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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 190 THEOREM XLIX 196. "
The Elements of Geometry - Page 146
by Webster Wells - 1894 - 378 pages
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...BC2, and also that AD2 + CD2 = AC2, we shall obtain BC2 = AB2 + AC2 + 2 AB x AD. THEOREM XvI. 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, diminished ly twice the product of one of these sides, Iy the projection...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...BC2, and also that AD2 + CD2 = AC2, we shall obtain BC2 = AB2 + AC2 + 2AB x AD. THEORRM XVI. 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, diminished by twice the product of one of these sides, by the projection...
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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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Report ... on the common school system of the United States and of the ...

James Fraser (bp. of Manchester.) - 1866 - 480 pages
...altitudes are proportional to their bases. (Book IV., Prop. 3.) 8. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of tne base and the other side, diminished by brice (he rectangle of the base and the distance...
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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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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...square of either of the two small sides. Fig. 78. B m 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...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...the side of a square are incommensurable. PRorosrrioN xii. THEOBEM. In any triangle, the square of a side opposite an acute angle, is equal to the sum of the squares of the base and the other side, diminished by twice the rectangle of tht base and the distance...
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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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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...twice either of the rects. А С, С D, or В С, С Е. THEOREM LV. In any triangle, the square on a side opposite an acute angle is equal to the sum of the squares containing the acute angle, less twice the rectangle contained by either of these sides and...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...square is to one of the sides as V2 is to 1. PROPOSITION IX. THEOREM. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other sides, diminished by twice the rectangle of the base and the distance from the...
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