 | Charles Davies - Geometry - 1854 - 436 pages
...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... | |
 | Edward Olney - Geometry - 1872 - 96 pages
...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... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...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... | |
 | Edward Olney - Geometry - 1872 - 102 pages
...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... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...; 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 the... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...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... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...AGHB , or 67i Corollary. Since re- 2 —Tff +TC2 THEOREM XXVIII. 68. 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... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...THEOREM XII. 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 minus twice the rectangle contained by one of these sides and the projection on it of the other. Let a, b, c, be the sides of the triangle, A va... | |
 | George Albert Wentworth - Geometry - 1885 - 424 pages
...th perpendicular CP; that is, D P. PROPOSITION IX. THEOREM. 335. In any triangle, the square on ihe 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... | |
 | George Albert Wentworth - 1889 - 264 pages
...equivalent to the sum of the squares upon the two legs. 191. Theorem. In a triangle the square upon a side opposite an acute angle is equivalent to the sum of the squares upon the other two sides, diminished by twice the rectangle of one of these sides and the projection... | |
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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. 
