 | William Nicholson - 1821 - 356 sider
...obtuse, and the side C D. To the sine DC 56.88 1.75485 Axiom III. In every plane triangle, it will be as the sum of any two sides is to their difference ; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. Which half difference, being added... | |
 | William Nicholson - 1821 - 356 sider
...9.72198 1.75485 The side BC BD Sum 109 76 109 76 .Axiom III. In every plane triangle, it will be us the sum of any two sides is to their difference ; so is the tangent of half the sum of the angles opposite there, to the tangent of half their difference. AVhich half difference, being added... | |
 | 1821 - 708 sider
...the other sides to the sine of its opposite angle. THEOREM III. In every plane triangle, it will be, as the sum of any two sides is to their difference, so is the tangtnt of half the sum of the two opposite angles to the tangent 'of half their difference (by art.... | |
 | Edward Riddle - 1824 - 572 sider
...triangle. Or the angles opposite the given sides may be determined as follows. As the sum of the 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, (Trig. Prop. 6.) And this half difference of the angles added to... | |
 | Abel Flint - 1825 - 252 sider
...Angles and Side. Fig. 49. 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... | |
 | Nathaniel Bowditch - 1826 - 764 sider
...the tame angla. Thus, in the triangle ABC, if we call AB the base, it will be 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 difference. Dan. With the longest leg CB as radius,... | |
 | William Galbraith - 1827 - 412 sider
...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... | |
 | 1829 - 196 sider
...the remaining side and angle, 1! i ii. As the SUM of the TWO GIVEN SIDES, is to THEIR DIFFERBNCE ; so is the TANGENT OF HALF THE SUM OF THEIR OPPOSITE ANGLES to the tangent of HALF THE DIFFERENCE of those angles. Then if we add the half difference of the angles, so found, to their... | |
 | Abel Flint - 1830 - 322 sider
...angles and side. Fig. 48. 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 TANQENT OF HALF THE SUM OF THE TWO OPPOSITE ANGLES TO THE TANGENT OF HALF THE DIFFERENCE BETWEEN THEM.... | |
 | Alexander Ingram - 1830 - 458 sider
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sura 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. Having thus found the half difference,... | |
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To find the other side: — 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 their difference... 
