| John Playfair - Geometry - 1855 - 336 pages
...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 - Surveying - 1855 - 436 pages
...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 - Geometry - 1855 - 336 pages
...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 - Trigonometry - 1855 - 192 pages
...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 - Surveying - 1856 - 478 pages
...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 - Geometry - 1856 - 460 pages
...(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 - 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 sum of the angles** opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle,... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 pages
...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 - Geometry - 1862 - 514 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 to tfie... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...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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