Sentence Examples

  • Taking the same example as before the process leads to the system of equations acx 4 +alx 3 +a2x 2 +a3x =0, aox 3 +a1x 2 +a2x+a 3 = 0, box +bix -1-b2x =0, box' +b i x 2 -{-h 2 x = 0, box + b i x + b:: = 0, whence by elimination the resultant a 0 a 1 a 2 a 3 0 0 a 0 a 1 a 2 a3 bo b 1 b 2 0 0 0 bo b 1 b 2000 bo b 1 b2 which reads by columns as the former determinant reads by rows, and is therefore identical with the former.
  • Hesse's canonical form shows at once that there cannot be more than two independent invariants; for if there were three we could, by elimination of the modulus of transformation, obtain two functions of the coefficients equal to functions of m, and thus, by elimination of m, obtain a relation between the coefficients, showing them not to be independent, which is contrary to the hypothesis.
  • V., established the important result that in the case of a form in n variables, the concomitants of the form, or of a system of such forms, involve in the aggregate n-1 classes of aa =5135 4 +4B8 3 p) =0, =5(135 4 - 4A 2 p 4) =0, P yield by elimination of S and p the discriminant D =64B-A2.
  • The first effect of the roasting is the elimination of sulphur as sulphurdioxide, with formation of oxide and sulphate of lead.
  • With ammonia, benzaldehyde does not form an aldehyde ammonia, but condenses to hydrobenzamide, (C 6 H 5 CH) 3 N 2, with elimination of water.

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