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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. "
A Text-book of Geometry - Page 157
by George Albert Wentworth - 1888 - 386 pages
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...THEORRM XVI. 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, by the projection of the other on the preceding one, produced if necessary. If the angle...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...THEOREM. 52. In any triangle, the square of the side opposite to 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 upon that side. Let C be an acute angle of the triangle...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...XV.—THEOREM. 52. 7)i any triangle, the square of the side opposite to 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 •upon thnt side. Let C be an acute angle of the triangle...
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Catalogue - Harvard University

Harvard University - 1874 - 668 pages
...proportionally. 6. In any triangle the square of the side opposite to an acute angle is equal to the Bum 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. 7. The area of a trapezoid is equal to...
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 886 pages
...length. 3. Prove that in any triangle the square of a side opposite an aeute angle is equal > th« sum of the squares of the other two sides diminished by twice the product of R- of these sides and the projection of the other upon that side. Show how to draw tangent to a given...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...THEOREM. 335. 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...sides and the projection of the other upon that side. A Lot C be an acute angle of the triangle ABC, and DC the projection of AC upon B C. We are to prove...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...THEOREM. 335. ln 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...of those sides and the projection of the other upon thai side. Let С be ал acate angle of the triangle ABС, and D С the projection of AС upon B С....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 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 с ^в Let С be the obtuse angle of the triangle ABC, and CD be the projection of...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...the square on the side opposite an ande angle is equivalent to the sum of the squares of the oiler two sides diminished by twice the product of one of those sides and t he projection of the other upon that side. D Fig. 1. Fig. 2. Let С be an acute angle of the triangle...
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...[acute'] angle is equal to the sum of the squares of the other two sides [,£jj twice the rectangle of one of those sides, and the projection of the other upon it. HYPOTH. In the triangles ABC, the angle ACB is obtuse in Fig, 1, and acute in Figs. 2 and 3 (produced)...
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