 | Adrien Marie Legendre - 1874 - 500 σελίδες
...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 hy... | |
 | William Hamilton Richards - 1875 - 216 σελίδες
...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... | |
 | Cornell University - 1875 - 1012 σελίδες
...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 - 1875 - 284 σελίδες
...£(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 - 1876 - 204 σελίδες
...proposition, therefore, applies in every case. BOOK Ш. 2. In any plane triangle, the sum of any two sides is to 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 - 1876 - 254 σελίδες
...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 - 1876 - 130 σελίδες
...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... | |
 | Edward Olney - 1877 - 220 σελίδες
...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... | |
 | Eugene Lamb Richards - 1878 - 134 σελίδες
...since C is a right angle, its sine is 1 (Art. 35). Also 49. In any triangle, the SUM of any TWO RIDES is to their DIFFERENCE as the TANGENT of HALF the sum of the OPPOSITE ANGLES 18 to the TANGENT of HALF their DIFFERENCE. Let A CB be any triangle. Then EC+CA _... | |
 | 1878 - 710 σελίδες
...TRIGONOMETRY. Scientific Clatt. 1. Demonstrate, that in any plane triangle, the sure of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 2. Give the limiting values of the circular... | |
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C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 
