 | William Thomas Read - 1862 - 144 pàgines
...angle, to find the rest. Proposition HI. may here be written as a rule. " 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. And the half difference added to half the... | |
 | Olinthus Gregory - 1863 - 482 pàgines
...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 equidifferent arcs, it will... | |
 | Samuel Alsop - 1865 - 440 pàgines
...180° : the remainder will be the sum of the remaining angles. Then, As the sum of the given sides is to their difference, so is the tangent of half the sum of the remaining angles to the tangent of half their difference. This half difference added to the half sum... | |
 | William Davis Haskoll - 1868 - 252 pàgines
...angle will be acute. When two sides and their included angle are given. — As the sum of any two sides is to their difference, So is the tangent of half the sum of their opposite angles, to the tangent of half their difference. Then the half difference of these angles,... | |
 | William Thomas Read - 1869 - 176 pàgines
...DC a 1. Sin В Or Sin A : sin B : : a : Ъ. (2) In any plane triangle, as the sum of any two sides is to their difference, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference. From the preceding, we have, a^_ sin A Ъ... | |
 | Horatio Nelson Robinson - 1875 - 288 pàgines
...sum 71° 50' 48" Here we will apply the following theorem in trigonometry. As the sum of two sides is to their difference, so is the tangent of half...the base, to the tangent of half their difference. Let x= the half difference between D and C. Then, Or, 3268 817 412 103 Log. 103 Tan. 71° 50" 48" tan.... | |
 | William Hamilton Richards - 1875 - 216 pàgines
...150° T — 29° 3'. and \ (E + F) = 14° 31' 30". The sum of the two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Ar. co. Log. (e + /) 3922'92 = 6'406347 Log. (e -/) 1769'86 = 3'247939 Log. tan. i (E + F) 14° 31'... | |
 | Daniel Kinnear Clark - 1878 - 1022 pàgines
...the included angle are gii'cn. RULE 4. To find the other side: — 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 their difference — add this half difference to the half... | |
 | William Findlay Shunk - 1880 - 362 pàgines
...will be the sum of the other two angles. Then, by proposition 3, — As the sum of the given sides is to their difference, So is the tangent of half the sum of the remaining angles to the tangent of half their difference. Half the sum of the remaining angles added... | |
 | Simon Newcomb - 1882 - 188 pàgines
...a more convenient method founded on the following theorem : THEOREM IV. As the sum of any two sides is to their difference, so is the tangent of half the sum of the angles opposite these sides to the tangent of half their difference. Proof. From the equation 5 : c :: sin/?... | |
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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. 
