 | Horatio Nelson Robinson - Navigation - 1858 - 356 pages
...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 - 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... | |
 | Euclides - 1860 - 288 pages
...In the 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... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...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 - Geometry - 1860 - 472 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.... | |
 | John Playfair - Geometry - 1860 - 334 pages
...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... | |
 | War office - 1861 - 714 pages
...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 - Geometry - 1862 - 518 pages
...^ (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... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...£ (^l — " B) (R7\ smA—maB ~ <^rt1[ (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 tlie tangent of half their difference, or as the cotangent of half their difference is... | |
 | Charles Davies - Navigation - 1862 - 410 pages
...AC . : sin C : sin B. THEOREM IL In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of tt1e two oif1er angles, to the tangent of half their difference. 22. Let ACB be a triangle: then will... | |
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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 those sides, to the tangent of half their difference. 
