 | Charles Davies - 1854 - عدد الصفحات: 436
...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 - 1872 - عدد الصفحات: 96
...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 - 1872 - عدد الصفحات: 562
...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 - 1872 - عدد الصفحات: 102
...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 - 1877 - عدد الصفحات: 436
...; 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 - 1877 - عدد الصفحات: 262
...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 - 1880 - عدد الصفحات: 260
...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 - 1883 - عدد الصفحات: 326
...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 - 1885 - عدد الصفحات: 424
...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 - عدد الصفحات: 264
...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. 
