 | John Playfair - Euclid's Elements - 1837 - 332 pages
...difference between either 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 of half their difference. Let ABC be any plane triangle ; CA+AB : CA-AB... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...sine of a right angle is equal to the radius. PROP. III. 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, is to the tangent of half their difference. Let ABC be a triangle, a, b any two of... | |
 | Charles Davies - Navigation - 1837 - 342 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...demonstrated that AB : BC = sin C : sin A. PROPOSITION VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of me angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... | |
 | Jeremiah Day - Geometry - 1838 - 416 pages
...equal to the sum, and FH to the difference 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... | |
 | Charles William Hackley - Trigonometry - 1838 - 338 pages
...tan £ (A -f- B) : tan \ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. This proportion is employed when two sides... | |
 | Adrien Marie Legendre - Geometry - 1839 - 372 pages
...— 6=2p — 2b; hence THEOREM V. fit every rectilineal triangle, the sum of two sides is to tlieir difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin A (Theorem III.). Hence, AB +... | |
 | Thomas Keith - 1839 - 498 pages
...chords of double their opposite angles. PROPOSITION IV. (115) In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of their opposite angles is to the tangent of half their difference, Let ABC be any triangle ; make BE... | |
 | Jeremiah Day - Geometry - 1839 - 434 pages
...equal to the sum, and FH to the difference 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... | |
 | Charles Davies - Surveying - 1839 - 376 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angk, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of haJ/ their difference. 58. Let ACB be a triangle : then will AB+AC:... | |
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In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. 
