| Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...'.'. BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is to their differenee **as the tangent of half the sum of the angles opposite to** those sides to the tangent of half their differenee. QED PROP. V. THEOR. If a perpendieular be drawn... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...them, in a plane triangle, any three 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 any two... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 438 pages
...plane triangle are as the sines of the opposite angles. (73.) The sum of two sides of a plane triangle **is to their difference as the tangent of half the sum of the** opposite angles to the tangent of half their difference. •* ^74.) Formulae for the sine, cosine,... | |
| 1829 - 536 pages
...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,... | |
| 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 ;... | |
| 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... | |
| Jeremiah Day - Measurement - 1831 - 520 pages
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the **sides is to their difference; as the tangent of half the sum of the** opposite angles, to the tangent <if half their difference. Therefore, R :tan(ACH-45°)::tan|(ACB +... | |
| 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... | |
| John Radford Young - Geometry, Spherical - 1833 - 286 pages
...I<; consequently, from the equation above, n + 4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, **in any plane triangle the sum of any two sides is...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... | |
| John Radford Young - Astronomy - 1833 - 314 pages
...of 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 as the tangent of half the sum of the** opposite angles to the tangent of half their difference . . . .21 20. Formulas for determining an angle... | |
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