THE MESSENGER OF MATHEMATICS, EDITED BY W. ALLEN WHITWORTH, M.A., FELLOW OF ST. JOHN'S COLLEGE, CAMBRIDGE. C. TAYLOR, M.A., FELLOW OF ST. JOHN'S COLLEGE, CAMBRIDGE. R. PENDLEBURY, M.A., FELLOW OF ST. JOHN'S COLLEGE, CAMBRIDGE. J. W. L. GLAISHER, M.A., F.R.S., FELLOW OF TRINITY COLLEGE, CAMBRIDGE. VOL. X. / [MAY, 1880-APRIL, 1881.] MACMILLAN AND CO. EDINBURGH: EDMONSTON & CO. GLASGOW: JAMES MACLEHOSE. DUBLIN: HODGES, FOSTER & CO. OXFORD: JOHN HENRY AND J. PARKER. 1881. CONTENTS. ARITHMETIC, ALGEBRA, AND TRIGONOMETRY. A geometrical construction relating to imaginary quantities. By Professor Trigonometrical theorems involving the products of four sines or four cosines. The symmetric functions of the roots of an equation. By A. R. Forsyth Note on an algebraical identity. By J. W. L. Glaisher On some algebraical expressions which are unaltered by certain substitutions. Addition to a note "A trigonometrical identity" By Harry Hart General expression for the radius of curvature in dipolar coordinates. By On the criteria for determining the nature of the conic represented by the general equation in areal coordinates. By Harry Hart The method of perspective: "Was it known to the Greek geometers?" By On conics circumscribed about, or inscribed in, triangles which are self-conjugate with respect to a given conic. By A. F. Torry A property of pedal curves. By P. A. Mac Mahon DIFFERENTIAL AND INTEGRAL CALCULUS AND Supplement to "Exercises." By Sir James Cockle On the curves represented by the equation Note on a theorem relating to quadratic expressions. By Professor H. Lamb |