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" Construct, by 145, a right triangle, of which the hypothenuse BC (fig. 79) is equal to the side of the greater square, and the leg AB is equal to the side of the less square ; and AC is the side of the required square. "
An Elementary Treatise on Plane and Solid Geometry - Page 79
by Benjamin Peirce - 1837 - 159 pages
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...side of the less square ; and AC is the side of the required square. . . Proof. For, by 257, ^C2 = BC2— AB2. 263. Problem. To make a square equivalent...AC, and equal to the side of the third given square. To make a Square in a give i Ratio to a given Square. Join AD, and draw DE, perpendicular to AD, and...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 150 pages
...equal to the side of the less square; and AC is the side of the required square. Proof. For, by 257, 263. Problem. To make a square equivalent to the sum...Solution. Take AB (fig. 132) equal to the side of ono of the given squares. Draw BC, perpendicular to AB, and equal to the side of the second given square....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1865 - 150 pages
...less square ; and AC is the side of the required square. Proof. For, by 257, AC* = BC*— JIB2. 263. Problem. To make a square equivalent to the sum of any number of given squares. Solution. Take JIB (fig. 132) equal to the side of ono of the given squares. Draw BC, perpendicular to JIB, and equal...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 150 pages
...the side of the less square ; and AC is the side of the required square. Proof. For, by 257, AC2 = BC2— AB2. 263. Problem. To make a square equivalent...Solution. Take AB (fig. 132) equal to the side of ono of the given squares. Draw BC, perpendicular to AB, and equal to the side of the second given square....
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...be a side of the required square (II. 27). 38. Scholium. By continuing the same process we can find a square equivalent to the sum of any number of given squares. PROBLEM XXVIII. 39. To construct a square equivalent to the difference of two given squares. Construct...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 238 pages
...be a side of the required square (II. 27). 38. Scholium. By continuing the same process we can find a square equivalent to the sum of any number of given squares. PROBLEM XXVIII. 39. To construct a square equivalent to the difference of two given squares. Construct...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 398 pages
...S = R' — R. .". S is the square required. R Ri B*. APROPOSITION XVIII. PROBLEM. 348. To construct a square equivalent to the sum of any number of given squares. \ F/ \ A \ \ \ r Let m, H, o, p, r be sides of the given squares. It is required to construct a square...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...be a side of the required square (II. 66). 38. Scholium. By continuing the same process we can find a square equivalent to the sum of any number of given squares. PROBLEM XXVIII. 39. To construct a square equivalent to the difference of two given squares. PROBLEM...
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Elements of Geometry

George Albert Wentworth - 1881
...required. QE F R R в\ ! \ , R A' ->;— x - --- ~' С PROPOSITION XVIII. PROBLEM. 348. To construct a square equivalent to the sum of any number of given squares. о P &B m Let m, n, o, p, r be sides o the given squares. It is required to construct a square...
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Elements of Geometry, Plane and Solid

John Macnie - Geometry - 1895 - 374 pages
...Then 2 2 2 SCHOLIUM. It is obvious that, by a continuation of the process, we can obtain the side of a square equivalent to the sum of any number of given squares. 362. To construct a square equivalent to the difference of two given squares. Draw BM A. to BN, and...
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