BOOK III.] OF NATURAL PHILOSOPHY. 43o in N as 360AT2 to 39,6355 AZ 2 ; that is, as 9,OS27646AT2 to AZ'. Wherefore if we suppose the circumference NA/* of the whole circle to he divided into little equal parts, such as Aa, the time in which the sun would describe the little arc Aa, if the circle was quiescent, will be to the time of which it would describe the same arc, supposing the circle together with the nodes to be revolved about the centre T, reciprocally as 9,0827646 AT2 to 9,082764 6 AT'2 + AZ2; for the time is reciprocally as the velocity with which the little arc is described, and this velocity is the sum of the velocities of both sun and node. If, therefore, the sector NTA represent the time in which the sun by itself, without the motion of the node, would describe the arc NA, and the indefinitely small part ATa of the sector represent the little moment of the time in which it would describe the least arc Aa ; and (letting fall a Y perpendicular upon N//) if in AZ we take c/Z of such length that the rectangle of dZ into ZY may be to the least part AT« of the sector as AZ2 to 9,OS27646AT2 -f AZ2, that is to say, that dZ may be to