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" 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. "
Elements of Geometry: With Notes - Page 35
by John Radford Young - 1827 - 208 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...hence, by extracting the square root of each term, we have, AC : AB : : y^ : 1 ; 107 PROPOSITION XII. THEOREM. 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...
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Calendar of the McGill University, Montreal

McGill University - 1865 - 332 pages
...the rectangle under the parts. • a. The square of a line is four times the square of its half. 2. In any triangle the square of a side opposite an acute angle is less than the sum of the squares of the sides containing it by twice the rectangle under either of them and the intercept...
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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
...polygons. 7. Rectangles having equal 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...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...Therefore AC2=AB2+BC2+2AB.BD. QED BDADB THEOREM XXXVII. In any triangle, the square of the side subtending an acute angle is less than the squares of the base and the other side by twice the rectangle of the base and the distance of the perpendicular from the acute...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...root of each member of this equation, we shall have AC=ABv/2 ; or AC : AB : : v/2 : D PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite...squares of the base and of the other side, by twice thi rectangle contained by the base, and the distance from the acute angle tc the foot of the perpendicular...
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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...the hypothenuse is double of the 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...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...consequently, the diagonal and 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...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...:: \/2 : 1 ; that is, the diagonal of a 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...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...AC2, AC2: AL = AB2 :: AB2, KD = BC2 ... AC : AK. Also, AC2: BC2 :: AC : KC. 211. Proposition XII. — Theorem. In any triangle, the square of a side opposite an acute angle is equivalent to the sum of tlie squares of tlie otlier sides, minus twice tlie rectangle of one of these...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...incommensurable with its side. PROPOSITION XII. THEOREM. In any triangle, the square of the side opposite to an acute angle is less than the squares of the base...twice the rectangle contained by the base, and the distance from the acute angle to the foot of the perpendicular let fall from the opposite angle. Let...
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