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XXXIX.—On Centres, Faisceaux, and Envelopes of Homology
Published online by Cambridge University Press: 17 January 2013
Extract
One of the theorems of a paper which Professor Kelland did me the honour to read to the Society, in March 1865, opens up a field of geometrical investigation so interesting and fertile, that I venture to ask attention to some of the results of a partial examination of it in the following series of propositions. I think it right to explain, that I do not venture to expect attention to them on account of any importance attaching to them individually, but on account of their number and somewhat elegant relations. Considered individually, they may be of little importance, having no claim to rank, so to speak, among propositions of a planetary magnitude. But a system of moons, however diminutive, may become interesting if they present elegant relations among their mean motions and longitudes; and an orbit that would be grudged to a pigmy planet may be willingly accorded to a host of planetoids. If this is still too exalted language in which to speak of the following results, I can at least confidently affirm that they indicate a direction in which an analyst of very moderate attainments may easily discover for himself a shower of meteors.
- Type
- Research Article
- Information
- Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 24 , Issue 3 , 1867 , pp. 591 - 615
- Copyright
- Copyright © Royal Society of Edinburgh 1867
References
page 591 note * I fear this terminology may give an aspect of pretentiousness to the paper which is far from being intended. But if I was to avoid the indefinite title, “On a Certain Class,” &c., I confess I could find no other sufficiently descriptive.
page 592 note * The idea of the inverse of the problem of the Envelope seems first to have occurred to Boole. See his paper—characterised by his usual high generality and beautiful originality—in “Cambridge and Dublin Mathematical Journal,” vol. vii. p. 156.
page 594 note * The reader will find this subject elegantly treated in “Études Analytiques sur la Théorie Général des Courbes Planes,” par M. Felix Lucas (Paris, 1864); where, among other results, a very pretty proposition concerning a property of conics circumscribing the same quadrilateral (due to M. LAMÉ), is thus generalised:—Les polaires d'ordre quelconque d'un point du plan, relativement aux diverses courbes d'un faisceau pivotant, forment elles-mêmes un faisceau pivotant.