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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.
Schultze and Sevenoak's Plane and Solid Geometry - Page 192
by Arthur Schultze, Frank Louis Sevenoak - 1918 - 457 pages

College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...Prove that in any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by twice the product of one of these sides and the projection of the other upon that side. 4. Prove that regular polygons of the same...

Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...THEOREM 420. 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...one of those sides and the projection of the other upon it. FIG. 1 FIG. 2 Given, in the triangle ABC, that p is the projection of the side b upon the...

Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...THEOREM 420. 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...one of those sides and the projection of the other upon it. FIG. 1 FIG. 2 Given, in the triangle ABC, that p is the projection of the side b upon the...

Proceedings of the Annual Session

Arkansas Education Association - Education - 1912 - 270 pages
...theorem, "In any oblique 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 two sides and the projection of the other one on that one." When we come to this theorem we know already...

Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...as follows : 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 these sides and the projection of the other side upon it. Ex. 726. If the sides of a triangle are 7,...

Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...side opposite an obtuse angle of a triangle equals the sum of the squares of the two other sides plus twice the product of one of those sides and the projection of the other upon it. Given a A with sides a, b, c, side a being opposite an obtuse angle, and m being the projection...

Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...side opposite an acute angle of a triangle equals the sum of the squares of the two other sides minus the product of one of those sides and the projection of the other upon it. Given a A with the sides a, b, c, side a being opposite an acute angle and m being the projection...

Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...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...side upon it. Given in A abc, p the projection of 6 upon c, and the angle opposite a an acute angle. To prove a2 = 62 + <? — 2 cp. Proof. Denote the...