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. Plane and Solid Geometry - Page 169by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pagesFull view - About this book
| George Bruce Halsted - Geometry - 1886 - 394 pages
...greater than the sum of the squares on the other two sides by twice the rectangle contained by either **of those sides and the projection of the other side upon it.** HYPOTHESIS. A ABC, with £ CAB obtuse. CONCLUSION, a* = b* + C* + 2bj. PROOF. By 294, (b + JY = P +... | |
| George Albert Wentworth - Geometry - 1888 - 272 pages
...the side opposite an acute Z 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** upon that side). Add these two equalities, and observe that BM= MC. Then IS + AC* = 2 BM* + 2 AM*.... | |
| George Albert Wentworth - Geometry, Analytic - 1889 - 264 pages
...side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by **twice the product of one of those sides and the projection of the** otJier upon that side. A e Let C be the obtuse angle of the triangle ABC, and CD be the projection... | |
| George Irving Hopkins - 1891 - 210 pages
...364. In an obtuse triangle the square of the side opposite the obtuse angle is equal to the sum of **the squares of the other two sides, plus twice the...one of those sides and the projection of the other** upon that side. Sug. Form an equation by placing the projection of the side opposite the obtuse angle... | |
| Euclid - Geometry - 1892 - 460 pages
...of the squares on the sides containing the obtuse angle by twice the rectangle contained by either **of those sides, and the projection of the other side upon it.** Prop. 13 may be written AC2=AB2+BC2-2CB.BD, and it may also be enunciated as follows : In every triangle... | |
| George Albert Wentworth - Geometry - 1893 - 270 pages
...side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by **twice the product of one of those sides and the projection of** tJie other upon that side. A Let C be the obtuse angle of the triangle ABC, and CD be the projection... | |
| Webster Wells - Geometry - 1894 - 400 pages
...triangle having an obtuse angle, the square of the side opposite the obtuse angle is equal to the sum of **the squares of the other two sides, plus twice the product of one of** these sides and the projection of the other side upon it. Let C be an obtuse angle of the triangle... | |
| Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...XIII. THKORKM. 279. The square on the side opposite an obtuse angle of a triangle equals the sum of **the squares of the other two sides plus twice the product of one of** the tides by the projection of the other side upon that side. K Let AB Cbea triangle, of which the... | |
| Joe Garner Estill - 1896 - 214 pages
...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** upon that side. Show very briefly how to construct a triangle having given the base, the projections... | |
| George Albert Wentworth - Mathematics - 1896 - 68 pages
...side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by **twice the product of one of those sides and the projection of the other** upon that side. 344. I. The sum of the squares of two sides of a triangle is equal to twice the square... | |
| |