| 1863
...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 - 428 páginas
...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 - 184 páginas
...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 - 154 páginas
...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... | |
| 1875
...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
...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 - 984 páginas
...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 - 318 páginas
...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 - 168 páginas
...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/?... | |
| William Hamilton Richards - 1883 - 226 páginas
...angle are known, and the third side is required. 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.** Let the known sides be / 1076-53 and e 2846-39, and B the contained angle 150° 7', to find the other... | |
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