The Principles of Fluxions: Designed for the Use of Students in the UniversityKimber and Conrad, 1812 - 256 lappuses |
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a²+x² AB=x abscissa angle arithmetic progression Assume attraction axis BC=y centre of gravity circle circular arc consequently constant quantity constant ratio contrary flexure cosine cotemporary increment curvature cycloid cylinder density described distance ellipse find F find the centre find the fluxion fluent Art fluents are found force of gravity found by Art given hence Art hyperbola increase uniformly infinite latus rectum Let F limiting ratio logarithm logarithmic spiral motion multiplied ordinate parabola parallel parallelogram particle perpendicular PROP radius ratio of equality resistance root second fluxion similar triangles sine solid spiral square substitute subtangent surface take the fluxion tangent triangles unity Va² vanish varies velocity vinculum whole number
Populāri fragmenti
1. lappuse - 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. lappuse - ... 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. lappuse - ... 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. lappuse - 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. lappuse - 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. lappuse - 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. lappuse - 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.