Sentence Examples

  • The majority, in which Cardinal Manning pla t ed a very active part, took their stand on theological reasons o the strongest kind; they invoked the promises of Our Lord o St Peter: " Thou art Peter, and upon this rock will I build y Church, and the gates of hell shall not prevail against her " and again, " I have prayed for thee, Peter, that thy faith ail not; and do thou in thy turn confirm thy brethren "; they showed the popes, in the course of the ages, acting as the g ardians and judges of the faith, arousing or welcoming dogmati controversies and authoritatively settling them, exercising the supreme direction in the councils and sanctioning their decis ons; they explained that the few historical difficulties did not in olve any dogmatic defect in the teaching of the popes; they i sisted upon the necessity of a supreme tribunal giving judg ent in the name of the whole of the scattered Church; and finally, they considered that the definition had become opportu e for the very reason that under the pretext of its inopportuneness the doctrine itself was being attacked.
  • Since A lk is a determinant we similarly obtain Alk = a21Alk+� � � +a2,k-iAl,k +a2,k+lAl,k+ ���+a2 21 2,k-1 2, k +1 2,n and thence = Xalia2kAli where k; i,k 2k and as before A = a1, an A i> k i,k I ail, auk 12k an important expansion of A.
  • Of the area A, f f xdxdy = o, ffydxdy = 0, (6) R = p hA, (7) xhA = - cos a f f x 2 dA - sin affxydA, fxydA, (8) yhA = - cos a ff xydA - sin ail y 2 dA.
  • O16u3) If we replace 440136u3 in this expression by g405 6 u 3, the method of § 68 gives A -Q AIL h (uo + 5 u 1 + u2 + 6u3 + u4 + 5 14 6 + us); the expression on the right-hand side being an approximate expression for B, and differing from it only by s1eH5 6 u 3.
  • If anything ail a man, so that he does not perform his functions, if he have a pain in his bowels even--for that is the seat of sympathy--he forthwith sets about reforming--the world.

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