In any obtuse triangle, the square of the 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 these sides and the projection of the other side upon it. Elements of Geometry: Plane geometry - Page 148by Andrew Wheeler Phillips, Irving Fisher - 1896Full view - About this book
| James Hayward - Geometry - 1829 - 228 pages
...(170). And substituting c 2 for its value, we have a 2 =2 c 2 -f6 2 +2(6xx). We therefore say—In **an obtuseangled triangle, the square of the side opposite the obtuse angle^ is** equivalent to the sum of the squares of the other two sides, plus twice the rectangle contained by... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...consequently, c+BC-ZCDxBC (P. 9). Adding Iff to both, we find, as before, PROPOSITION XIII. THEOEEM. In any **obtuse-angled triangle, the square of the side opposite the obtuse angle is** equivalent to the squares of the base and the other side, augmented by twice the rectangle contained... | |
| Charles Davies - Geometry - 1854 - 436 pages
...9). Adding A~ff to both, we find, as before, ^ B CD. BOOK IV. 101 PROPOSITION XIII. THEOREM. Tn any **obtuse•angled triangle, the square of the side opposite the obtuse angle is** equivalent to the sum of the squares of the base and the other side, augmented by twice the rectangle... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...square of the difference of the perpendiculars which determine this projection. THEOREM Xv. In any **obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the** squares of the other two sides, increased by twice the product of either of the sides containing the... | |
| George Roberts Perkins - Geometry - 1860 - 470 pages
...square of the difference of the perpendiculars which determine this projection. THEOREM XV. In any **obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the** squares of the other two sides, increased by twice the product of either of the sides containing the... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...By adding AD to each of these equals, we find, as before, PROPOSITION XIII. — THEOREM. 245. In any **obtuse-angled triangle, the square of the side opposite the obtuse angle is** equivalent to the sum of the squares of the two other sides plus twice the rectangle contained by the... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...adding A D2 to each of these equals, we find, as before, PROPOSITION XIII. — THEOREM. 24-"). In anif **obtuse-angled triang-le, the square of the side opposite the obtuse angle is** equivalent to the sum of the squares of the two other tides plus twice the rectangle contained by the... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...= AB\ and CD2 + AD2 =" AC* : hence, Z52 = BCZ + AC2 - 2BC x CD ; PROPOSITION XIII. THEOREM. In any **obtuse-angled triangle, the square of the side opposite the obtuse angle is equal to the sum of the** squares of the base and the other side, increased ~by twice the rectangle of the base and the distance... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...By adding AD to each of these equals, we find, as before, PROPOSITION XIII. — THEOREM. 245. In any **obtuse-angled triangle, the square of the side opposite the obtuse angle is** equivalent to the sum of the squares of the two other sides plus twice the rectangle contained by the... | |
| Benjamin Greenleaf - Geometry - 1868 - 338 pages
...By adding AD to each of these equals, we find, as before, PROPOSITION XIII. — THEOREM. 245. In any **obtuse-angled triangle, the square of the side opposite the obtuse angle is** equivalent to the sum of the squares of the two other sides plus twice the rectangle contained by the... | |
| |