Sentence Examples

  • He proceeded as far as Aix-la-Chapelle, where he fell sick of a fever, and suffered so much from weakness and poverty, that he made his way on foot to Amsterdam, and came back to Norway.
  • In the Norse version of the Carolingian epic Guillaume appears in his proper historical environment, as a chief under Charlemagne; but he plays a leading part in the Couronnement Looys, describing the formal associations of Louis the Pious in the empire at Aix (813, the year after Guillaume's death), and after the battle of Aliscans it is from the emperor Louis that he seeks reinforcements.
  • From the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields ai-2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-aix n- +a2x n-2.
  • To represent the simplest perpetuant, of weight 7, we may take as base either A2B 1 B 2 or A l A 2 B2, and since Ai+Bi =o the former is equivalent to A 2 ArB 2 and the latter to A 2 B i B2; so that we have, (1 -f-aix) (1 + a2x).
  • 816) of Lyons, being on one of these commissions, persuaded Felix to appear before a synod at Aix-laChapelle in 799.

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