## An elementary treatise on the theory of equations |

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a₁ Algebra approximation b₁ b₂ biquadratic equation c₁ c₂ changes of sign cloth coefficients column contour contrary signs Crown 8vo cubic equation d₁ denote derived function determinant divide divisible equa equal roots equation f(x equation f(x)=0 equation x³ example expression factors following equations Fourier's functions given equation greater greatest common measure Hence identity imaginary roots integer last term Let f(x method multiply negative root Newton's method nth degree nth roots number of changes obtain odd number original equation P₁ P₂ positive roots preceding Article proposed equation quadratic quotient real roots reciprocal equation result rule of signs shew shewn solution solve the equation Sturm's functions Sturm's theorem substitute suffixes superior limit suppose symmetrical function Theory of Equations tion transformed equation Treatise unity unknown quantities vanish zero

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Page 5 - For really ripe scholarship. extensive acquaintance with Latin literature, and familiar knowledge of continental criticism, ancient and modern, it is unsurpassed among English editions.

Page 276 - Routh. — AN ELEMENTARY TREATISE ON THE DYNAMICS OF THE SYSTEM OF RIGID BODIES. With Numerous Examples. By EDWARD JOHN ROUTH, MA, late Fellow and Assistant Tutor of St. Peter's College, Cambridge; Examiner in the University of London. Second Edition, enlarged. Crown 8vo. cloth.

Page 268 - PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.

Page 2 - ... which can be altered only by the changes of entire units or integral multiples of units in the fundamental conditions of the problem ; the other concerning those chances which have respect to insensible gradations in the value of the element measured), the present tract has been drawn up.

Page 269 - Mr Smith's Work is a most useful publication. The Rules are stated with great clearness. The Examples are well selected and worked cut with just sufficient detail without being encumbered by too minute explanations; and there prevails throughout it that just proportion of theory and practice, which is the crowning excellence of an elementary work.

Page 2 - It is of importance that those who wish to cultivate any subject may be able to ascertain what results have already been obtained, and thus reserve their strength for difficulties which have not yet been conquered. The Author has endeavoured in this work to ascertain distinctly what has been effected in the Progress of the Calculus, and to form some estimate of the manner in which it has been effected.

Page 272 - Mathematics. Each chapter is followed by a set of Examples: those which are entitled Miscellaneous Examples, together with a few in some of the other sets, may be advantageously...

Page 48 - ... any of the positive roots. For transform the proposed equation into one whose roots are the reciprocals of the roots of the proposed equation, and then the reciprocal of the superior limit of the positive roots of the transformed equation will be an inferior limit of the positive roots of the proposed equation. Thus suppose the proposed equation to be put — for x, and multiply by y...

Page 10 - The author has endeavoured to connect the history of the New Testament Canon with the growth and consolidation of the Church, and to point out the relation existing between the amount of evidence for the authenticity of its component parts, and the whole mass of Christian literature. Such a method of inquiry will convey both the truest notion of the connection of the written Word with the living Body of Christ, and the surest conviction of its divine authority.

Page 2 - In order to spare astronomers and observers in natural philosophy the confusion and loss of time which are produced by referring to the ordinary treatises embracing both branches of probabilities (the first...