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

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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 deſcribed the line PD, is to the time in which the ſame body has deſcribed the line PE, in the ſubduplicate ratio of PD to PE; that is (the very ſmall line DE being juſt naſcent) in the ratio of PD to to 2PD + DE, and by diviſion to the time in which the body hath deſcribed the ſmall 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 deſcribed the very ſmall line DE is to the time in which the body moving unequably hath deſcribed the line De, as thearea DLME to the area DLme; and ex æquo the firſt mentioned of theſe times is to the laſt as the rectangle 2PD x DL to the area DLme.


Book 3, Section 7 - End decoration
Book 3, Section 7 - End decoration