| Dionysius Lardner - 1828 - 317 páginas
...of a 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, tangent, and cotangent... | |
| 1829
...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 sum of the opposite angles** to the tangent of half their difference.'" This half difference added to half the sum, gives the greater,... | |
| 1829
...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, gives the greater,... | |
| 1829
...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 - 1830 - 120 páginas
...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 - 1830 - 300 páginas
...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 - 1831 - 370 páginas
...sines of their opposite angles. It follows, therefore, from the preceding proposition, (Alg. 389.) that **the sum of any two sides of a triangle, is to their...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 - 1831 - 370 páginas
...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 Playfair - 1832 - 333 páginas
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. **The sum of any two sides of a triangle is to their difference,** at the tangent of half the sum of the angles opposite to those sides, to the tangent of half their... | |
| John Playfair - 1833 - 333 páginas
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV.. **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... | |
| |