118 Sir Isaac Newto n’s Book I.

a. These powers or forces are by Sir I s a a c Newtoncalled centripetal; and their first effect is to cause the body, onwhich they act, to quit the straight course, wherein it wouldproceed if undisturbed, and to describe an incurvated line,which shall always be bent towards the center of the force.It is not necessary, that such a power should cause the bodyto approach that center. The body may continue to recedefrom the center of the power, notwithstanding its being drawnby the power; but this property must always belong to itsmotion, that the line, in which it moves, will continually beconcave towards the center, to which the power is directed.Suppose A (in fig. 71.) to be the center of a force. Let abody in B be moving in the direction of the straight line B C,in which line it would continue to move, if undisturbed; butbeing attracted by the centripetal force towards A, the bodymust necessarily depart from this line B C, and being drawninto the curve line B D, must pass between the lines A B andB C. It is evident therefore, that the body in B being gra-dually turned off from the straight line B C, it will at first beconvex toward the line BC, and consequently concave to-wards the point A: for these centripetal powers are supposedto be in strength proportional to the power of gravity, and,like that, not to be able after the manner of an impulse to turnthe body sensibly out of its course into a different one in an in-stant, but to take up some space of time in producing a visi-ble effect. That the curve will always continue to have itsconcavity towards A may thus appear. In the line B C nearto B take any point as E, from which the line E F G may be so

drawn