 | George Roberts Perkins - Geometry - 1860 - 472 pages
...THEORRM XVI. 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 these sides, by the projection of the other on the preceding one, produced if necessary. If the angle A is ac,ute,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...THEOREM. 52. In 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...sides and the projection of the other upon that side. Let C be an acute angle of the triangle ABC, A *e' Pthe projection of A upon BC by the perpendicular... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...side opposite to the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other upon that side. Let C be the obtuse angle of the triangle ABC, P the projection of A upon BC (produced) ; then, AB*=BC2... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...THEOREM. 52. In 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...and the projection of the other •upon that side. Let C be an acute angle of the triangle ABC, P the projection of A upon BC by the perpendicular AP,... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...XV.—THEOREM. 52. 7)i 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...these sides and the projection of the other •upon thnt side. Let C be an acute angle of the triangle ABC, ' BOOK III. AB*=BC' + AC' — 2-6(7 X PC. For,... | |
 | Harvard University - 1874 - 668 pages
...proportionally. 6. In 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...sides and the projection of the other upon that side. 7. The area of a trapezoid is equal to the product of its altitude by half the sum of its parallel... | |
 | William Chauvenet - Geometry - 1877 - 396 pages
...THEOREM. 52. In 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...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 - 416 pages
...THEOREM. 335. 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 those sides and the projection of the other upon that side. A Lot C be an acute angle of the triangle... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...335 (in any Л the square on the side opposite an acute 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... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...335. In any triangle, the square un the side opposite an acute angle is equivalent to tfie sum of (he 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. F1g. 2. Let С be an acute angle of the... | |
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In 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. 
