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Books Books 81 - 90 of 185 on C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides....  
" C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. "
A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ... - Page 336
by Philip Ronayne - 1717 - 408 pages
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A Treatise on Land-Surveying Comprising The Theory Developed from Five ...

W.M. Gillespie, A.M., Civ. Eng - 1855
...to each other as the opposite sides. THEOREM II. In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. In every plane...
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Elements of Plane Trigonometry, Surveying and Navigation

William Smyth - Plane trigonometry - 1855 - 223 pages
...tan ~ ; lU 4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,...
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Elements of geometry and trigonometry: with applications in mensuration

Mathematics - 1855 - 324 pages
...sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC:AB-AC::t1M)(C+)...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - Trigonometry - 1855 - 178 pages
...i(A+B) . sin. A-sin. B~sin. i(AB) cos. i(A+B)~tang. i(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Dividing formula (3) by (4), and considering...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1856 - 454 pages
...to each other a* the opposite sides. THEOREM II. In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. In every plane...
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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...(2.) In the same way it may be shown that THEOREM II. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem I., we have 5 : c : : sin. B...
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A treatise on land-surveying: comprising the theory developed from five ...

William Mitchell Gillespie - Surveying - 1857 - 524 pages
...to each other at the opposite sides. THEOREM II. In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. In every plane...
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ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY

ELIAS LOOMIS, LL.D. - 1859
...|(A+B) ^ sin. A~sin. B~sin. i(AB) cos. J(A+B)~tang. J(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. .Dividing formula (3) "by (4), and considering...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...it may be shown that .] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : : sin....
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