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abscissa angle arithmetic progression Assume attraction axis body revolving centre of force centre of gravity circle circular arc circumference consequently constant quantity constant ratio contrary flexure cosine cotemporary increment curvature cycloid cylinder denominator density described distance earth ellipse expressed find F find the fluxion fluent Art force of gravity fore found by Art hence Art hyperbola increase uniformly latus rectum length Let F Let the curve limiting ratio logarithm logarithmic spiral maximum or minimum motion multiplied odd number ordinate parabola parallel parallelogram particle perpendicular plane point of contrary Prop radius radius of curvature ratio of equality resistance root second fluxion similar triangles sine solid spiral square substitute subtangent suppose take the fluxion tangent triangles unity vanish variable quantities varies velocity vinculum whole number
Page 1 - 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.
Page 15 - ... 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.
Page 5 - ... 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...
Page 19 - 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...
Page 256 - 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.
Page 7 - 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...