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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. "
Lessons on form, for teachers [of geometry]. - Page 39
by Richard Pears Wright - 1882
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...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
...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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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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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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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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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...the 0 EBD tijstance BE js tne projection of AB on CD. XIV. Theorem. 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 [,£jj twice the rectangle of one of those sides, and the projection...
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Elements of Quaternions

Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...same notation, .-. S(PQ.QO) = 0, or PQ and QO are at right angles. 5. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other sides, less or twice the product of the base and the line between the acute angle...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...shall be 3, 4, and 5 ? Suppose the sides were 6, 9, and 12? THEOREM XII. 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 rectangle contained by one of these sides and the projection...
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