 In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.  Documents of the City of Boston - Pàgina 139per Boston (Mass.). City Council - 1869Visualització completa - Sobre aquest llibre
 | Boston (Mass.). School Committee - 1868 - 508 pàgines
...difference between Algebra and Arithmetic? In Algebra 3 had 100 per cent. 9 " 95 to 99 " 6 " 90 to 94 " 12 " 80 to 89 " 26 under 80 " TRIGONOMETRY. 1. Define...other angles, to the tangent of half their difference. 3. Given two sides and an opposite angle, in what different ways may a triangle be constructed ? 4.... | |
 | Eli Todd Tappan - 1868 - 444 pàgines
...BA-cos. A. That is, b = a cos. C -J- e cos. A. 869. Theorem — The sum of any two sid.es of a triangle is to their difference as the tangent of half the sum of the two opposite angles is to the tangent of half their difference. By Art. 867, a : b : : sin. A : sin. B.... | |
 | William Mitchell Gillespie - 1868 - 530 pàgines
...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... | |
 | Lefébure de Fourcy (M., Louis Etienne) - 1868 - 350 pàgines
...tang } (A + B) a — b tang} (A — B) *• ; which shows that, in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. We have A + B=180° —... | |
 | New-York Institution for the Instruction of the Deaf and Dumb - 1869 - 698 pàgines
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. This young man also worked out a problem... | |
 | William Mitchell Gillespie - 1869 - 550 pàgines
...to each other at the opposite sides. THEOREM EL — 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... | |
 | Charles Davies, Adrien Marie Legendre - 1869 - 470 pàgines
...(14.) Hence, we have the following principle : In any plane triangle, the sum of the sides including either angle, is to their difference, as the tangent of half the sitm of the tioo other angles, is to the tangent of half their difference. The half sum of the angles... | |
 | Charles Davies - 1870 - 392 pàgines
...AB, АО, in a similar manner, we should find, AB : А О : : sin 0 : sin B. Theorems. THEOREM II. In any triangle, the sum of the two sides containing...other angles, to the tangent of half their difference. Let ACB be a triangle: then will AB + AC: AB— AC: : tan %(C + B) : tan %(C— S). With A as a centre,... | |
 | New-York Institution for the Instruction of the Deaf and Dumb - 1871 - 370 pàgines
...we have the principle. When two sides and their included angles are given : The sum of the two sides is to their difference as the tangent of half the sum of the other two angles is to the tangent of half their difference. This young man also worked out a problem... | |
 | Elias Loomis - 1871 - 302 pàgines
...^(A+B) . sin. A-sin. B~sin. ^(AB) cos- ^(A+B)~tang. ^(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. COS f*fvt Dividing formula (3) by (4), and considering... | |
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