Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/510

 46] A longer emi-axis CA, in the fubdupliezte proportion of the longer axis to the um of the -two axes 5 as may be eaily proved. WHAT has been aid, may be enough to hew the form of the equant, and the manner of' the motion about the upper focus in general. But the precie determination of the inequality of the nrotiori, requires the knowledge of the quadrature of the everal ectors of the equant, or at leat, if any other method be taken, of that which is equivalent to lilch a quadrature. There are divers methods for hewing the relation between the mean and true motion of a planet round the Sun, or round the other focus, ome more exact than others. But the following eems the molt proper for exhibiting in one view, all the several hypotheses, and rules, which are in common uein the modern Astronomy, whereby it may easily appear, how far they agree or differ from each other, and how much each of them errs from the precie determination of the motion, according to the true law of an equal decription of areas about the Sun. UPON the center F decribe the el# lipfis LN I, equal and imilar to the clliptic orbit /1 SD iP; but having its axes FN