 | Jeremiah Day - Geometry - 1824 - 440 pages
...119.) THEOREM II. lit. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDE*. To THEIR DIFFERENCE J SO IS THE TANGENT OF HALF THE SUM OF 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... | |
 | Abel Flint - Surveying - 1825 - 252 pages
...solution of this CASE depends on the following PROPOSITION. In every Plane Triangle, as the sum of any two Sides is to their difference, so is the Tangent of half the sum of the two opposite Angles to the Tangent of half the difference between them. Add this half difference to... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 764 pages
...the tame angla. Thus, in the triangle ABC, if we call AB the base, it will be as the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, ВАС, to the tangent of half their difference. Dan. With the longest leg CB as radius,... | |
 | Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...sines of the opposite angles. (73.) The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference. •* ^74.) Formulae for the sine, cosine, tangent, and cotangent of half the difference of any two... | |
 | 1829 - 530 pages
...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 sum of the opposite angles to the tangent of half their difference." This half difference added to half the sum, gives the greater, and subtracted from the half sum, gives... | |
 | Alexander Ingram - Mathematics - 1830 - 458 pages
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sura of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference. Having thus found the half difference, add... | |
 | Jeremiah Day - Measurement - 1831 - 394 pages
...angle greater than 45° : And radius is to the tangent of the excess of this angle above 45° ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. In the triangle ABC, (Fig. 39.) let the sides AC and AB, and the angle A be given. Through A draw DH... | |
 | Jeremiah Day - Logarithms - 1831 - 418 pages
...angle greater than 45° : And radius is to the tangent of the excess of this angle abort 45° ; os the tangent of half the sum of the opposite angles, to the tangent of ha1f their difference. In the triangle ABC, (Fig. 39.) let the sides AC and AB, and the an<rle A be... | |
 | Jeremiah Day - Measurement - 1831 - 520 pages
...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 <if half their difference. Therefore, R :tan(ACH-45°)::tan|(ACB + B) : tan iHACB^B) Ex. In the triangle... | |
 | John Radford Young - Astronomy - 1833 - 286 pages
...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 of the sides . 22 21. Remarks on these... | |
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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
