 | 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 - 600 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 - Measurement - 1815 - 388 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 - 434 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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In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 
