| Abel Flint - 1838 - 334 páginas
...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... | |
| Jeremiah Day - 1839 - 370 páginas
...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 páginas
...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... | |
| John Playfair - 1842 - 317 páginas
...then will the radius be to the tangent of the difference between that angle and half a right angle, as **the tangent of half the sum of the angles, at the base** of the triangle to the tangent of half their difference. Let ABC be a triangle, the sides of which... | |
| Enoch Lewis - 1844 - 228 páginas
...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... | |
| 1845
...sine of half their difference: also, that the base is to the sum of the other two sides as the cosine **of half the sum of the angles at the base, to the** cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle... | |
| Nathan Scholfield - 1845 - 232 páginas
...sine of half their difference : also, that the base is to the sum of the other two sides as the cosine **of half the sum of the angles at the base, to the** cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle... | |
| Nathan Scholfield - 1845
...Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine **of half the sum of the angles at the base, to the** sine of half their difference : also-, that the base is to the sum of the other two sides as the cosine... | |
| Nathaniel Bowditch - 1846 - 451 páginas
...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, describe... | |
| Dennis M'Curdy - 1846 - 138 páginas
...J(AC-(AB): tan. J(AC—AB). QED 4 Th. In any triangle, the sum of two sides is to their difference, as **the tangent of half the sum of the angles at the base** is to the tangent of half their difference. Given the triangle ABC, the side AB being greater than... | |
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