| Adrien Marie Legendre - 1857 - 448 páginas
...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, in which the right... | |
| William Mitchell Gillespie - 1857 - 524 páginas
...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... | |
| Horatio Nelson Robinson - 1858 - 347 páginas
...point without a circle, by theorem 1 8, book 3, we have, Hence, . . AB : AE=AF : AO QED PROPOSITION 7. **The sum of any two sides of a triangle, is to their difference, as the tangent of** the half sum of the angles opposite to these sides, to the tangent of half their difference. Let AB... | |
| 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... | |
| Euclides - 1860
...same manner it may be 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... | |
| John Playfair - 1860 - 317 páginas
...it may be shewn that cos. AB+cos. AC : sin. AC—sin. AB : : R : tan. j(AC—AB). PROP. IV. THEOR. **The sum of any two sides of a triangle is to their difference, as the tangent of** naif the sum of the angles opposite to those sides, to the tangent ofhalft\tv difference. CA+AB : CA—AB... | |
| Horatio Nelson Robinson - 1860 - 453 páginas
...by Cor. Th. 18, B. HI, we have AE x AF — AB x Aa Hence, AB : AE = AF : Ad. t PROPOSITION VII. Tlie **sum of any two sides of a triangle is to their difference, as the tangent of** one half the sum of the angles opposite to these sides, is to the tangent of one half their difference.... | |
| George Roberts Perkins - 1860 - 443 páginas
...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.... | |
| War office - 1861 - 12 páginas
...what angle is the sine of the supplement equal to the sine of the complement. Find sin 15°. Prove **the sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the** angles opposite to these sides, is to the tangent of half their difference. 3. What is the angle of... | |
| Benjamin Greenleaf - 1862 - 490 páginas
...^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles **is to their difference as the tangent of half the sum of the** angles is to the tangent of half their difference, or as the cotangent of half their difference is... | |
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