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
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...vertex of their included angle to the opposite side is 4; required the third side. THEOREM XIII. In any triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of (he other two sides phis twice the rectangle contained by one of these sides and the projection... | |
| Euclides - 1884 - 434 pages
...that are divided internally or externally in medial section. In obtuse.angled triangles, the square on the side opposite the obtuse angle is equal to the sum of the squares on the other two sides increased by twice the rectangle contained by either of those sides... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...AD2 = AB*, and CD2 + AD2 = AC2 : hence, AB3 = BC2 + AC2 - 2BCxCD; 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... | |
| Webster Wells - Geometry - 1886 - 392 pages
...right triangles, by § 338, and JD2+ (752= JO2. AB2= BC2+AC2- 2 BC x CD. PROPOSITION XII. THEOREM. 342. In an 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 one of these sides and the projection... | |
| George Albert Wentworth - 1889 - 276 pages
...the product of one of these sides and the projection of the other upon it. 163. Theorem. 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, increased by twice the product of one of these sides and the projection... | |
| George Albert Wentworth - 1889 - 264 pages
...the product of one of these sides and the projection of the other upon it. 163. Theorem. 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, increased by twice the product of one of these sides and the projection... | |
| Edward Albert Bowser - Geometry - 1890 - 420 pages
...of the squares of the tsvo numbers diminished by twice their product. Proposition 27. Theorem. 331. In an 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 one of these sides by the projection... | |
| Edward Albert Bowser - Geometry - 1890 - 418 pages
...the squares of the two numbers diminished by twice their product. Proposition 27. Theorem. 331. In nn 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 one of these nides by the projection... | |
| George Irving Hopkins - 1891 - 210 pages
...squares of the perpendicular, and then combine the terms by using Theorem 360 (a). 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 product of one of those sides and the projection of... | |
| 1891 - 644 pages
...that part together with the square on the other part. 6. In an obtuse-angled triangle the square on the side opposite the obtuse angle is equal to the sum of the squares on the other sides together with twice the rectangle contained by one of them and by the straight... | |
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