 | Abel Flint - Geometry - 1835 - 366 pages
...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 TO HALF... | |
 | 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... | |
 | Thomas Holliday - Surveying - 1838 - 404 pages
...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 - 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 OF THE TWO OPPOSITE ANGLES TO THE TANGENT OF HALF THE DIFFERENCE BETWEEN THEM. ADD THIS HALF DIFFERENCE TO HALF... | |
 | Robert Gibson, James Ryan - Surveying - 1839 - 452 pages
...20, sect. 4). But the wholes are as their halves; that is, AH i IH ii CE i ED; that is, as the sum of the two sides AB and BC is to their difference,...and C to the tangent of half their difference. QED ny right-lined plane triangle ABD, the base AD trill be to the tum of er sides AB, BD as the difference... | |
 | 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
...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... | |
 | 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 radius,... | |
 | John Gummere - Surveying - 1846 - 566 pages
...133.2. CASE 3. Two sides and the included angle being given, to find the other angles and side. RULE. So is the tangent of half the sum of the two unknown angJes, To the tangent of half their difference.* This half difference of the two unknown angles, added... | |
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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. 
