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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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An Introduction to Plane and Spherical Trigonometry

Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...(A) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the angle included by them. First, let the triangle А В С be...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...opposite to 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 upon that side. Let (7 be an acute angle of the triangle ABC, A Pthe projection of A upon BC by the...
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The Elements of Plane and Spherical Trigonometry ...

Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...(А) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the anale included by them. First, let the triangle А В С be...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...the sum of the squares of the two remaining sides is equal to twice the rectangle contained by either one of these sides and the projection of the other side upon that side. Fig- 35. F'g- 36. Let ABC be any triangle, then the square of any side, as AC, shall be...
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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...H THEOREM. 91. 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, minus twice the product of one of these sides by the projection on it of the other. Def. The projection of one line on another is the part of the...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...opposite to 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 •upon that side. Let C be an acute angle of the triangle ABC, P the projection of A upon BC by the...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...opposite to the obtuse angle is equal to the sum of the squares of the other two sides, increased by tunce the product of one of these sides and the projection of the other upon that side. Let C be the obtuse angle of the triangle ABC, -j^ P the projection of A upon BC (produced);...
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Catalogue - Harvard University

Harvard University - 1874 - 668 pages
...opposite to an acute angle is equal to the Bum of the squares of the other two sides diminished by twice the product of one of these sides and the projection of the other upon that side. 7. The area of a trapezoid is equal to the product of its altitude by half the sum...
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Plane and Spherical Trigonometry

Henry Nathan Wheeler - Trigonometry - 1876 - 204 pages
...of half their difference . . 78 § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their included angle 73 § 74. Formula for the side of a triangle, in...
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The Elements of Plane Trigonometry

Henry Nathan Wheeler - 1876 - 128 pages
...— C)' 6 — c tani(B — C)' § 73. The square 'of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their included angle. FIG. 43. FIG 44. Through c in the triangle ABC...
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