Elements of mechanics: for the use of colleges, academies, and high schools (1859)
Peck, William G. (William Guy), 1820-1892 · New York, A. S. Barnes & Burr · leaf 76
bstituting in (32), we have, x, — fx\/dx2 + dy2f^W+dy* Vi = fyVdx2+_dy2f -y/dx2 + dy2 (33.) Centre of Gravity of an arc of a circle.66. Let AB C be the arc, 0 the origin of co-ordinatesand centre of the circle, OX the axis ofabscissas, perpendicular to the chord ofthe arc, and 0 Y the axis of… … Differentiating, 2xdx + 2ydy = 0 ; x2 + y1 = r2. dx2 = ^dy* Substituting in the first of Formulas (33), and reducing,we find, frdy rdy f: vV - if Integrating both numerator and denominator between thelimits y = — £c, and y — + \c, we have, + ic rdy = re ; / — jo 74 MECHANICS. and, f rdy Hence, by…
Mechanics
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