Book IV. of Natural Philosophy.

that is, 3 is to 2 as N equal to F P, is toE V, which therefore is proportional to 2 thirdParts of the Force which is exprefs’d by F P •,but EV is the Sine of the Angle ET V at theCenter, which is double the Angle EF V at theCircumference, equal to the Angle FTL, whichis the distance of thp Moon frpm the Syzygy ;therefore a$ the Radius T A Pr T E is to a Sine 1 306and an half of double the distance of the Moon fromthe Syzygy, namely , F P, so the Addition of Gravityin the Quadratures (which is exprefs’d by the Ra-dius T A) is to the Force which accelerates or retardsthe Moon in its Orbit.

The Computation of this Diminution of GraTvity, and of its Increase at a less distance fromthe Quadratures, is dedgc’d from the fame Prin-ciples,

This Diminution is represented by the LineF Q, which is equal to QJT, minus the Radius ;but from the Consideration of the Triangles a-bove-mention’d, VF taken once and an half isequal to QT ; therefore V T and an half, withhalf the Radius added to it, expresses the requir’dDiminution of Gravity ; and the Radius is to the 1307Sum or Difference of once and a half the Co-fine ofdouble the difiance of the Moon from the Syzygy andhalf the Radius ; as the Addition of Gravity in theQuadratures, to the Diminution or Increase of Gravi-ty in that Situation of the Moon, concerning which theComputation is made.

We make use of the difference of the Go-sinefrom half the Radius, when the Angle, whose theCo-sine is, is greater than a right Angle, becausein that Cafe we make use of the Co-sine of theComplement of the Angle to two right Angles;when in this fame Cafe the Co-sine and a half,

\vhich we make use of, is greater than half the

Radius,