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. 1854 Excerpt: ...angle EFC is equal to ABC; therefore the sine of BC is to the radius as the sine of AC is to the sine of the angle ABC. In like manner it may be shown that the sine of BC is to the radius, as the sine of AB is to the sine of ACB. Cor. Let the angles of the triangle ABC righlangled at A, be denoted by A, B, C, and the ...
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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. 1854 Excerpt: ...angle EFC is equal to ABC; therefore the sine of BC is to the radius as the sine of AC is to the sine of the angle ABC. In like manner it may be shown that the sine of BC is to the radius, as the sine of AB is to the sine of ACB. Cor. Let the angles of the triangle ABC righlangled at A, be denoted by A, B, C, and the opposite sides (or the angles measured by them) by a, b, c, respectively; and let the corresponding parts of a triangle complemental to ABC, be denoted by A', B', C, a', b', c the angle A' being a right angle. Then (Art. 4), if B'=B; C=comp. 5, 5'=comp. C, a'=comp. c, c'= comp. a: and if C=C; B'=comp. c, c'=comp. B, a'= comp. b, J'=comp. a. Now by the preceding proposition, sin a: R:: sin b: sin B; hence if unity be put for R, (1) sin b=sin a sin B. Likewise, since the same equation holds good in the complemental triangles, sin 5'=sin a' sin B'; from which equation are derived the two following; one for the case in which B'=B, the other for that in which C'=C; sin comp. C=sin comp. c sin B, sin comp. a=sin comp. b sin comp. c; or (2) cos C=cos e sin B, (3) cos a=cos b cos c. 6. In a right-angled spherical triangle, the sine of either of the sides containing the right angle is to the radius as the tangent of the other of these sides is to the tangent of the opposite angle. Let ABC be a triangle right-angled at A, the sine of AC is to the radius as the tangent of AB is to the tangent of the opposite angle ACB. Let D be the center of the sphere; join DA, DB, DC, draw AE perpendicular to CD; and AF a tangent to AB, meeting DB produced in F; also draw EF; this will be perpendicular to CD. For since AF is a tangent to AB, it is perpendicular to AD; and being drawn in the plane BAD at right angles to AD the intersection of this plane with the plane CA..
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Add this copy of An Elementary Treatise of Spherical Geometry and to cart. $15.42, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of An Elementary Treatise of Spherical Geometry and to cart. $26.58, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
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Fine. Sewn binding. Cloth over boards. 126 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of An Elementary Treatise of Spherical Geometry and to cart. $29.59, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2022 by Legare Street Press.
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New. Sewn binding. Cloth over boards. 126 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.