 | William Chauvenet - 1852 - 268 pages
...written a — (22°) v J and we may infer the same relation between 4, c, J?, C and a, c, A, C. 119. The square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the... | |
 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...Sin. В °r' с ~ Sin. C' ie, b : с : : Sin. В : Sin. C, (A) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the... | |
 | Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...Sin. В ог' с - ЖГс' ie, b : с :: Sin. В : Sin. С, (А) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...A-\- sin B : sin ^4 — sin B : : .-. a-\-b : a — b : : tan \(A-}-B) : tan %(A — B). 97. Theorem. The square of any side of a triangle is equal to the sum of the squares of the other sides, minus twice their product into the co-sine of their included angle.... | |
 | Aaron Schuyler - Measurement - 1864 - 512 pages
...tan£(^+Б) : tan\(AB). ... a + b : a — b : : tan \(A+B) : tan %(A— B). 97. Theorem. The sqmre of any side of a triangle is equal to the sum of the squares of the other sides, minus twice their product into the co-sine of their included angle.... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...A-\- sin B : sin A — sin В : : . • . a + 6 : a — b : : tan — B). •' tan K^~ -0)97. Theorem. The square of any side of a triangle is equal to the sum of the squares of the other sides, minus twice their product into the co-sine of their included angle.... | |
 | Henry Nathan Wheeler - 1886 - 250 pages
...theory of proportions, — a -f- b sin A -f- sin B In like manner — C) r _ ' a' b — c~~ § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their... | |
 | Henry Nathan Wheeler - 1876 - 128 pages
...~ In like manner _ tanj (B + C) nn(1 _ ' _ _ a — c"~tani(A — C)' 6 — c tani(B — C)' § 73. The square 'of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their... | |
 | Harvard University - 1876 - 554 pages
...of halt' the sum of the opposite angles is to the tangent of half their difference. 10. Prove that the square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the... | |
 | George Albert Wentworth - Trigonometry - 1882 - 160 pages
...— ZabcosC. The three formulas have precisely the same form, and the law may be stated as follows : The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of... | |
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The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle. 
