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" 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 diminished by twice the product of one of those sides and the projection of the other side upon it. "
Elements of Geometry: With Notes - Page 35
by John Radford Young - 1827 - 208 pages
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...16, find p. Ex. 956. In A abc, if b = 15, p = 9, and c = 25, find a. PROPOSITION XXXVI. THEOREM 331. 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 diminished by twice the product of one of those...
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Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...andd2+/i2 = a2. 376 Why? Similarly, if b' is the projection of b upon CB, it can be proved that 381. Theorem. In any 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-...
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Solid Geometry

Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...plus twice the product of one of those sides and the projection of the other side upon it. 381. Theorem. In any 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...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...= 25, find a. Ex. 957. In A abc, express a in terms of 6, c, and p. PROPOSITION XXXVI. THEOREM 331. 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 diminished by twice the product of one of those...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...hypotenuse of a rigid triangle is equivalent to the sum of the squares on the two legs. Prop. 158. 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, diminishul by twice the product of one of these...
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Plane Geometry: Experiment, Classification, Discovery, Application ...

Clarence Addison Willis - Geometry, Modern - 1922 - 320 pages
...= c2 are called Pythagorean numbers; many such series exist in higher values. 252. Theorem XI. — In any triangle, the square of a 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...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...16, find p. Ex. 956. In A abc, if 6 = 15, p = 9, and c = 25, find a. PROPOSITION XXXVI. THEOREM 331. 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 diminished by twice the product of one of those...
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Plane Geometry: (Revised)

Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 pages
...78, Ax. 8 Similarly, if b' is the projection of b upon a, it can be proved that c2 = o2+62+2a6'. 338. Theorem. In any 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...
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