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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 186
by George Albert Wentworth - 1877 - 398 pages
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 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 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
...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
...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
...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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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. 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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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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Treasurer's Report ...: Also, Reports of the Selectmen; the Trustees of the ...

Brookline (Mass.) - Brookline (Mass.) - 1881 - 676 pages
...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. Prove. 4. To find a mean proportional between...
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Elements of Geometry

George Albert Wentworth - Geometry, Plane - 1882 - 268 pages
...and the projection of the other on that side) ; and A~C* = MD* + ~M*—2MC X MD, 335 (in any Л the. square on the side opposite an acute Z is equivalent...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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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 that AB* = BC*...
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The College Student's Manual: A Hand-book of Reference for Professors ...

Henry Elmer Moseley - Universities and colleges - 1884 - 187 pages
...that the square of a side of a triangle 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 upon that side. 7. Two tangents drawn from the same point...
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