Chap. 2. PHILOSOPHY.

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ctator to fall directly down. Suppose at the distance of time,wherein the body by its own progressive motion would havemoved from A to E, it should appear to the spectator tohave fallen through a length equal to EF : then the body atthe end os this time will actually have arrived at the point F.If in the space of time, wherein the body would have mov-ed by its progressive motion from A to G, it would have ap-peared to the spectator to have fallen down the Ipace G H:then the body at the end of this greater interval of timewill be arrived at the point H. Now if the line AFHI bethat, through which the body actually passes; from whathas here been said, it will follow, that this line is one of those,which I have been describing under the name of the parabo-la. For the distances EF, GH, through which the body isseen to fall, will increase in the duplicate proportion of thetimes a ; but the lines A E, A G will be proportional to thetimes wherein they would have been described by the singleprogressive motion of the body : therefore the lines EF, GHwill be in the duplicate proportion of the lines AF, AG; andthe line AFHI possesses the property of the parabola.

89. If the earth be not supposed to move along with thebody, the cafe will be a little different. For the body be-ing constantly drawn directly towards the center of the earth,the body in its motion will be drawn in a direction a little ob-lique to that, wherein it would be drawn by the earth in mo-tion, as before supposed. But the distance to the center of the

* See above Ch.2. § 17.

earth