The Principles of FluxionsKimber and Conrad, 1812 - 256 lappuses |
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a²+x² a²x² AB=x abscissa angle arithmetic progression Assume attraction axis BC=y centre of force centre of gravity circle circular arc circumference consequently constant quantity constant ratio contrary flexure cosine curvature cycloid cylinder density described distance draw Earth ellipse equation find F find the fluxion fluent Art fluid force of gravity found by Art given hence Art hyperbola increase uniformly Let F limiting ratio logarithm logarithmic spiral MAXIMA AND MINIMA motion multiplied negative ordinate parabola parallel parallelogram perpendicular point of contrary PROP radius ratio of equality resistance root second fluxion similar triangles sine solid spiral square substitute subtangent take the fluxion tangent triangles unity Va² vanish varies velocity vinculum whole number
Populāri fragmenti
3. 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.
4. lappuse - I have no controversy about your conclusions, but only about your logic and method. How you demonstrate? What objects you are conversant with, and whether you conceive them clearly? What principles you proceed upon; how sound they may be; and how you apply them? It must be remembered that I am not concerned about the truth of your theorems, but only about the way of coming at them; whether it be legitimate or illegitimate, clear or obscure, scientific or tentative.
86. lappuse - Multiply the weight of the several particles by the squares of their distances from the centre of motion, and divide the sum of the products by the weight of the whole mass ; the square root of the quotient will be the distance of the centre of gyration...
236. 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.