| Thomas Holliday - 1838
...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... | |
| Jeremiah Day - 1839 - 370 sider
...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 - 1842 - 1089 sider
...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 - 1844 - 228 sider
...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 sider
...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 - 1848 - 153 sider
...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... | |
| James Elliot - 1851
...the remainder will be the sum of the two required angles. Then say,— As the sum of the two given **sides is to their difference, so is the tangent of half the sum of the two** required angles, to the tangent of half their difference. Having found the said half difference, add... | |
| Alexander Ingram - 1851
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sum 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 (Theor. 4. Trig.) Having thus found the half... | |
| Sir Henry Edward Landor Thuillier - 1851 - 718 sider
...angle between them, to find the other two angles and the third side. 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. Half the difference thus found added to half... | |
| Jeremiah Day - 1851
...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, (Fig. 25.) is... | |
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