## An Elementary Treatise on the Theory of Equations: With a Collection of Examples |

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according Algebra apply approximation Assume becomes biquadratic equation calculate called changes of sign Chapter cloth coefficients College column common measure consider constituents continued Crown 8vo cubic equation denote derived determinant divide divisible Edition element equal equation f equation f(x example expression factors four fraction function give given greater Hence higher identity imaginary roots increases integer involves less lies method multiply namely number of changes obtain occur original positive roots powers preceding Article present proceed proposed equation prove quadratic quantities quotient rational real roots reciprocal equation relation remainder repeated respect result rows rule rule of signs satisfy shew solution solve square student Sturm's substitute successively suppose symbols taken theorem theory third tion transformed Treatise true unity vanish zero

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Seite 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.

Seite 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.

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

Seite 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.

Seite 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.

Seite 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.

Seite 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...

Seite 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...

Seite 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.

Seite 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...