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" 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 and the projection of the other side upon it. "
An Examination Manual in Plane Geometry - Página 104
por George Albert Wentworth, George Anthony Hill - 1894 - 138 páginas
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 páginas
...and side of a square are incommensurable. PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite an acute angle is equivalent to the sum of the squares of the base and the other side, diminished by twice the rectangle contained by the base and the d1stance...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 443 páginas
...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 A is ac,ute,...
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A TREATISE ON SPECIAL OR ELEMENTARY GEOMETFH.

EDWARD OLNEY - 1872
...also as a direct consequence of (360), \ FIG. 377. 669. In an oblique angled triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by twice the rectangle of the base, and the distance from the acute...
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A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - 1872 - 84 páginas
...also as a direct consequence of (36O). FIG. 377. 669. In an oblique angled triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by twice the rectangle of the base, and the distance from the acute...
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A Treatise on Special Or Elementary Geometry, Volúmenes1-2

Edward Olney - 1872
...direct consequence of (360). fc~— — J Fio. 877. 66,9. In an oblique angled triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by twice the rectangle of the base, and the distance from the acute...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...side) ; and 17?=^ + A~М*-2MСХ MD, §335 (in any Л the square on the side opposite an ас1аe Z is equivalent to the sum of the squares on the other...two sides, diminished by twice the product of one of those sides and the projection of the other upon that side). Add these two equalities, and observe...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1877 - 368 páginas
...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...one of these sides and the projection of the other vpon that side. Let C be an acute angle of the triangle AB C, A ng' L Pthe projection of A upon BC...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...; that is, D P. GEOMETRY. — BOOK IV. PROPOSITION IX. THEOREM. 335. In any triangle, the square un 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 those sides and the projection of...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - 1877 - 240 páginas
...AGHB ; or 671 Corollary. Since ~A~T? and BOOK IL THEOREM XXVIII. 68 1 In a triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides minus twice the product of one of these sides and the distance from the vertex...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 páginas
...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 those sides and the projection of the other upon thai side. Let С be ал acate angle of the triangle...
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