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
| Trinity College (Dublin, Ireland) - 1909 - 546 pages
...intersect, their common chord is bisected at right angles by the line joining their centres. 6. Prove that in an obtuse-angled triangle the square of the side opposite the obtuse angle is greater than the sum of the squares on the other sides by twice the rectangle under one side and the... | |
| William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...Substituting these values, BC2 = AT? + AC' - 2 AB x AD. QED PROPOSITION XXXVIII. THEOREM. 399. In any 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 tivice the product of one of those sides by the projection... | |
| George William Myers - Mathematics - 1910 - 304 pages
...the equation for a2; for 62. PROPOSITION VI 244. Theorem: In an obtuse-angled triangle the square on the side opposite the obtuse angle is equal to the sum of the squares on the oiher two sides, increased by two times the product of one of them and the projection... | |
| Geometry, Plane - 1911 - 192 pages
...triangles are similar when the sides of one are perpendicular, respectively, to the sides of the other. 6. 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... | |
| Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...h2 + c?+p2-2pc. (From 1.) 5. But h2+p- = b2. 6. Hence, a2 = b2 + <? - 2 pc. THEOREM XLIX 196. 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, plus twice the product of one of these sides and the projection of... | |
| Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...the second is 2, find the third side of the triangle. PROPOSITION XXIX. THEOREM 455. 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... | |
| Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...the second is 2, find the third side of the triangle. PROPOSITION XXIX. THEOREM 455. 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... | |
| William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...that in the above proposition c2 = a2 + I2 — 2 ab cos C. PROPOSITION XXI. THEOREM 421. 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 and the projection... | |
| William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...the above proposition c2 = a2 + 62 — 2 al cos C. PROPOSITION- XXL THEOREM • 421. 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 and the projection... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...upon 21. [See practical problems, pp. 298 and 299.] PROPOSITION XXXVII. THEOREM 333. 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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