| Harvard University - 1873 - 732 pages
...proportional to the sines of the opposite angles. (4.) The sum of any two sides of a plane triangle ia **to their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. 4. Two sides of a plane oblique triangle... | |
| Adrien Marie Legendre - Geometry - 1874 - 512 pages
...have tl1e following principle : In any plane triangle, the sum of the sides including either angle, **is to their difference, as the tangent of half the sum of the** two other angles, is to the tangent of half their difference. The half sum of the angles may he found... | |
| William Hamilton Richards - 1875 - 216 pages
...given angle from 180°, E + F = 180° 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.... | |
| Cornell University - 1875 - 1012 pages
...cos'^r — sin'.r=:2cosa;r — 1 = I — 2sinV. 4. Prove that in any plane triangle the sum of cither **two sides is to their difference as the tangent of half the sum of the** opposite angles is to the tangent of hall' their difference. 5. Given two sides of a triangle equal... | |
| Aaron Schuyler - Measurement - 1875 - 276 pages
...£(Л + ß) : tan £(Л — B). Hence, In any plane triangle, the sum of the sides inchuling an angle **is to their difference as the tangent of half the sum of the** other two angles is to the tangent of half their difference. We find from the proportion, the equation... | |
| Benjamin Greenleaf - Trigonometry - 1876 - 208 pages
...the results would have been the same. The proposition, therefore, applies in every case. BOOK Ш. 2. **In any plane triangle, the sum of any two sides is...their difference as the tangent of half the sum of the** opposite angles is to the tangent of half their difference. For, by (90), a : 6 : : sin A : sin B;... | |
| Henry Nathan Wheeler - Trigonometry - 1876 - 254 pages
...sides of any triangle are proportional to the sines of { 72. The surn of any two sides of a triangle **is to their difference as the tangent of half the sum of the** opposite angles Is to the tangent of half their difference . . 78 § 73. The square of any side of... | |
| Henry Nathan Wheeler - Plane trigonometry - 1876 - 130 pages
...that sin B is equal to the sine of its supplement CBP. § 72. The sum of any two sides of a triangle **is to their difference as the tangent of half the sum of** tlie opposite angles is to the tangent of half their difference. From [67] we get, by the theory of... | |
| Elias Loomis - Geometry - 1877 - 458 pages
...of ABC, their sines are equal, Art. 13. Therefore sin. ABC : sin. C : : AC : AB. THEOREM II. . . 54. **In any plane triangle, the sum of any two sides is to their** differenee as the tangent of half the sum of the opposite angles is to the tangent of half their difference.... | |
| Edward Olney - Trigonometry - 1877 - 220 pages
...horizontal parallax. PLANE TR1GONOMETRY. 86. Prop.— The sum of any two sides of aplane triangle 's **to their difference, as the tangent of half the sum of the angles** oppos'te is to the tangent of half their difference. DEM. — Letting a and b represent any two sides... | |
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