76 NEWTON S PRINCIPIA. 



of the planet is B; the perihelion A; the arch BP, or 

 angle BSP is the true anomaly; BO being to the whole 

 circumference as the time in B P to the whole periodic 

 time, BO, or O S B, is the mean anomaly, and Q B, or 

 Q C B, is the eccentric anomaly, C being the centre of the 

 ellipse : A and B are likewise called the apsides (or apses), 



and AB, the transverse axis, is called the line of the ap- 



o r^ 



sides ; S C, or more generally -r-p i g the eccentricity. 



(2.) The next subject of inquiry is the comparison of 

 ; bodies moving in a straight line towards the centre of 

 forces, with those moving by the same centripetal force in 

 the conic sections whose axis is that straight line. If the 

 projectile force by which a body revolves in any of those 

 curves round the focus as a centre, suddenly ceases, and 

 the body falls towards the centre of the curve, it is shown 

 that its place at any given time, will be the point at which 

 the line of descent is cut by a perpendicular from the 

 point of the curve where the radius from the vertex makes 

 its area proportional to the time consumed in the fall. 

 For take the parabola whose area is f sc y, and let the 

 distance of the point where the body begins to descend in 

 a straight line be C ; the parabolic sectors, which are as the 



fx + 3 C\ / 

 times, are expressed by y x ( ~ ) f = f x y + 



(C x) ~ ) or ^ x (x + 3 C) ; and if another parabola 



