 | Nautical astronomy - 1821 - 708 pages
...angle*. Thus, in the triangle ABC, if we call AB the base, it will he as the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, BAG', to the tangent of half their difference. Dem. With the longest leg CB as radius,... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...sine DC 56.88 1.75485 Axiom III. In every plane triangle, it will be as the sum of any two sides is to their difference ; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. Which half difference, being added... | |
 | William Nicholson - Natural history - 1821 - 356 pages
...Sum 109 76 109 76 .Axiom III. In every plane triangle, it will be us the sum of any two sides is to their difference ; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. AVhich half difference, being added... | |
 | Abel Flint - Surveying - 1825 - 252 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...the Angles and you will have the greater Angle, and subtract the half difference from the half sum and you will have the lesser Angle. In the Triangle... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...THEOREM HI. . In every plane triangle, it will be, as the sum of any two sides is to their difference, su is the tangent of half the sum of the two opposite angles to the tangent 'tif half their difference (by art. u'J, Geom.) THEOREM IV. As the base of any plane triangle is to... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 764 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... | |
 | Abel Flint - Surveying - 1830 - 322 pages
...PROPOSITION. IN EVERY PLANE TRIANGLE, AS THE SUM OF ANY TWO SIDES IS TO THEIR DIFFERENCE, SO IS THE TANQENT OF HALF THE SUM OF THE TWO OPPOSITE ANGLES TO THE...THE ANGLES AND YOU WILL HAVE THE GREATER ANGLE, AND SUBTRACT THE HALF DIFFERENCE FROM THE HALF SUM AND YOU WILL HAVE THE LESSER ANGLE. In the triangle... | |
 | Alexander Ingram - Mathematics - 1830 - 458 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... | |
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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. 
