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" The square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three dimensions. "
Solid Geometry, with Problems and Applications - Page 38
by Herbert Ellsworth Slaught, Nels Johann Lennes - 1911 - 190 pages
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...instead of Euc. i. 47, the truth of the theorem may be proved. 26. This is to shew that the square of the diagonal of a rectangular parallelopiped is equal to the sum of the squares of its three edges. 27. Let a rectangular parallelogram ABCD be formed by four squares, each...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...A'B'C', and by Euc. i. 47, and note page 82, the truth of the property is shewn. 45. This is to shew that the square on the diagonal of a rectangular parallelopiped is equal to the sum of the squares on its three edges. 46. This mav be effected in several ways, the most 'simple is by drawing...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...equal. Therefore these diagonals are all equal to each other. QED THEOREM VIII. 692. The square of each diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three edges which meet at any vertex. Hypothesis. Same as in Theorem VII. Conclusion....
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The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...The edges of a regular tetraedron are each 2e. Show that the surface is 4« 2 j/3. 6. The square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of three edges meeting at a common vertex. 7. Two prisms, or pyramids, having equivalent bases,...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 166 pages
...and ABC give by aid of §§ 338 and 528, A'C2 = AA* + AC2 = AA!*- + A& + AD\ That is, the square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three edges meeting at any vertex. PROPOSITION VIII. THEOREM. 534. The sum of the squares...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...597. COR. 1. The diagonals of a rectangular parallelopiped are equal. 598. COR. 2. The square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three edges meeting at any vertex. For, if AG is a rectangular parallelopiped, the rt....
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 464 pages
...to the cone. Ex. 511. The diagonals of a parallelopiped bisect each other. Ex. 512. The square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of its three dimensions. PROPOSITION XXXVI. THEOREM. 668. Every section of a circular cone...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...of their bases. 766. The diagonals of a rectangular parallelopiped are equal. 767. The square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three diagonals meeting in any vertex. 768. The volume of a triangular prism is equal...
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A history of elementary mathematics

Florian Cajori - Mathematics - 1896 - 336 pages
...a point (known to Archimedes, but not proved by him). He also gives the theorem that the square of the diagonal of a rectangular parallelopiped is equal to the sum of the three squares of its sides.1 Algebraically are solved problems like this : To inscribe in an equilateral...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...by projecting the edges of a cube upon a plane perpendicular to a diagonal? 433. The square of any diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three edges meeting at any vertex. 434. The sum of the squares of the four diagonals...
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