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" In any obtuse triangle, the square of the 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. "
Elements of Geometry: Plane geometry - Page 148
by Andrew Wheeler Phillips, Irving Fisher - 1896
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...13, 14, and 15. Find the projection of 13 upon 14. PROPOSITION XXXVIII. THEOREM 322. In any obtuse triangle, the square of the 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...
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Plane and Solid Geometry

Arthur Schultze - 1901 - 392 pages
...13, 14, and 15. Find the projection of 13 upon 14. _PROPOSITION XXXVIII. THEOREM 322. In any obtuse triangle, the square of the 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...
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Plane Geometry

Arthur Schultze - 1901 - 260 pages
...13, 14, and 15. Find the projection of 13 upon 14. PROPOSITION XXXVIII. THEOREM 322. In any obtuse triangle, the square of the 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...
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Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...^lB = 6ft., 4C=5ft., and BC = 1 ft. Find the projection of AC upon BC. PROPOSITION XIII. THEOREM 662. In an obtuse-angled triangle the square of the side opposite the obtuse angle is equivalent to the sum of the squares of the other two sides, increased by twice the product of one...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...= 6ft., AC =5 ft., and BC = 7 ft. Find the projection of AC upon BC. PROPOSITION XIII. THEOREM 662. In an obtuse-angled triangle the square of the side opposite the obtuse angle is equivalent to the sum of the squares of the other two sides, increased by twice the product of one...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...ZZ>2 = AB\ Z + DC = AC. § 371 BOOK 111. PLANE GEOMETRY. PROPOSITION XXX. THEOREM. 376. In any obtuse triangle, the square of the 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 those sides by the projection...
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Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - Geometry - 1904 - 324 pages
...the acute angle A. a2 -h2 = (b -j)2=b2 - 2bj + j*=b2 - 2bj + c* -h*; :.a*-b*-abj+c*. 306. Theorem. In an obtuse-angled triangle the square of the side opposite the obtuse angle is greater than the sum of the squares of the other two sides by twice the product of either of those...
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Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - Geometry - 1904 - 322 pages
...sides, and h denote b's altitude, and / the sect from its foot to the acute angle A . 306. Theorem. In an obtuse-angled triangle the square of the side opposite the obtuse angle is greater than the sum of the squares of the other two sides by twice the product of either of those...
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Catalogue ...

Yale University. Sheffield Scientific School - 1905 - 1074 pages
...opposite sides of a quadrilateral circumscribed about a circle equals the sum of the two other sides. 4. In an obtuse-angled triangle the square of the 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 by the projection...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...the projections of b and c upon a. NUMERICAL PROPERTIES PROPOSITION XXIX. THEOREM 374 In an obtuse triangle, the square of the 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 those sides and the projection...
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