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 those sides and the projection of the other side upon it. Plane and Solid Geometry - Page 169by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pagesFull view - About this book
| F. J. Beck - 1899 - 288 pages
...side opposite an acute angle is equivalent to the sum of the squares of the two sides diminished by **twice the product of one of those sides and the projection of the other** upon that side. 6. To construct a square equivalent to the sum of any number of given squares. 7. If... | |
| Webster Wells - Geometry - 1899 - 424 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 other side upon it. Given C an obtuse Z of A ABC, and CD 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 - 1901 - 260 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 those 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
...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 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, Frank Louis Sevenoak - Geometry - 1901 - 394 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 those 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
...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 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
...opposite the obtuse angle is equivalent to the sum of the squares on the other two sides increased by **twice the product of one of those sides and the projection of the other** upon that side. Given. — Let ABC be a triangle, of which A is an obtuse angle, AB its base, and AD... | |
| Euclid - Euclid's Elements - 1904 - 488 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. EUCLID-S... | |
| Isaac Newton Failor - Geometry - 1906 - 440 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 those sides and the projection of the other side upon it.** HYPOTHESIS. In the A ABC, the ^ C is obtuse, and CD is the projection of AC upon BC produced. Let AB... | |
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