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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. "
Plane and Solid Geometry - Page 169
by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pages
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...opposite the obtuse angle is equivalent to the sum of the squares of the other two sides increased by twice the product of one of those sides and the projection of the other on that side. A Let С be the obtuse angle of the triangle ABC, and С D be the projection of A С...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...XXIX. 70. In a triangle the square of the 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 these sides and the distance from the vertex of the obtuse angle to the foot of the perpendicular let...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...aide opposite the obtuse Z is cquivalent to the sum of the squares on the other two sides increased by twice the product of one of those sides and the projection of thе other on that side) ; and A~C* = STC* + AM* — 2MCX MD, 335 (in any Д the square on the side...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...obtuse-angled trianr/le the square of the side opposite the obtuse anyle is equivalent to the sum of the squares of the other two sides plus twice the product of one of these sides and the distance from the vertex of the obtuse angle to the foot of the perpendicular let...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...side opposite the obtuse Z is equivalent to the sum of the squares on the other two sides increased by twice the product of one of those sides and the projection of the other on that side) ; and ГC* ^ ЖТ? + AM* -2MCX MD, 335 any A the square on the side opposite an acute...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...less than the sum of the squares on the other two sides by twice the rectangle contained by either of those sides and the projection of the other side upon it. Hypothesis. ABC, any triangle having the angle at A acute ; CD, the perpendicular dropped from C on...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...260. In any obtuse-angled triangle, the square on the side opposite the obtuse angle equals the sum of the squares of the other two sides plus twice the...one of those sides and the projection of the other upon that side. In the A ABC, let c be the obtuse Z., and PC the projection of AC upon BC produced....
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...square on the side opposite an acute anale 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 с be an acute Z., and PC the projection of AC upon BC. A To prove...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...side opposite an acute Z is equivalent to the sum of the squares on the other two sides, diminished by twice the product of one of those sides and the projection of tlie other upon that side). Add these two equalities, and observe that BM = M С. . Then A~ff + AC?...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...less than the sum of the squares on the other two sides by twice the rectangle contained by either of those sides and the projection of the other side upon it. HYPOTHESIS. A ABC, with C acute. CONCLUSION, c2 -f- zbj = a2 -f- b2. PROOF. By 295, ^_ b2 + j2 =...
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