 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
 | Webster Wells - Geometry - 1898 - 284 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 oiher side upon it. Given C an obtuse Z of A ABC, and CD the projection of side AC upon side BC produced.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...gives, by substitution, AB* = AC* - DC* + (DC - BC) 2 or by cancellation, PROPOSITION XI. THEOREM. 269. 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 tm'ce the product of one of these sides by the projection... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...= BC* + AC 2 - 2 BC x CD. . ».' PROP. XXVI. THEOREM. 278. In any 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 '. sides and the projection of the... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...x DC. But IT? + DE* = AF, and AJ? + JJf? = ~AC\ § 371 PROPOSITION XXX. THEOREM. 376. 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 those sides by the projection... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...Then A& + CD* = BC* + AD* + BD!-2BCxBD. (?) BD. (?) QED Proposition 152. Theorem. 187. 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 - Geometry, Modern - 1899 - 272 pages
...DC. But 11? + ~DJ? =, AS?, and Iff + 'DC* = 1C*. § 371 PROPOSITION XXX. THEOREM. 376. 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 those sides by the projection... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...have AB2 = BC2 + AC2 - 2 5C x CD. PROP. XXVI. THEOREM. 278. In any 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... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...have Z = BC2 + AC2 —2 BC x CD. PROP. XXVI. THEOREM. 278. In any 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... | |
 | Education - 1900 - 612 pages
...half the difference of the intercepted arcs. 4 Complete and demonstrate the following: In any obtuse triangle the square of the side opposite the obtuse angle is equal to ... 5 Prove that the areas of two rectangles having equal altitudes are to each other as their bases,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...13, 14, and 15. Find the projection of 13 upon 14. PROPOSITION XXXVIII. THEOREM 322. 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... | |
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