 | Euclides - 1860 - 288 pages
...base to the cosine of half their difference. 13. The base of a triangle is to the difference of its sides, as the sine of half the sum of the angles at the base to the sine of half their difference. 14. The base of a triangle is to the difference of its segments, as the sine of the vertical angle... | |
 | Euclides - 1860 - 142 pages
...cos. DEC : cos. ECB. EXERCISE XIII. — THEOREM. The base of a triangle is to the difference of its sides as the sine of half the sum of the angles at the base to sine of half their difference. Let ABC be any triangle of which BC is the base, then BC : AB - AC =... | |
 | Olinthus Gregory - 1863 - 482 pages
...will be, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. 16. In any plane triangle it will be, as the co'sine of the difference... | |
 | Horatio Nelson Robinson - 1875 - 288 pages
...following theorem in trigonometry. As the sum of two sides is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let x= the half difference between D and C. Then, Or, 3268 817 412... | |
 | William Hamilton Richards - 1875 - 216 pages
...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... | |
 | William Findlay Shunk - 1880 - 362 pages
...trianf/le, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half ( the difference... | |
 | William Hamilton Richards - 1883 - 256 pages
...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... | |
 | William Findlay Shunk - 1890 - 360 pages
...triangle, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half the difference of... | |
 | William Findlay Shunk - 1908 - 386 pages
...triangle, as the sum of the sides about the vertical angle is to their difference, so is the tangent of half the sum of the angles at the base to the tangent of half their difference. 4. In any plane triangle, as the cosine of half the difference of... | |
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Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also, that the... 
