 | Euclid, John Playfair - 1846 - 334 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 - 354 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 - 162 páginas
...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 - 826 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 - 202 páginas
...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 - 418 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, (Fig. 25.) is... | |
 | Horatio Nelson Robinson - 1851 - 96 páginas
...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 - 844 páginas
...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 - 288 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 - 156 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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AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. 
