 | 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
...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 - 488 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 - 338 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 - Surveying - 1838 - 348 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 - 404 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 - 340 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 - 434 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... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...of the said unknown angles ; and using the following ratio, we have — As the sum of the two given sides Is to their difference, So is the tangent of half the sum of their opposite angles To the tangent of half the difference of the same angles. Now the half sum of... | |
 | Enoch Lewis - Conic sections - 1844 - 240 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... | |
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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. 
