 | George Washington Hull - 1807 - 408 sider
...by projecting the edges of a cube upon a plane perpendicular to a diagonal? 433. The square of any diagonal of a rectangular parallelepiped 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... | |
 | Euclides - 1864 - 448 sider
...and join the points where the perpendiculars meet the plane. 29. This is to shew that the square on the diagonal of a rectangular parallelepiped is equal to the sum of the squares on its three edges. 30. This theorem is analogous to the corresponding theorem respecting a... | |
 | Robert Potts - 1865 - 528 sider
...the projection of GH on the plane AH. DD THEOREM IL Prove that four times the square described upon the diagonal of a rectangular parallelepiped, is equal to the sum of the squares described en the diagonals of the parallelograms containing the parallelepiped. Let AD be any... | |
 | Robert Potts - 1868 - 434 sider
...and join the points where the perpendiculars meet the plane. 29. This is to shew that the square on the diagonal of 'a rectangular parallelepiped is equal to the sum of the squares on its three edges. 30. This theorem is analogous to the corresponding theorem respecting a... | |
 | Robert Potts - 1876 - 446 sider
...and join the points where the perpendiculars meet the plane. 29. This is to shew that the square on the diagonal of a rectangular parallelepiped is equal to the sum of the squares on its three edges. 30. This theorem is analogous to the corresponding theorem respecting a... | |
 | James White - 1878 - 160 sider
...octahedron (eight sides); (4) a dodecahedron (twelve sides); (5) an icosahedron (twenty sides.) XVI. The square of the diagonal of a rectangular parallelepiped is equal to the sum of the squares of its three edges. XVII. The volume of a pyramid is one-third of the product of its base and... | |
 | Edward Albert Bowser - 1891 - 424 sider
...597. COR. 1. The diagonals of a rectangular parallelopiped are equal. 598. COR. 2. The square of a diagonal of a rectangular parallelepiped is equal to the sum of the squares of the three edges meeting at any vertex. For, if AG is a rectangular parallelepiped, the rt.... | |
 | Euclid - 1892 - 460 sider
...intersects two pairs of opposite faces, the common sections form a parallelogram. 8. The square on the diagonal of a rectangular parallelepiped is equal to the sum of the squares on the three edges conterminous with the diagonal. 9. The square on the diagonal of a cube... | |
 | William John McClelland, Thomas Preston - 1893 - 402 sider
...cos2 a + cos2/3 = sin2 7. Therefore cos2 a + cos2 13 + cos2 7 = 1.* * This relation merely asserts that the square of the diagonal of a rectangular parallelepiped is equal to the sum of the squares of its three edges ; the diagonal in this case heing the radius to P, and the edges the perpendiculars... | |
 | George Albert Wentworth - 1895 - 458 sider
...to the cone. Ex. 511. The diagonals of a parallelepiped bisect each other. Ex. 512. The square of a diagonal of a rectangular parallelepiped 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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This is to shew that the square on the diagonal of a rectangular parallelepiped is equal to the sum of the squares on its three edges. 
