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" 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, minus twice the product of one of these sides and the projection of the other side upon it. "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 190
1898 - 208 pages
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Plane Trigonometry, for Colleges and Secondary Schools

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...
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A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI ..., Book 1

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...
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Plane Geometry

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...
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Plane and Solid Geometry

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...
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Elements of Plane Geometry

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...
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Plane and Solid Geometry

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 —...
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Biennial Report

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....
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Elements of Plane and Solid Geometry

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...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

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...
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Plane Trigonometry

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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