| Daniel Alexander Murray - Plane trigonometry - 1899 - 350 pages
...formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of **the squares of the other two sides minus twice the product of** these two sides multiplied by the cosine of their included angle. NOTE. In Fig. 49 a, A is acute and... | |
| Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...than the sum of the squares on the sides containing that angle, by twice the rectangle contained by **one of these sides and the projection of the other side upon it.** (ii) Comparing the Enunciations of II. 12, I. 47, II. 13, we see that in the triangle ABC, if the angle... | |
| Arthur Schultze - 1901 - 260 pages
...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.** JD Hyp. In Aabc, p is the projection of 6 upon c, and the angle opposite a is obtuse. To prove a 2... | |
| Arthur Schultze - 1901 - 392 pages
...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.** Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is obtuse. To prove a2 = 62... | |
| Alan Sanders - Geometry, Modern - 1901 - 260 pages
...opposite the obtuse angle is equivalent 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.** B Let ABC be an obtuse-angled A, and CD be the projection of BC on AC (prolonged). To Prove AB2 = BC'2... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...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.** c Hyp. In Aabc, p is the projection of 6 upon c, and the angle opposite a is obtuse. To prove a2 —... | |
| Education - 1903 - 630 pages
...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.** 7. Prove : The area of a regular polygon is equal to one-half the product of its perimeter and apothem.... | |
| Alan Sanders - Geometry - 1903 - 392 pages
...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** oiher side upon it. b B Let ABC be a A in which BC lies opposite an acute angle, and AD is the projection... | |
| Euclid - Euclid's Elements - 1904 - 488 pages
...than the sum of the squares on the sides containing that angle, by twice the rectangle contained by **one of these sides and the projection of the other side upon it.** (ii) Comparing the Enunciations of II. 12, i. 47, II. 13, we see that in the triangle ABC, if the angle... | |
| James Morford Taylor - History - 1904 - 192 pages
...about the triangle ABC. Law of cosines. In any triangle the square of any side is equal to the sum of **the squares of the other two sides minus twice the product of** these two sides into the cosine of their included angle. In figures 35 regard AD, DB, and AB as directed... | |
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