 | Allan Menzies - 1854 - 520 pages
...Suppose AC, CB, and angle C to be given, then rule is, — Sum of the two sides (containing given angle) is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference ; half the sum = ^ (180 — angle C), then having... | |
 | Charles Davies - Navigation - 1854 - 446 pages
...AC :: sin G : sin B. THEOREM II. In any triangle, the sum of the two sides containing either *ngle, is to their difference, as the tangent of half the sum of the two oilier angles, to the tangent of half their difference. 22. Let ACS be a triangle: then will AB+AC... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| 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 their difference. 91. In case of a right•angled triangle,... | |
 | Jeremiah Day - Logarithms - 1855 - 344 pages
...THE OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, ^ ^ ^ c is to their difference ; as the tangent of half the sum of the angles ACB and ABO, to the tangent of half their difference. Demonstration. Extend CA to G, making AG equal to AB;... | |
 | 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 - 340 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+£)... | |
 | William Smyth - Navigation - 1855 - 234 pages
...tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,... | |
 | 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,... | |
 | Peter Nicholson - Cabinetwork - 1856 - 518 pages
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle 4 then, of the two sides,... | |
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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. 
