 | Robert Simson - Trigonometry - 1806 - 546 pages
.... * Let ABC be a plane triangle, live sura of any two sides, AB, AC will be to their difiV.-rt.-nce as the tangent of half the sum of the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
 | Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...AB : BC :: S,C : S, A. PROP. X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. In the triangle ABC, AB + AC : AB-AC : : T,°-±?: 2 IT" O—... | |
 | John Dougall - 1810 - 734 pages
...to EF; AD, however, is the sum of the sides, and AE their difference; while DC was shown above to be the tangent of half the sum of the angles at the base, and EF is the tangent of rulf their difference ; the proposition is, therefore, demonstrated. PROP.... | |
 | William Enfield - Astronomy - 1811 - 476 pages
...triangle SRM, the sides RS, RM, being thus found, the sum of the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the base RSM, RMS, is to the tangent of half their difference. To half the sum add half the difference, and... | |
 | Charles Butler - 1814 - 582 pages
...the preceding article. 72. In a plane triangle, the sum of any two sides : is to their difference : : as the tangent of half the sum of the angles at the base : to the tangent of half the difference. Let ABC be a triangle, from € as a centre with the least... | |
 | Euclides - 1816 - 588 pages
...are parallel (2. 6.), EC is to CF, as EB to BG; that is, the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. PROP. IV. FIG. 18. IN any plane triangle BAG, whose two sides... | |
 | Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...triangle it will be, as the sum of the sides about the vertical angle, is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. By the preceding prop. AC : BC :: sin B : sin A, .-. by comp.... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...supplement are the same. PROP. X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difi ference. In the triangle ABC, AB+AC : AB— AC : : From the vertex... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...then will the radius be to the tangent of the difference between that angle and half a right angle, as the tangent of half the sum of 'the angles at t,he base of the triangle to the tangent of half their difference. Let ABC be a triangle, the sides of which are BC and CA, and... | |
 | Thomas Leybourn - Mathematics - 1819 - 430 pages
...proof. 8. Prove, geometrically, that in any plane triangle, the sum of the sides is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. 9. Shew that tan.3 60 = 3 tan. 60 to rad. == i. 10. P and... | |
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In any plane triangle, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 
