A Treatise on Fluxions

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CP being taken upon Cd, in the same ratio to Ca as A is to C +a, a right line from D parallel to CF will intersect CL pa rallel to DP in G, so that CG will represent the direction in which C will descend and the force that accelerates its motion; and CG will be described by it in the same time that it would have described CD by falling freely in the vertical. If we sup pose CF (fig. 232, N. To coincide with the vertical CD, Da will in this case be perpendicular to CD, and af being per pendicular to Ca, the point m will fall upon D, and CD is to be divided in G so that CG may be to DG in the compound ratio of C to A and of CD to cf, or of the square of CD to the square of Ca. These last are the two cases consideredbymr.bernouilli which have been lately published, comm.acad.petropol. Tom. 5; and these constructions agree with the computations which he deduces by resolving the force of C into two infinite pro gressions. If the body C impel in like manner two equal bo dies A and B (fig. 232, N. 3) in directions CF and CH that form equal angles with the vertical, and f Cb be one continued horizontal line, CD is to bedivided in G, so that CG may be to GD in the compound ratio of C to the sum of the bodies A and B and of the duplicate ratio of the sine of the angle fcd to its cosine and CG will represent the force that accelerates the motion of C, providing it always impel A and B in the same directions from the beginning of its descent.

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