. A treatise on plane and spherical trigonometry. - cot —4 n and since F = £ X i r» r== a» -^tanUcot* — 24 ^ 7i (352) (353) Fig. 37. 194. To find the surface and volume of a parallelopiped, given the edges am, their incli-nations to each other. Let OP, Fig. 37, be a pzraUelopipei,whose edges 0 A = a, OB r= b, 0 C = c,and their inclinations B 0 C = a, AO C= @,A 0 B = y, are given.±p The area of any face, as B C, is found bythe formula b c sin a, and therefore foithe whole surface, we haveS= 2 {b c sin a -f- a c sin /2 -|- a b sin 5,) (354)To find the volume, let CD be the alti-tude, thenF=base^

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. A treatise on plane and spherical trigonometry. - cot —4 n and since F = £ X i r» r== a» -^tanUcot* — 24 ^ 7i (352) (353) Fig. 37. 194. To find the surface and volume of a parallelopiped, given the edges am, their incli-nations to each other. Let OP, Fig. 37, be a pzraUelopipei,whose edges 0 A = a, OB r= b, 0 C = c,and their inclinations B 0 C = a, AO C= @,A 0 B = y, are given.±p The area of any face, as B C, is found bythe formula b c sin a, and therefore foithe whole surface, we haveS= 2 {b c sin a -f- a c sin /2 -|- a b sin 5,) (354)To find the volume, let CD be the alti-tude, thenF=base^-Bx C7> = a b sin j, x CDSuppose a sphere to be described about 0, whose intersections with the planesBOC, AOC, AOB and DOC are BC = *, AC = A AB = y, and CD. Thetriangle ACD is right-angled at 7>, whence CD = c sin C7/ = c sin 0 sin (46), if, = *(* + l-f>)p 2 c C D = -— ,*/ [sin »■ sin (a- — a) sin (s- — @) sin (s- — y)~\sin v F= 2 abc^/lsin <r sin (s-— *) sin (s- — £) sin (s- — y)~) (355) THE whence f* It DATE DUE \ 30334 CAYLORD PRINTED IN

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Keywords: ., bookcentury1800, bookdecade1870, booksubjecttrigono, bookyear1876