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

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46] A longer ſemi-axis CA, in the fubdupliezte proportion of the longer axis to the ſum of the -two axes 5 as may be eaſily proved. WHAT has been ſaid, may be enough to ſhew the form of the equant, and the manner of' the motion about the upper focus in general. But the preciſe determination of the inequality of the nrotiori, requires the knowledge of the quadrature of the ſeveral ſectors of the equant, or at leaſt, if any other method be taken, of that which is equivalent to lilch a quadrature. There are divers methods for ſhewing the relation between the mean and true motion of a planet round the Sun, or round the other focus, ſome more exact than others. But the following ſeems the molt proper for exhibiting in one view, all the several hypotheses, and rules, which are in common uſein 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 preciſe determination of the motion, according to the true law of an equal deſcription of areas about the Sun. UPON the center F deſcribe the el# lipfis LN I, equal and ſimilar to the clliptic orbit /1 SD iP; but having its axes FN