# A Collection of Examples of the Applications of the Differential and Integral Calculus Volume 1-2; PT. 1820

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## Description

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1820 edition. Excerpt: ...to the rectangle under the ordinate PQ, and the diameter of the circle. (4). If the equations are y =, and. =--(l--cos 6), m the portion of the curve which they represent, which is cut off by a double ordinate, passing through the centre of the generating circle, constitutes the harmonic curve, or one of the figures which a vibrating chord may assume in its different positions. Fig. 90. The radius of curvature or a l + sin1 --!--. ', mi cos which varies very nearly inversely as cos or p Ai, when m is considerable. If any two harmonic curves be constructed upon equal bases and upon the same straight line, but whose centres are at any given distance from each other, the curve whose ordinate is equal to the sum of the corresponding ordinates of the given curves, is likewise an harmonic curve. (5). If one circle revolve upon another as its base and in the same plane with it, the curve described by any point in its plane, is called the Epitrochoid, which becomes the Epicycloid, when the describing point is in the circumference of the revolving circle. If a circle revolve, in a similar manner, upon the concave part of the circumference of another circle, the curve described by a point in its plane, is called the Hypotrochoid, which becomes the Hypocycloid, when that point is in the circumference. If a be the radius of the base, b the radius of the generating circle, the angle ACQ, (Fig. 91.), and Q being the points of the base, which are first and last in contact with the generating circle, CP=x, udPM=y, then the equations of the Epicycloid are If 4 be negative, these equations represent the corresponding Hypocycloid in this case Fig. 92 If 6' be the distance of the...show more

## Product details

• Paperback | 42 pages
• 189 x 246 x 2mm | 95g
• Miami Fl, United States
• English
• black & white illustrations
• 1236530020
• 9781236530028