 | 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... | |
 | 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... | |
 | Jeremiah Day - Measurement - 1831 - 394 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... | |
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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. 
