was deſcribed, or equal to what is called the mean motion; and an angle V, the firſt equation of the mean motion to the angle Y, the greateſt firſt eqation, as the line of double the angle T is to the radius; and an angle X, the ſecond equation, to the angle Z, the ſecond greateſt equation, as the cube of the ſine 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 ſum of the angles T, V, X, if the angle T is leſs than a right angle; or equal to T + X - V the difference of the ſame, if that angle T is greater than one and leſs than two right angles; and if HP meets the ellipſis in P, draw SP, and it will cut off the area BSP nearly proportional to the time.
This practice ſeems to be expeditious enough, becauſe the angles V and X, taken in ſecond minutes if you pleaſe, being very ſmall, it will be ſufficient to find two or three of their firſt figures. But it is likewiſe ſufficiently accurate to anſwer to the theory of the planets motions. For even in the orbit of Mars, where the greateſt equation of the centre amounts to ten degrees, the error will ſcarcely exceed one ſecond. But when the angle of the mean motion equated BHP is found, the angle of the true motion BSP, and the diſtance SP are readily had by the known methods.
And ſo far concerning the motion of bodies in curve lines. But it may aſcend come to paſs that a moving body ſhall aſcend or deſcend in a right line; and I ſhall now go on to explain what belongs to ſuch kind of motions.
