerated.

You may determine the Forces upon whichthese Effects depend, by comparing them with theknown Force whereby Gravity is increas’d in the

*1291 Quadratures*, and which is represented by theMoon’s distance from the Center of the Earth.

1305 The Lijies MI, H F, S T, are equal by Con-struction ; therefore when the Points I and N ateconfounded, M N is equal to S T, and M S > sequal toNT; the Lines M F and S T representthe Forces whereby the Moon at F and the Earthat T are carried towards the Sun S, thereforethey are as the Square of the Line TS to the

*1208 Square of the Line F S* ; wherefore as F G lSthe difference qf thpfe Lines, F M and T S diner

*1293 from one another double the Line G F*, and ad-ding GF to the Line F M, the difference be-tween G M and T S, that is, M S will be triplethe Line F G ; and therefore this is also theQuantity of the Line N T ; now as F E is double

*1300 F G*, therefore N T will be to F E as Threeto Two.

Let F T be continu’d, if need be, and fr offlE draw EV perpendicular to it, the Triangle?E V F and N QT, which are rectangular, v/ ‘be similar, by reason of the alternate AngE s

*1300 YFE and QT N* j therefore NT is to FE,

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