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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 and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...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...one of those sides and the projection of the other side upon it. Fig. 1 Fig. 2 HYPOTHESIS. In the A ABC, the B is acute, and BD is the projection of...
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Exercises in Concrete Geometry: With Supplementary Discussions

David Sands Wright - Geometry - 1906 - 104 pages
...described on the side of a triangle opposite an acute angle is equal to the sum of the squares described on the other two sides diminished by twice the product of one of those sides by the projection of the other side upon it. Problem. To find the area of a triangle, when the three...
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Exercises in Geometry

Grace Lawrence Edgett - Geometry - 1909 - 104 pages
...square of the side opposite an acute angle, in any triangle, 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 upon that side. 10. In any obtuse-angled triangle the square...
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The Science-history of the Universe, Volume 8

Francis Rolt-Wheeler - History of mathematics - 1909 - 356 pages
...equal to the sum of the squares on the other two sides diminished (increased) by twice the rectangle of one of those sides and the projection of the other upon it. The figure of the Pythagorean theorem was called by the Persians the Princess, and other two figures...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1909 - 360 pages
...oblique 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 time sides by the projection of the other side upon it. KB. 2 Given acute ZC in A ABC, and DC the projection...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...AB 2 . PROPOSITION XL THEOREM 341. In any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares on the other...diminished by twice the product of one of those sides by the projection of the other upon that side. c a' DB FIG. 1 FIG. 2 Given the triangle ABC, A being...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 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 of one of those sides by the projection of the other upon that side. Given the A ABC, A being acute and CD J. AB. To prove...
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Practical Algebra, 2d Course by Jos. V. Collins, Book 2

Joseph Victor Collins - Algebra - 1911 - 330 pages
...opposite an acute aiujle in a triangle is equal to the sum of the squares of the other two sides dimmished by twice the product of one of those sides and the projection of the other on that side. To prove a3 = 62 + я3 — 2 cm. PROOF. а2=1? + 1Ш' (61.) = P2+ (cm)2 =p2 + C2 _...
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Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...side opposite an acute angle is equal to the sum of the squares of the other two sides diminished % twice the product of one of those sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 370 pages
...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 by the projection of the other upon that side. THEOREM. A similar statement for the obtuse triangle....
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