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abscissa angle appears Assume attraction axis becomes body called centre circle consequently consider constant continually correction corresponding cosine cotemporary curve cylinder decrease denominator density descends described difference direction distance divide draw Earth equal equation EXAMPLES expressed fall find F fluent fluid fluxion force given gives gravity greater greatest hence increase increments infinite length less limiting ratio logarithm manifest manner maximum motion move multiplied negative ordinate parabola parallel particle perpendicular plane positive produce PROP quantity radius ratio represent resistance revolving root rule sides similar sine solid space spiral square substitute suppose surface tangent triangles true uniform uniformly unity vanish variable varies velocity whole
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.