Rule Of Signs Research Articles

Rule of Signs for Lens and Mirror Equation

Rule of Signs for Lens and Mirror Equation

A Rule of Signs Involving Certain Orthogonal Polynomials

A Rule of Signs Involving Certain Orthogonal Polynomials

893. The Rule of Signs

893. The Rule of Signs

558. [A. i.] The Rule of Signs for a Product: the Completed Multiplication Table

558. [A. i.] The Rule of Signs for a Product: the Completed Multiplication Table

Recent Extentions of Descartes' Rule of Signs

Recent Extentions of Descartes' Rule of Signs

Extensions of Descartes' Rule of Signs Connected with a Problem Suggested by Laguerre

Extensions of Descartes' Rule of Signs Connected with a Problem Suggested by Laguerre

Extensions of Descartes’ rule of signs connected with a problem suggested by Laguerre

Extensions of Descartes’ rule of signs connected with a problem suggested by Laguerre

An extension of descartes' rule of signs

An extension of descartes' rule of signs

(1) A School Algebra (2) A Treatise on Hydromechanics (3) Les Appareils d'Intégration (4) Einführung in die höhere Mathematik für Naturforscher und Aerzte (5) Elements of the Precision of Measurements and Graphical Methods (6) Matrices and Determinoids

(i)MESSRS. LANE'S “Algebra” looks as if it would prove a useful school-book. In dealing with the binomial and exponential series the authors state certain properties, with the explicit warning that they are not proving them. This is as it should be; but the chapter on exponentials and logarithms is not so clear as it might be; in particular, Arts. 135–7 would be better if arranged in the reverse order. In the earlier pages we have the old fallacious and meaningless statement: “to multiply a number a by a second number b, we do to a what is done to the unit to obtain b.” It would be much better to give the rule of signs as a rule pure and simple, and then to show by cases of (a – b)(c – d) that it does actually work out in practice. There are hundreds of examples—some, alas, of a highly artificial character; for instance, “If the hypotenuse of a right-angled triangle is x, and the other sides are y and z units of length, show that (1) A School Algebra. By F. O. Lane J. A. C. Lane. Pp. viii + 333. (London: Edward Arnold, n.d.) Price 3s. 6d. (2) A Treatise on Hydromechanics. Part ii. Hydrodynamics. By A. S. Ramsey. Pp. xiii + 360. (London: G. Bell and Sons., Ltd., 1913.) (3) Les Appareils d'Intégration. By H. de Morin. Pp. 208. (Paris: Gauthier-Villars, 1913.) Price 5 francs. (4) Einführung in die höhere Mathematik für Naturforscher und Aerzte. By Dr. J. Salpeter. Pp. xii + 336. (Jena: Gustav Fischer, 1913.) Price 12 marks. (5) Elements of the Precision of Measurements and Graphical Methods. By Prof. H. M. Goodwin. Pp. 104. (London: Hill Publishing Co., Ltd.; New York: McGraw-Hill Book Co., 1913.) (6) Matrices and Determinoids. By Prof. C. E. Cullis. Vol. i. Pp. xii + 430. (Cambridge University Press, 1913.) Price 215. net.

Scientific Serials

Bulletin of the New York Mathematical Society, vol. iii. No. 6. (New York: Macmillan. March, 1894). — Prof. Warkness (pp. 135–141) gives a careful and appreciative abstract of the Cours d'Analyse de l'École Polytechnique, by Camille Jordan, a work commended by Prof. Klein in “The Evanston Colloquium,” and which, in its second edition, is “entièrement refondue.” Three interesting, though short, notes on Permutations (pp. 142–148) are furnished by Prof. F. Morley. They are headed a plea for the chess-board in teaching determinants, a special rule of signs, and the enumeration of positions. There are numerous references to the authorities on the subject. Notes and new publications are full as usual.

Rules for the Algebraic Signs of Hyperbolic Formulae

Rules for the Algebraic Signs of Hyperbolic Formulae

A New Theory of the Rule of Signs [Continued

A New Theory of the Rule of Signs [Continued

A New Theory of the Rule of Signs

A New Theory of the Rule of Signs