Sentence Examples

  • For the few cases where data are available - data, however, belonging to engines representing standard practice in their construction and in the design of cylinders and steam ports and passages - the law connecting p and v is approximately linear and of the form p=c - bv (28) where b and c are constants.
  • Schlafli 1 this equation may be directly formed and exhibited as the resultant of two given equations, and an arbitrary linear non-homogeneous equation in two variables.
  • Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
  • Linear Equations.-It is of importance to study the application of the theory of determinants to the solution of a system of linear equations.
  • For further information concerning the compatibility and independence of a system of linear equations, see Gordon, Vorlesungen fiber Invariantentheorie, Bd.

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