 | John Playfair - 1855 - 334 σελίδες
...radius to the tangent of the difference between either of them and 45°. PROP. IV. THEOR. The sum of any two sides of a triangle is to their difference, as the tangent of half the sum oft/te angles opposite to those sides, to the tangent ofhalft\tw difference. Let ABC be any plane triangle... | |
 | William Mitchell Gillespie - 1855 - 436 σελίδες
...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 triangle,... | |
 | Charles Davies - 1855 - 340 σελίδες
...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 - 1855 - 192 σελίδες
...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 - 1856 - 478 σελίδες
...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 triangle,... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...(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... | |
 | William Mitchell Gillespie - 1857 - 538 σελίδες
...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 triangle,... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 σελίδες
...AC :: sin C : sin B, THEOREM II. 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. 22. Let A CB be a triangle : then will AB... | |
 | Benjamin Greenleaf - 1862 - 532 σελίδες
...£ (^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 to tfie... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...sin ^1 sin £ siu C7° (89) (90) (91) (92) (93) 112. 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. For, by (90), a : b : : sin A : sin B ;... | |
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C' (89) (90) (91) (92) (93) 112. 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. 
