| 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.)... | |
| 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... | |
| Abel Flint - Geometry - 1835 - 368 pages
...the other angles and side. The 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... | |
| 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... | |
| 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... | |
| 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.)... | |
| Abraham Crocker - 1841 - 486 pages
...II Rule for the Second Case. As the sum of the two given sides is to the difference of those sides, **so is the tangent of half the sum of their opposite angles, to the tangent of** hajf their difference. This half-difference, added to the half sum, will give the greater angle * :... | |
| 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...sum of their opposite angles To the tangent of half** the difference of the same angles. Now the half sum of any two quantities increased by their half difference... | |
| 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... | |
| Nathaniel Bowditch - 1846 - 854 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... | |
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