. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . s =V di V v^ d s nate /. = / = , — = v .ds, v .ds + sdv = Q. Integrating, we get u . s = 0. dy dys Taking d to represent the perpendicular C E to the tangent at the initial point A, and c theinitial velocity, it will be evident that when v becomesc, s becomes d ; therefore c d = C, and the correctedintegral will \)Q v . s = c d. The areas of all parallelograms circumscribing anellipse formed by drawing tangents at the extremitiesof two conjugate diamet
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . s =V di V v^ d s nate /. = / = , — = v .ds, v .ds + sdv = Q. Integrating, we get u . s = 0. dy dys Taking d to represent the perpendicular C E to the tangent at the initial point A, and c theinitial velocity, it will be evident that when v becomesc, s becomes d ; therefore c d = C, and the correctedintegral will \)Q v . s = c d. The areas of all parallelograms circumscribing anellipse formed by drawing tangents at the extremitiesof two conjugate diameters are constant, each beingequal to the rectangle under the axes. Take a to represent the semi-transverse axis, and hthe semi-conjugate axis ; P C, C D, Fig. 3348, two semi-conjugate diameters, 6. a = P P C D, —^ = P P. 0 D The angles made by the focal distances with tlie tangent are equal and the angle at P is equal to tlie angle at E on account of the tangent being parallel to the diameter E D ; tlicrefore, by similar triangles, s PF2/ : s : : P E : P P, —-— = p P. n straight Unes be drawn from the foci to a vertex of any. y 5 T 1746 GUNNERY. diameter, the distance from the vertex to the intersection of the conjugate diameter with eitherfocal distance is equal to the semi-transverse axis, b .a ^^, s .a i> -y PE = PP CD = PP y CD The rectangle under the focal distances of the vertex of any diameter is equal to the square of thesemi-conjugate diameter, F P. ?/ = C D^ ; but the focal distances are equal to the transverse axis,FP -1- y = 2a, F P = (2a - y). Substituting value for F P, (2 a - ?/) .y = CD\ V(2a - y)y = C D. Substituting this value in s = tttTj ^^ for s in the equation vv^. b^. y cd, V .dv C-. d\ (_2a^y)y,vc^. fp a .dy V{C2a-2/)¿/l62. y = c2. d\ (2 a - t/), «2 Substituting this value y)y] ^ ,a 1 hui—fdy = ; :.fdy = —v V{C2«-2/)!/ - = c d, = ^{(2ac^.d^ 2a —y dv, fdy = — — Differentiating, we obtainc^.d^ a,
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Keywords: ., bookcentury1800, bookdecade1870, bookidsp, booksubjectengineering
