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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. "
Elements of geometry, with ... trigonometry - Page 71
by André Darré - 1872
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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...
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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...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - Trigonometry - 1876 - 204 pages
...of half their difference . . 78 § 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 included angle 73 § 74. Formula for the side of a triangle, in...
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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 product of those sides into the cosine of their included angle. FIG. 43. FIG 44. Through c in the triangle ABC...
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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 let fall upon...
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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 let fall upon...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...THEOREM VII. 259. In any triangle, the square on the side opposite an acute angle. equals the sum of the squares of the other two sides minus twice the product of one of those sides and the projection of the other upon that side. In the A ABC, let c be an acute Z., and...
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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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Elements of Plane and Spherical Trigonometry

Edwin Schofield Crawley - Trigonometry - 1890 - 184 pages
...pairs of sides. (83) FIG. 21 bis. о 63. //( any 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 sides and the cosine of the included angle. We are to prove a2 = I', + ca — 2bc cos A. In one...
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Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...respective sides. 363. 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 those sides and the projection of the other upon that side. If C be the acute angle, then by a glance...
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