 | William Mitchell Gillespie - Surveying - 1856 - 478 pages
...triangle, the sines of the angles are to each other a* the opposite sides. THEOREM II. — In every plane triangle, the sum of two sides is to their difference...angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the cosine of any angle is equal to a fraction... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...B. . . (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 - Cabinetwork - 1856 - 518 pages
...+ 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 two sides,... | |
 | William Mitchell Gillespie - Surveying - 1857 - 538 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...angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, the cosine of any angle is equal to a fraction... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...90. We also have (Art. 22), a + b : a - b : : tan %(A + B) : tan %(A - B) : that is, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half thtir difference. 91. In case of a right•angled triangle,... | |
 | W. M. Gillespie - Surveying - 1859 - 540 pages
...the angles are to each other at the opposite sides. THEOREM II — In every plane triangle, the turn of two sides is to their difference as the tangent...angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle, t/m cosine of any angle is equal to a fraction... | |
 | Elias Loomis - Trigonometry - 1859 - 218 pages
...AxAC=sin. BxBC, or sin. A : sin. B : : BC : AC. THEOREM II. (50.) 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. Let ABC be any triangle ; then will CB+CA... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...|(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... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...cos. A— sin. B : cos. (AB) ....... (44) THEOREM in. (ART. 9.) In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the ai,(/lei opposite to^them is to the tangent of half then- difference. „ . a sin. A , (Theorem 2.)... | |
 | James Pryde - Navigation - 1867 - 506 pages
...add the sides a and b and also subtract them, this will give a + b and a — b/ then the sum of the sides is to their difference as the tangent of half the sum of the remaining angles to the tangent of half their difference. The half sum and half difference being added,... | |
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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. 
