| Philip Ronayne - Algebra - 1717 - 478 pages
...Eucl. El.) proportional ; E С --ЕВ >; FA - FG; that is in Words, half the Sum of the Legs, is to **half their difference, as the Tangent of half the Sum of the** oppofice Angles, is to the Tangent of half their difference; Fer i Sum -(- •', difference of any... | |
| John Ward (of Chester.) - Mathematics - 1747 - 516 pages
...6 Eucl. £7. ) proportional ; EC:EB : : FA : FG ; that is in Words, half the Sum of the Legs is to **half their Difference, as the Tangent of half the Sum of the** oppofite Angles is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore... | |
| Asiatick Society (Calcutta, India) - Asia - 1811 - 598 pages
...Yerracondah, and the observed angles PSY and PYS, we have, the tangent of half the sum of the first, **to the tangent of half their difference, as the tangent of half the sum of the** second, to tangent of 2° 54' 25"-9^i their half difference : from which we get the greater angle at... | |
| Francis Nichols - Plane trigonometry - 1811 - 162 pages
...angle to the opposite side, or base, the cotangent of half the sum of the angles at the base will be **to the tangent of half their difference, as the tangent of half the sum of the** segments of the vertical angle is to the tangent of half their difference; that is, cot. | (A + B)... | |
| Jeremiah Day - Logarithms - 1815 - 172 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 appKed to the solution of oblique... | |
| Jeremiah Day - Mathematics - 1815 - 392 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 - Geometry - 1824 - 440 pages
...sum, and FH to the di/erencc 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 of half their difference. Therefore, R : Tan(ACH-45°)::Tan^(ACB-fB) : Tan^(ACB.^B)... | |
| Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...(A + B) : tang i (^ — B), which may be enunciated thus ; The sum of two sides of a triangle is to **their difference, as the tangent of half the sum of the opposite angles** to tht tangent of half their difference. Every term in this proportion is known but A — B, for if... | |
| Dionysius Lardner - Plane trigonometry - 1828 - 430 pages
...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 - 536 pages
...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,... | |
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