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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 diminished by twice the product of one of those sides and the projection of the other upon that side. "
Elements of Plane and Solid Geometry - Σελίδα 186
των George Albert Wentworth - 1877 - 398 σελίδες
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Solid Geometry

Walter Burton Ford, Charles Ammerman - 1913 - 107 σελίδες
...triangle the square on the side opposite an acute angle is equal to the sum of the squares on t/ie other two sides diminished by twice the product of...of those sides and the projection of the other upon it. 200. Theorem VIII. In any obtuse triangle the square on the side opposite the obtuse angle is equal...

Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - 1913 - 304 σελίδες
...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...one of those sides and the projection of the other side upon it. Given in A abc, p the projection of b upon c, and the angle opposite a an acute angle....

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1913 - 457 σελίδες
...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...one of those sides and the projection of the other side upon it. Given in A abc, p the projection of b upon c, and the angle opposite a an acute angle....

Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - 1913 - 321 σελίδες
...opposite the acute angle is equal to the sum of the squares on the other two sides diminished by tivice the product of one of those sides and the projection of the other upon it. 138 Fio. 139 Given the A ABC in which C is an acute angle. Let a, b, c be the sides opposite the...

Plane and Sperical Trigonometry (with Five-place Tables): A Text-book for ...

Robert Édouard Moritz - 1913 - 520 σελίδες
...embody the so-called Law of Cosines: In any triangle, the square on any side is equal to the sum of the squares on the other two sides diminished by twice the product of those two sides times the cosine of the included angle. (b) Second proof. The law of cosines may be...

Logarithmic and Trigonometric Tables

Herbert Ellsworth Slaught - 1914 - 97 σελίδες
...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 diminished by twice the product...sides and the projection of the other upon that side. Theorem 2. In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the...

Plane Trigonometry and Applications

Ernest Julius Wilczynski - 1914 - 265 σελίδες
...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 diminished by twice the product...sides and the projection of the other upon that side. Theorem 2. In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the...

Elementary Mathematical Analysis: A Text Book for First Year College Students

Charles Sumner Slichter - 1914 - 490 σελίδες
...square of any side opposite an acute angle of an oblique triangle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides by the projection of the other side on it. Thus in Fig. 119 (1) : o2 = 62 _|_ C2 _ 2bd (1) Now: d =...

Analytic Geometry

Wallace Alvin Wilson - 1915
...the side opposite an acute angle is equal to the sum of the squares of the other two sides decreased by twice the product of one of those sides and the projection of the other upon it ; (б) the sum of the squares of two sides is equal to twice the square of one half the third side,...

Plane geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - 1915 - 277 σελίδες
...side opposite the obtuse angle is equivalent to the sum of the squares of the other two sides, plus twice the product of one of those sides and the projection of the other side upon it. Given the obtuse triangle ABC, the angle ACB being obtuse, and d and AD being the projections...




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