Sentence Examples

  • Since the determinant having two identical rows, and an3 an3 ��� ann vanishes identically; we have by development according to the elements of the first row a21Au+a22Al2 +a23A13+��� +a2nAin =0; and, in general, since a11A11+a12A12 +ai 3A13+�� � +ainAin = A, if we suppose the P h and k th rows identical a A +ak2 A 12 +ak3A13+��� +aknAin =0 (k > i) .and proceeding by columns instead of rows, a li A lk +a21A2k + a 31A3k+���+aniAnk = 0 (k .>
  • This system of equations must involve the three conditions of equilibrium of the extraneous forces which are already identically satisfied, by hypothesis; there remain therefore 2n ~ independent relations to determine the 2n3 unknown stresses.
  • +XL vanishes identically, and X is indeterminate.
  • The nomenclature of the numerous ranges in this part of the Kuen-lun is extremely confusing, owing to different travellers having applied the same name to different ranges and to different travellers have applied different names to what is probably often identically the same range.
  • On the ist of August Palmerston wrote to Ponsonby impressing upon him that the representatives of the powers, in their communications with the Porte, "should act not only simultaneously in point of time, but identically in point of manner" - a principle important in view of later developments.