The Principles of Fluxions: Designed for the Use of Students in the University

Kimber and Conrad, 1812 - 256 ページ

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1 ページ - Lines are described, and thereby generated, not by the apposition of parts, but by the continued motion of points ; superficies by the motion of lines ; solids by the motion of superficies ; angles by the rotation of the sides ; portions of time by continual flux : and so on in other quantities.
15 ページ - ... to demonstrate any proposition, a certain point is supposed, by virtue of which certain other points are attained; and such supposed point be it self afterwards destroyed or rejected by a contrary supposition; in that case, all the other points attained thereby, and consequent thereupon, must also be destroyed and rejected, so as from thence forward to be no more supposed or applied in the demonstration.
5 ページ - ... 8. It has been said, that when the increments are actually vanished, it is absurd to talk of any ratio between them. It is true; but we speak not here of any ratio then existing between the quantities, but of that ratio to which they have approached as their . limit; and that ratio still remains. Thus, let the increments of two- quantities be denoted by...
19 ページ - Given x -f- y + z — a, and xt/: z; a maximum, to find x, y, z. As x, y, z, must have some certain determinate values to answer these conditions, let us suppose such...
256 ページ - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.
7 ページ - Hence it appears, that whether the root be a simple or a compound quantity, the fluxion of any power of it is found by the following general Rule : Multiply by the index, diminish the index by unity, and multiply by the fluxion of the root. Thus the fluxion...
29 ページ - Prove that the problem, to describe a circle with its centre on the circumference of a given circle so that the length of the arc intercepted within the given circle shall he a maximum, is reducible to the solution of the equation 0 = cot 0.