 | Jeremiah Day - Measurement - 1831 - 394 pages
...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 applied to the solution of oblique... | |
 | Jeremiah Day - Measurement - 1831 - 520 pages
...THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... | |
 | John Radford Young - Astronomy - 1833 - 286 pages
...and cosine of their aum and difference . / .19 ARTIcLE. PAGE. 19. In a plane triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference . . . .21 •20. Formulas for determining an angle in terms... | |
 | Euclid - 1835 - 540 pages
...half the difference, and it will give the less. PROP. III. FIG. 8. 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 their difference. Let ABC be a plane triangle, the sum of... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...difference; and since BC, FGare parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the fides 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. F1G. 8. In a plane triangle,... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...b + c=2p; we have a + 6 — c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their 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... | |
 | John Playfair - Geometry - 1836 - 148 pages
...triangle, any three being given, the fourth is also given. PROP. III. i 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 their difference. Let ABC be a plane triangle, the sum of... | |
 | 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... | |
 | 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,... | |
 | 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:... | |
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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. 
