 | James Hayward - 1829 - 218 pàgines
...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... | |
 | James Hayward - 1829 - 228 pàgines
...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... | |
 | John Radford Young - 1830 - 390 pàgines
...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... | |
 | John Radford Young - 1838 - 296 pàgines
...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... | |
 | John Radford Young - 1848 - 300 pàgines
...— 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... | |
 | John Radford Young - 1850 - 294 pàgines
...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... | |
 | Charles Davies, Adrien Marie Legendre - 1869 - 470 pàgines
...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 =... | |
 | Adrien Marie Legendre - 1871 - 490 pàgines
...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*... | |
 | William Chauvenet - 1872 - 382 pàgines
...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... | |
 | Charles Davies - 1872 - 464 pàgines
...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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parallelepiped, the square of the diagonal is equal to the sum of the squares of the three edges. 
