Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/223

 was decribed, or equal to what is called the mean motion; and an angle V, the firt equation of the mean motion to the angle Y, the greatet firt eqation, as the line of double the angle T is to the radius; and an angle X, the econd equation, to the angle Z, the econd greatet equation, as the cube of the ine of the angle T is to the cube of the radius. Then take the angle BHP the mean motion equated equal to T + X + V the um of the angles T, V, X, if the angle T is les than a right angle; or equal to T + X - V the difference of the ame, if that angle T is greater than one and les than two right angles; and if HP meets the ellipis in P, draw SP, and it will cut off the area BSP nearly proportional to the time.

This practice eems to be expeditious enough, becaue the angles V and X, taken in econd minutes if you pleae, being very mall, it will be ufficient to find two or three of their firt figures. But it is likewie ufficiently accurate to anwer to the theory of the planets motions. For even in the orbit of Mars, where the greatet equation of the centre amounts to ten degrees, the error will carcely exceed one econd. But when the angle of the mean motion equated BHP is found, the angle of the true motion BSP, and the ditance SP are readily had by the known methods.

And o far concerning the motion of bodies in curve lines. But it may acend come to pas that a moving body hall acend or decend in a right line; and I hall now go on to explain what belongs to uch kind of motions.