Prop. iii. Every body that, by a radius drawn to another body, howsoever moved, describes areas about that centre proportional to the times is urged by a force compounded out of the centripetal force tending to that other body and of all the accelerative force by which that other body is impelled. [3] If the periodic times are in the sesquiplicate ratio of the radii, and therefore the velocities reciprocally in the subduplicate ratio of the radii, the centripetal forces will be in the duplicate ratio of the radii inversely; and the converse. [4] _i.e._, showing convexity when in such a position as that, to an observer on the earth, a line drawn between it and the sun would subtend an angle of _90_ deg. or thereabouts. TRANSCRIBER NOTE: Variant spelling and punctuation have been preserved.