 | Jeremiah Day - Logarithms - 1815 - 172 pages
...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 difference; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem... | |
 | Jeremiah Day - Measurement - 1815 - 388 pages
...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 difference; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem... | |
 | John Playfair - 1819 - 354 pages
...difference as the radius to the tangent of the difference between either of them and 4 So. 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... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...radius to the tangent of the difference between either of them and 45o. * PROP. IV. The sum of any troo 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... | |
 | Rev. John Allen - Astronomy - 1822 - 516 pages
...ratios for the former, the cotangent of the half sum of the angles A and ABC is to the tangent of half their difference, as the tangent of the half sum of the angles ACD and BCD is to the tangent of half their difference; and, forming rectangles from the two first... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...40, page 41) AD+BD : AC + BC : : AC - BC : AD - BD. TRIGONOMETRY. — THEOREM 2. 234. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle... | |
 | Jeremiah Day - Geometry - 1824 - 440 pages
...sines of their opposite angles. It follows, therefore; from the preceding proposition, (Alg. 339.) 'et 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 thesecoud theorem... | |
 | Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...proportion, a + 6 : a — 6 : : tang \ (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... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...differenee as the radius to the tangent of the differenee between either of them and 45°. PROP. IV. The sum of any two sides of a triangle is to their differeuee, as the tangent of half the sum of the angles opposite to those sides, to the tangent of... | |
 | 1829 - 538 pages
...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... | |
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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. 
