 | Jeremiah Day - Logarithms - 1848 - 354 pages
...perpendicular to BG. (Euc. Def. 1. 1.*) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum; the... | |
 | Jeremiah Day - Geometry - 1851 - 418 pages
...perpendicular to BG. (Euc. Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...of them and 45°. PROP. IV. THEOR. 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 ofhalftheir difference. Let ABC be any plane triangle ; CA+AB : CA— AB : : tan. £ (B+C) : tan. £... | |
 | John Playfair - Geometry - 1860 - 334 pages
...PROP. IV. THEOR. The sum of any two sides of a triangle is to their difference, as the tangent of naif the sum of the angles opposite to those sides, to the tangent ofhalft\tv difference. CA+AB : CA—AB : : sin. B+sin. C : sin. B—sin. C. But, by the last, sin.... | |
 | Samuel Alsop - Surveying - 1865 - 440 pages
...enunciated in general terms; thus, As the sum of two sides of a plane triangle'is to their difference, so is the tangent of half the sum of the angles opposite those sides to the tangent of half the difference of those angles. Let ABC (Fig. 47) be the triangle... | |
 | Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...(A — B) *• ; which shows that, in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. We have A + B=180° — C; hence J(A+ B) = 90° — }C:... | |
 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...founded on the following theorem : THEOREM IV. As the sum of any two sides is to their difference, so is the tangent of half the sum of the angles opposite these sides to the tangent of half their difference. Proof. From the equation b : o :: sin ft : sin... | |
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Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the remaining... 
