Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/243

 uniform force from P, and in falling arrived at D, in the proportion of the curvilinear area DLme to the rectangle 2PD x DL. For the time in which a body falling with an uniform force hath decribed the line PD, is to the time in which the ame body has decribed the line PE, in the ubduplicate ratio of PD to PE; that is (the very mall line DE being jut nacent) in the ratio of PD to $$\scriptstyle PD + \frac 12DE$$ to 2PD + DE, and by diviion to the time in which the body hath decribed the mall line DE, as 2PD to DE, and therefore as the rectangle 2PD + DL to the area DLME; and the time in which both the bodies decribed the very mall line DE is to the time in which the body moving unequably hath decribed the line De, as thearea DLME to the area DLme; and ex æquo the firt mentioned of thee times is to the lat as the rectangle 2PD x DL to the area DLme.