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" In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it. "
Plane and Spherical Trigonometry - Page 73
by Henry Nathan Wheeler - 1876 - 208 pages
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An Introduction to Plane and Spherical Trigonometry

Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...(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 angle included by them. First, let the triangle А В С be acute...
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The Elements of Plane and Spherical Trigonometry ...

Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...(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 anale included by them. First, let the triangle А В С be acute...
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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...H THEOREM. 91. In any triangle the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides by the projection on it of the other. Def. The projection of one line on another...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - 1876 - 128 pages
...— 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...draw PC perpendicular to c. In each figure, then, but PB = PA-fC — — AP-fc (v. § 3, d.) .•.FB2 = AP2 — 2APC + C3, [69] but cos A = — , o .•....
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - Plane trigonometry - 1876 - 130 pages
...of half their difference . . 73 § 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...those sides into the cosine of their included angle 73 § 74. Formula for the side of a triangle, in terms of the cosines of the adjacent angles and the...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - Plane trigonometry - 1877 - 128 pages
...B) -_tan^ (B-fC) ' ~ ~ — 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...into the cosine of their included angle. FIG. 43. Through c in the triangle ABC (Figs. 43, 44, and 45) draw PC perpendicular to c. In each figure, then,...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...XXVIII. 68 1 In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - Plane trigonometry - 1878 - 198 pages
...of half their difference . . 73 § 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 Ihoir included angle 73 § 74. Formula for the side of a triangle, in terms of the cosines of the adjacent...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...XXVIII. 68. In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex of this acute angle to the foot of the perpendicular...
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Elements of Plane and Spherical Trigonometry with Logarithmic and ..., Volume 1

Simon Newcomb - Logarithms - 1882 - 188 pages
...III. Given the three sides. THEOREM III. In a triangle the square of any side is equal to the sum, of the squares of the other two sides minus twice the product of these two sides into the cosine of the angle included oy them. In symbolic language this theorem is...
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