The Principles of Fluxions: Designed for the Use of Students in the University
Kimber and Conrad, 1812 - Calculus - 256 pages
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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 described difference direction distance divide draw earth equal equation EXAMPLES expressed fall find F fluent 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 parallelogram particle passing 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
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...
Page 29 - 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.