 | Thomas Keith - Navigation - 1826 - 504 pages
...OF THE DIFFERENCES OF ARCS. PROPOSITION xiii. (Plate L Fig. 2.J (P) 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. Let BA and во be the two arcs ; draw the diameter... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...differenee as the radius to the tangent of the differenee between either of them and 45°. PROP. IV. The sum of any two sides of a triangle is to their differeuee, as the tangent of half the sum of the angles opposite to those sides, to the tangent of... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 764 pages
...triangle (supposing any aide to be the base, and calling the other two the tide*) the sum of the sida is to their difference, as the tangent of half the sum of tht ongfcs at the base is to the tangent of half the difference of the tame angla. Thus, in the triangle... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...being given, the fourth is also given. PROP. III. FIG. 8. In a plane triangle, the sum of any two sides 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 a plane triangle, the sum of... | |
 | Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...by [21] becomes g + 6_tan.i(A+B) a — b~tan.-^(A. — B)' Hence " the sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference." This formula is independent of the absolute magnitudes... | |
 | 1829 - 530 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...angles to the tangent of half their difference.'" This half difference added to half the sum, gives the greater, and subtracted from the half sum, gives the... | |
 | 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...angles to the tangent of half their difference." This half difference added to half the sum, gives the greater, and subtracted from the half sum, gives the... | |
 | 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 - 458 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 + C) : tan. £... | |
 | Charles Davies - Surveying - 1830 - 390 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 ;... | |
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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. 
