This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1789 Excerpt: ...communicated in anv other time AO may be found j and vice versa. 558. Cor. ' Nfcwt. Piin. Tom. I. Sect. VII. Euler'i Median. Ch. III. E e z 558. Cor. 2. If the force F be finite, and the time Ap infinitely small, the increment of velocity, y, is evanescent; because AB x Ap = a finite quantity multiplied into one that ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1789 Excerpt: ...communicated in anv other time AO may be found j and vice versa. 558. Cor. ' Nfcwt. Piin. Tom. I. Sect. VII. Euler'i Median. Ch. III. E e z 558. Cor. 2. If the force F be finite, and the time Ap infinitely small, the increment of velocity, y, is evanescent; because AB x Ap = a finite quantity multiplied into one that is.evanescent = o; and consequently the increment of velocity, or V, is infinitely small, and no finite change of velocity can be generated by F in an instant. $59. Cor. 3. Tf the body ascend pr descend, and the velocity be as the time in which it is acquired or destroyed, the force is invariable; for, from this proposition, the change of velocity is as AR, or as A0 (hypoth.) and consequently AR is a rectangular parallelogram, or 0 R is constant.... '. 1. FIG. 560. Prop. If PO represent the space described by the action of a 'force tending to S, and the ordinate OR be the relative magnitude of the force at the point O, the velocity, V, acquired at O will vary in a sub duplicate ratio os the corresponding area PR. Dem. Let V, F, S, be the velocity, force, and space described respectively, and because V is as F x T(), and ST is as-; VV'xs as Fx5, or as P B x Pp, and the fluent of VV, or--is as. 561. Cor. 1. If x be the distance of the moving body from the center of force, S, and the force be as any power of the distance, whose exponent is n--1; Vy$ as Fx--x, or as--x"-'x, and yt x"--is as V-correction: but when V = o at P, x = SP = t 2. n' - _r and--=--; therefore the correction =-, and Vis as s/p"--x 1 562. Cor. 562. Cor. 2. If the force be constant, or -== 1, then V being as Zp"--x" is as y/p--#, or in a fubduplicate ratio of the space described, either in acceding to S from a state of rest, or receding from S...
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