| Nathaniel Bowditch - Nautical astronomy - 1826 - 782 pages
...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,... | |
| William Galbraith - Astronomy - 1827 - 412 pages
...triangle when the two sides and contained angle are given. I. As the sum of the given sides, Is to **their difference ; So is the tangent of half the sum of the** opposite angles, To the tangent of half their difference. Half the difference added to half the sum... | |
| Alexander Ingram - Mathematics - 1830 - 462 pages
...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 - 520 pages
...other radius. (Art. 1 19.) THEOREM II. 144. In a plane triangle, AS THE SUM OF ANY TWO OF THE SIDES, To **THEIR DIFFERENCE ; - 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... | |
| William Galbraith - Astronomy - 1834 - 454 pages
...plane triangle when the two sides and contained angle are given. I. As the sum of the given sides Is to **their difference; So is the tangent of half the sum of the** opposite angles To the tangent of half their difference. Half the difference added to half the sum... | |
| Abel Flint - Geometry - 1835 - 370 pages
...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 HALF... | |
| Mathematics - 1836 - 488 pages
...as their opposite sides. Theorem II. In any plane triangle, As the sum of any two of the sides, to **their difference ; so is the tangent of half the sum of the** opposite angles, to the tangent of half their difference. .Theorem III. As the largest side, to the... | |
| Thomas Holliday - Surveying - 1838 - 404 pages
...contained between them are given, to find the rest. u2 Rule.—As the sum of the two given sides is to **their difference, so is the tangent of half the sum of the** unknown angles to the tangent of half their difference: this half difference being added to half the... | |
| Jeremiah Day - Geometry - 1839 - 432 pages
...other radius. (Art. 119.) THEOREM II. 144. In a plane triangle, As THE SUM OF ANY TWO OF THE SIDES, To **THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE** OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is... | |
| Enoch Lewis - Conic sections - 1844 - 234 pages
...bisecting the vertical angle ; it will be, as the cotangent of half the sum of the angles at the base **is to the tangent of half their difference, so is the tangent of half the** vertical angle to the tangent of the angle formed by the perpendicular and the arc bisecting the vertical... | |
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