| 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... | |
| 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... | |
| 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 - 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 - 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.... | |
| Charles Hamilton Ashton, Walter Randall Marsh - Trigonometry - 1902 - 186 pages
...circumscribed circle. 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. Сн. VI, § 41] OBLIQUE TRIANGLES differ slightly... | |
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