| William Smyth - Navigation - 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,... | |
| 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+£)... | |
| 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... | |
| William Mitchell Gillespie - Surveying - 1856 - 464 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... | |
| 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... | |
| Peter Nicholson - 1856
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle **is to their difference as the tangent of half the sum of the** angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of the... | |
| 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... | |
| 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... | |
| 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.... | |
| Euclides - 1860
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle **is to their difference as the tangent of half the sum of the** angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
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