| John Playfair - 1846 - 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... | |
| Jeremiah Day - 1848 - 153 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 ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their... | |
| James Elliot - 1851
...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,... | |
| Sir Henry Edward Landor Thuillier - 1851 - 718 páginas
...wholes are as their halves, or AH : IH : : CE :ED, that is, as the sum of the two sides AB and BC, **is to their difference ; so is the tangent of half the sum of the** two unknown angles A and C, to the tangent of half their difference. QED THEO. III. In any plane triangle... | |
| Alexander Ingram - 1851
...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... | |
| 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... | |
| H.N. ROBINSON - 1851
...Demonstrate that radius is to the tangent of the difference between this angle and half a right angle, as **the tangent of half the sum of the angles at the base** of the triangle, is to the tangent of half their difference, To obtain that certain angle, we must... | |
| John William Norie - 1852
...II. When two Sides and the Angle contained between them are given. 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 added to half the sum... | |
| Jeremiah Day - 1853 - 5 páginas
...radius. (Art. 119.) ff THEOREM II. /? 144. In a plane triangle, \. As THE SU^I OF ANY TWO OF THE SIDES, **To THEIR DIFFERENCE ] So IS THE TANGENT OF HALF THE SUM OF THE** OPPOSITK ANGLKS; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is... | |
| Andrew Duncan (surveyor.) - 1854 - 121 páginas
...their included angle are given to find the other angles and side. RULE. — As the sum of the sides **is to their difference so is the tangent of half the sum of the** opposite angles to the tangent of half the difference ; this half difference added to half the sum... | |
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