io8

Sir I s a a c Newto n’s Book I.

proportion, has been already explained \ Accordingly Imean here, that if the line M be taken to bear the lame pro-portion to EH, as EH bears to EF, HI will bear the fameproportion to F G, as M bears to EF; and if the line N bearsthe fame proportion to E K, as EX bears to EF, KL will bearthe fame proportion to F G, as N bears to EF; or if the lineO bear the fame proportion to EK, as EK bears to EH, KLwill bear the fame proportion to HI, as 0 bears to EH.

87 . This property is essential to the parabola, beingso connected with the nature of the figure, that every linepostesting this property is to be called by this name.

88 . Now suppose a body to be thrown from the point A(in fig. 6 9 .) towards B in the direction of the line A B. Thisbody, if left to it self, would move on with a uniform mo-tion through this line A B. Suppose the eye of a spectator tobe placed at the point C just under the point A ; and let usimagine the earth to be so put into motion along with thebody, as to carry the spectator’s eye along the fine C D parallelto AB; and that the eye should move on with the lame velo-city, wherewith the body would proceed in the line A B, ifit were to be lest to move without any disturbance from itsgravitation towards the earth. In this case if the body mov-ed on without being drawn towards the earth, it would ap-pear to the spectator to be at rest. But if the power of gra-vity exerted it self on the body, it would appear to the spe-

a Chap. 2. §r 17.

ctator