| 1829 - 536 pages
...solution of the first of these cases is shewn to depend on the theorem, that, " the sum of two sidi\s **of a triangle is to their difference, as the tangent of half the sum of the** opposite angles to the tangent of half their difference." This half difference added to half the sum,... | |
| 1829 - 538 pages
...given. The solution of the first of these cases is shewn to depend on the theorem, that, " the sum of **two sides of a triangle is to their difference, as the tangent of half the** mm of the opposite angles to the tangent of half their difference." This half difference^added to half... | |
| Alexander Ingram - Mathematics - 1830 - 462 pages
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB **is to their difference as the tangent of half the sum of the** opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan. £ (B... | |
| Charles Davies - Surveying - 1830 - 392 pages
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, **is to their difference, as the tangent of half the sum of the** other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle ;... | |
| Jeremiah Day - Measurement - 1831 - 394 pages
...opposite angles. It follows, therefore, from the preceding proposition, (Alg. 389.) that the sum of any **two sides of a triangle, is to their difference ; as the tangent of half the sum of the** opposite angles, to the tangent of half their difference. This is the second theorem applied to the... | |
| Jeremiah Day - Measurement - 1831 - 520 pages
...THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) **is to their difference ; as the tangent of half the sum of the angles** ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making AG equal... | |
| William Enfield - Astronomy - 1832 - 216 pages
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, **is to their difference, as the tangent of half the sum of the angles at the** baseRSM, RMS, is to the tangent of half their difference. Tohalfthe sum add half the difference, and... | |
| Naval art and science - 1880 - 1122 pages
...to the course, and the angle B will be the divergence of the apparent from the true direction. Now, **the sum of the two sides of a triangle is to their difference,** i the tangent of half the sum of their opposite angles is to the at of half their difference. B the... | |
| John Radford Young - Geometry, Spherical - 1833 - 286 pages
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, 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 help of this rule we may determine the... | |
| Euclides - 1834 - 518 pages
...given, the fourth is also given. PROPOSITION III. In a plane triangle, the sum of any two sides in **to their difference, as the tangent of half the sum of the** angle at Ihe base, to the tangent of half their difference. PROPOSITIONS III. IV. of the angles at... | |
| |