. Applied calculus; principles and applications . y _ _ h^dx a^y^ dx^ a^y^ Substituting these values in(3) of Art. 94 gives (a^ — 6^) x 145 /3 = (a^ - 6^) y^ ¥ W -hy ^ w - hy (2). Hence, the equation of the evolute of the eUipse aV + Ifx^ =a^b^ is (aa)^ + (h^ = (a - 6^)3. The evolute is C1C2C1C2. Ci is center of curvature for 146 DIFFERENTIAL CALCULUS A; C for P; C2 for B; Ci for A] C2 for B. In the figureshown a = 2h; when a = h V2, then the center of curvaturefor B is Sit B and for 5 at 5. When a <h V2, the centers for B and B are withinthe elHpse. The points Ci,C2, Ci, and C2 are
. Applied calculus; principles and applications . y _ _ h^dx a^y^ dx^ a^y^ Substituting these values in(3) of Art. 94 gives (a^ — 6^) x 145 /3 = (a^ - 6^) y^ ¥ W -hy ^ w - hy (2). Hence, the equation of the evolute of the eUipse aV + Ifx^ =a^b^ is (aa)^ + (h^ = (a - 6^)3. The evolute is C1C2C1C2. Ci is center of curvature for 146 DIFFERENTIAL CALCULUS A; C for P; C2 for B; Ci for A] C2 for B. In the figureshown a = 2h; when a = h V2, then the center of curvaturefor B is Sit B and for 5 at 5. When a <h V2, the centers for B and B are withinthe elHpse. The points Ci,C2, Ci, and C2 are length of the evoluteis evidently four times thedifference between R atB {a, h), and R Sit A (a, 0);that is, (1, Exercise XII),4 {ayb - by a) = 4 (a^ - h^)/ah. Corollary. — For circle,since a = b, the evolute isa point, the center of thecircle. Y\
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Keywords: ., bookcentury1900, bookdecade1910, bookpublishernewyo, bookyear1919
