 In any triangle, the square of the 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.  Plane and Solid Geometry - Page 168by Isaac Newton Failor - 1906 - 418 pagesFull view - About this book
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...Theorem. 186. 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 these sides and the projection of the other side upon it. CASE I. When the projection of the vertex... | |
 | Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1900 - 184 pages
...circumscribed circle. t 41. Law of the cosines. — The square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the product of these sides and the cosine of the included angle. Since we are making no use of the directions of the... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by one of those sides, and the projection of the other side upon it. The Enunciation of Prop. 12 thus stated should be carefully compared with that of Prop. 13. PROPOSITION... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...XXXVII. THEOREM 320. 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...sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...XXXVII. THKOREM 320. In any tnangle, 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...sides and the projection of the other side upon it- i Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove... | |
 | Arthur Schultze - 1901 - 260 pages
...XXXVII. THEOREM 320. 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...sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...XXXVII. THEOREM 320. 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...sides and the projection of the other side upon it. Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is an acute angle. To prove... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...any triangle the square on a side opposite an acute angle is equivalent to the sum of the squares on the other two sides, diminished by twice the product...one of those sides and the projection of the other upon that side. Given. — Let ABC be any triangle, B an acute angle, and BD the projection of BC on... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...THEOREM 659. In any triangle the square of a side opposite an acute angle is equivalent to the sum of the squares of the other two sides, diminished by twice the product of one of these sides and the projection of the other side upon it. B c Let ABC be a A in which BC lies opposite... | |
 | Josiah Willard Gibbs, Edwin Bidwell Wilson - Vector analysis - 1901 - 470 pages
...the cosine of the angle between them. Or, the square of one side of a triangle is equal to the sum of the squares of the other two sides diminished by twice the product of either of thpse sides by the projection of the other upon it — the generalized Pythagorean theorem.... | |
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