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" parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges. "
The principles of analytical geometry - Page 144
by Henry Parr Hamilton - 1826 - 326 pages
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...the co-ordinate planes, form the rectangular parallelepiped whose diagonal is AM. The square of this diagonal is equal to the sum of the squares of the three edges which meet at the proposed point (El. 245) ; that is (AM) a = (MM') 2 -f (MM") a -f(MM'") a . Whence...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 pages
...the co-ordinate planes, form the rectangular parallelopiped whose diagonal is AM. The square of this diagonal is equal to the sum of the squares of the three edges which meet at the proposed point (El. 245) ; that is (AM) 2 = (MM') 2 -f (MM") 2 + (MM 7 ") 2 . Whence...
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The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic ...

John Radford Young - Conic sections - 1830 - 390 pages
...y", z"), be the origin, then D = y'*' 2 + y2 + z". This shows that, in a right-angled parallelopiped, the square of the diagonal is equal to the sum of the squares of the three edges. PROBLEM VII. (181.) To find the relation which exists among the angles which any straight line makes...
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Analytical Geometry ...

John Radford Young - Geometry, Analytic - 1838 - 296 pages
...z"), be the origin, then D = «/y + y" + z' 2 . This shows that, in a right-angled parallelopiped, the square of the diagonal is equal to the sum of the squares of the three edges. PROBLEM VII. (221.) To find the relation that exists among the angles which any straight line makes...
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The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic ...

John Radford Young - Geometry, Analytic - 1848 - 300 pages
...— j/")2Ifone of the points, as (x", y", z"), be the origin, then Thts shows that, ma nght angled parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges. PROBLEM VII. (181.) To find the relation which exists among the angles which any straight line makes...
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The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic ...

John Radford Young - Geometry, Analytic - 1850 - 294 pages
...points, as (%", y f/ , z"}¡ be the origin, then D = v 1(0^ + ^.+ ^. This shows that, in a right angled parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges. PROBLEM VII. Parallel to any proposed line, draw a line from the origin, and make its length, D, equal...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...AB* AC 2 Cor. 4. The square described on the diagonal of a square is double the given square. For, the square of the diagonal is equal to the sum of the squares of the two sides; but the square of each side is equal to the given square : hence, AC 2 =...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1871 - 490 pages
...have, AC'' DC. Cor. 4. The square described on the diagonal square is double the given square. For, the square of the diagonal is equal to the sum of the squares of the two sides ; but the square of each side is equal to the given square : hence, ana AC*...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...Corollary. In a rectangular parallelepiped, the four diagonals are equal to each other; and the square of a diagonal is equal to the sum of the squares of the three edges which meet at a common vertex. Thus, if AG is a rectangular parallelepiped, we have, by dividing the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...JBD : DC. Cor. 4. The square described on the diagonal of a square is double the given square. For, the square of the diagonal is equal to the sum of the squares of the two sides ; but the square of each side is equal to the given square : hence, DO AC*...
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