| William Galbraith - Astronomy - 1834 - 428 pages
...45. In a 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... | |
| Mathematics - 1836 - 472 pages
...are 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... | |
| Abel Flint - Geometry - 1837 - 272 pages
...30'. CASE III. Two sides and their contained angle given, to find the other angles and side. Fig. 48. **The solution of this CASE depends on the following...DIFFERENCE TO HALF THE SUM OF THE ANGLES, AND YOU WILL** RAVE THE GREATER ANGLE, AND SUBSTRACT THE HALF DIFFERENCE FROM THE HALF SUM, AND YOU WILL HAVE THE... | |
| Abel Flint - Geometry - 1838 - 334 pages
...CASE depends on the following PROPOSITION. IN EVERY PLANE TRIANGLE, AS THE SUM OF ANY TWO SIDES ISTO **THEIR DIFFERENCE, SO IS THE TANGENT OF HALF THE SUM...THE ANGLES, AND YOU WILL HAVE THE GREATER ANGLE, AND** SUBSTRACT THE HALF DIFFERENCE FROM THE HALF SUM, AND YOU WILL HAVE THE LESSER ANGLE. In the triangle... | |
| Thomas Holliday - Surveying - 1838 - 80 pages
...the angle 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... | |
| Abel Flint - Geometry - 1839 - 334 pages
...sides and their contained angle given, to find the other angles and side, fig. 48. The solution &f **this CASE depends on the following PROPOSITION. IN...THEM. ADD THIS HALF DIFFERENCE TO HALF THE SUM OF** THB .MJGLES, AND YOU WILI, HAVE THE GREATER ANGLE, AND SXTBSTRACT THE HALF DIFFERENCE FROM THE HALF... | |
| Jeremiah Day - Geometry - 1839 - 370 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 - 228 pages
...cos CAD : cos CAB : : tan AD : tan AB. QED ART. 72. As the sum of the sines of any two unequal arcs **is to their difference, so is the tangent of half the sum of** those arcs, to the tangent of half their difference. Let AB, AC be the arcs ; L the centre of the circle... | |
| Nathaniel Bowditch - 1846 - 451 pages
...same angles. Thus, in the triangle ABC, if we call AB the base, it will l>e, 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 dinerence. DH Dem. With the longest leg, CB, as radius,... | |
| Jeremiah Day - Logarithms - 1848 - 153 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 ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their... | |
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