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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 - Page 188
by George Albert Wentworth - 1877 - 398 pages
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Plane Geometry

Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...GEOMETRY PROPOSITION VI. THEOREM 375. In any triangle the square on the side opposite to an acute angle is equivalent to the sum of the squares on the other two sides diminished by twice the rectangle of either of those sides and the projection of the other upon it. FiG. 1 Given triangle ABC...
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...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 it. DB Hypothesis. — In A ABC, Z. A is acute, a, b, and e are the sides opposite A, B, and (7, respectively,...
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Third-year Mathematics for Secondary Schools

Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...= 62+c2-2c6' (The square of the side opposite the 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 A other upon it.) FIG. 79 Since b' = b cos A, it follows that a2 = b2+c2-26c cos A. This means that...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...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....
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Solid Geometry

Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...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. 381. Theorem. In any triangle, the square of a side opposite an acute angle is equivalent...
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Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...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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Drill Book in Plane Geometry

Robert Remington Goff - 1922 - 136 pages
...side opposite an obtuse angle of a triangle equals 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 upon it. 341. Group articles 282, 339, and 340 under one general statement. 342. The sum of the squares...
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Essentials of Plane Geometry

David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...square of the side opposite an acute •angle of any triangle 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. BA Given the A ABC with an acute ZA, and a' and V, the projections of a and 6 respectively...
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Schultze and Sevenoak's Plane and Solid Geometry; Revised by Arthur Schultze

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...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 6 upon c, and the angle opposite a an acute angle....
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Essentials of Solid Geometry

David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...The square of the side opposite an acute angle of any triangle 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. In the \ABC the projection of AC upon AB is the segment AD cut off on AB by a perpendicular...
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