Prove that in any triangle the square on the side opposite an acute angle 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. Plane and Solid Geometry - Page 223by Elmer Adelbert Lyman - 1908 - 340 pagesFull view - About this book
| James Hayward - Geometry - 1829 - 228 pages
...value, we have a- = c 2 -\- fc* — 2 (6 X z); that is —In an oblique-angled triangle, the square of the side opposite an acute angle, is equivalent to the sum of the squares of the other two sides, minus twice the rectangle contained by one of the sides adjacent to this angle,... | |
| 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 - 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 - 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... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...twice the rectangle contained by either side and the projection on it of the other side. THEOR. n. In any triangle the square on the side opposite an acute angle is less than the squares on the other two sides by twice the rectangle contained by either side and the... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...the foot of the perpendicular С P ; that is, D P. GEOMETRY. BOOK IV. PROPOSITION IX. 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... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...foot of the perpendicular С P ; that is, D P. GEOMETRY. BOOK IV. PROPOSITION IX. THEOREM. 335. ln 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... | |
| 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... | |
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