Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/329

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Sect. III
of Natural Philoſophy
295

fine of the aforeſaid inclination to the radius; and AZ x TZ/1/2AT to 4 AT, as the ſine of double the angle ATn to four times the radius) as the ſine of the ſame inclination multiply'd into the ſine of double the diſtance of the nodes from the Sun, to four times the ſquare of the radius.

Colt. 4. Seeing the horary variation of the inclination, when the nodes are in the quadratures, is (by this prop.) to the angle 33". 10'''. 35iv, as IT x AZ x TG x Pp/PG to AT3, that is, as IT x TG/1/2AT x Pp/PG, to 2AT, that is, as the ſine of double the diſtance of the Moon from the quadratures multiply'd into Pp/PG to twice the radius: the ſum of all the horary variations during the time that the Moon, in this ſituation of the nodes, paſſes from the quadrature to the ſyzygy (that is in the ſpace of 177 1/6 hours) will be to the ſum of as many angles 33". 10'''. 33iv, or 5878", as the ſum of all the ſines of double the diſtance of the Moon from the quadratures multiply'd into Pp/PG, to the ſum of as many diameters; that is, as the diameter multiplied into Pp/PG to the circumference; that is, if the inclination be 5°. 1', as 7 x 874/10000 to 22 or as 278 to 10000. And therefore the Whole variation, compos'd out of the ſum of all the horary variations in the foreſaid time, 163". or 2'. 43".