| Jeremiah Day - 1831 - 370 páginas
...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.) is to... | |
| Olinthus Gregory - 1833 - 427 páginas
...the tangent of the sum or difference of the arcs. 11. As the sum of the sines of two unequal arcs, **is to their difference ; so is the tangent of half the sum of** those two arcs to the tangent of half their difference. 12. Of any three equidifferentarcs,it will... | |
| William Galbraith - 1834 - 428 páginas
...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 sum... | |
| Abel Flint - 1835 - 334 páginas
...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... | |
| Euclid, Robert Simson - 1835 - 513 páginas
...difference. Let ABC be a plane triangle, the sum of any two sides AB, AC will be to their difference as **the tangent of half the sum of the angles at the base** ABC, ACB, to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
| 1836 - 472 páginas
...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... | |
| John Playfair - 1836 - 114 páginas
...difference. Let ABC be a plane triangle, the sum of any two sides, AB, AC will be to their difference as **the tangent of half the sum of the angles at the base** ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
| John Playfair - 1837 - 318 páginas
...will the radius lie 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... | |
| Andrew Bell - 1837 - 240 páginas
...of half their difference. 3. The base of a triangle is to the difference of its sides, as the sine **of half the sum of the angles at the base to the** sine of half their difference. 4. The base of a triangle is to the difference of its segments, as the... | |
| Thomas Holliday - 1838 - 80 páginas
...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... | |
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