 | Enoch Lewis - 1844 - 240 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... | |
 | Nathaniel Bowditch - 1846 - 854 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,... | |
 | 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, add... | |
 | 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... | |
 | Sir Henry Edward Landor Thuillier - 1851 - 826 páginas
...between them, to find the other two angles and the third side. 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. Half the difference thus found added to 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... | |
 | 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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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
