Excerpt from A Treatise on Fluxions, Vol. 2 of 2 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 ...
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Excerpt from A Treatise on Fluxions, Vol. 2 of 2 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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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