 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 - Page 104by George Albert Wentworth, George Anthony Hill - 1894 - 138 pagesFull view - About this book
 | 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... | |
 | George Roberts Perkins - Geometry - 1860 - 472 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 A is ac,ute,... | |
 | 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 - 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... | |
 | 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... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...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... | |
 | William Chauvenet - Geometry - 1877 - 396 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...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... | |
 | 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... | |
 | 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... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...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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