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

Sect. III fine of the aforeaid inclination to the radius; and $AZ x TZ⁄1⁄2AT$ to 4 AT, as the ine of double the angle ATn to four times the radius) as the ine of the ame inclination multiply'd into the ine of double the ditance of the nodes from the Sun, to four times the quare 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 ''' . 35$iv$, as IT x AZ x TG x $Pp⁄PG$ to AT$3$, that is, as $IT x TG⁄1⁄2AT$ x $Pp⁄PG$, to 2AT, that is, as the ine of double the ditance of the Moon from the quadratures multiply'd into $Pp⁄PG$ to twice the radius: the um of all the horary variations during the time that the Moon, in this ituation of the nodes, paes from the quadrature to the yzygy (that is in the pace of $177 1⁄6$ hours) will be to the um of as many angles 33". 10 ''' . 33$iv$, or 5878", as the um of all the ines of double the ditance of the Moon from the quadratures multiply'd into $Pp⁄PG$, to the um 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 um of all the horary variations in the foreaid time, 163". or 2'. 43".