| 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 + 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 ;... | |
| Jeremiah Day - Measurement - 1831 - 394 pages
...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 solution of oblique... | |
| 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... | |
| John Radford Young - Astronomy - 1833 - 314 pages
...two arcs to find the sine and cosine of their sum and difference . . .19 ARTIcLE. PAGE 19. In a plane **triangle the sum of any two sides is to their difference...the tangent of half the sum of the opposite angles** to the tangent of half their difference . . . .21 20. Formulas for determining an angle in terms of... | |
| Euclid - 1835 - 540 pages
...half the sum subtract half the difference, and it will give the less. 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... | |
| Robert Simson - Trigonometry - 1835 - 544 pages
...difference; and since BC, FGare parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the fides **is to their difference, as the tangent of half the sum of the** angles at the base to the tangent of half their difference. * PROP. IV. F1G. 8. In a plane triangle,... | |
| John Playfair - Geometry - 1836 - 148 pages
...them, in r. plane triangle, any three being given, the fourth is also given. PROP. III. i 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... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...6 — c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of **two sides is to their difference as the tangent of half the sum of the** angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin... | |
| John Playfair - Geometry - 1837 - 332 pages
...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 of the** angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle... | |
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