Mathematical PapersMacmillan and Company, 1882 - 658 pàgines |
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Frases i termes més freqüents
ABCD algebra axis C₁ C₂ called circle circular points Clifford coefficients common tangents conicoids coordinates corresponding cubic curvature curve denote determined diagonal lines dimensions distance ellipsoid elliptic Elliptic Functions elliptic geometry equation evenly distant expression factor foci formula four geometry given Grassmann harmonic identical inner conic invariant involution Jacobian line at infinity linear locus London Mathematical Society magnitude manifoldness Mathematical measure-relations mediates meet metric multiplied n-fold n-gram oddly distant origin outer conic pair of obverses parabola parameters pass perpendicular plane points at infinity polygon proximate quadric quadric surface quantics quantities quaternion ratio regard relation represented result Riemann's surface rotor self-conjugate sin² space statement straight line surface tetrahedron theorem theory Theta functions tion touch transformation triangle types values vanishes variables vector vertices zero
Passatges populars
Pàgina 22 - I propose to extend the meaning of the term, so as to make it cover all that takes place beneath the ordinary threshold, or say, if preferred...
Pàgina 21 - That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave.
Pàgina 34 - ... from the centre on the tangent plane Ix + my + nz = p ........... . ......... (3), of the ellipsoid (2) ; that is, if we draw a plane perpendicular to the given axis to touch the ellipsoid (2), then p is the central perpendicular on this plane. It is also known* that the moment of inertia about any axis whatever, is equal to the moment about a parallel axis through the centre of gravity, together with the moment which the whole mass, if collected at the centre of gravity, would have about the...
Pàgina xlv - The geometer of to-day knows nothing about the nature of actually existing space at an infinite distance ; he knows nothing about the properties of this present space in a past or a future eternity. He knows, indeed, that the laws assumed by Euclid are true with an accuracy that no direct experiment can approach, not only in this place where we are, but in places at a distance from us that no astronomer has conceived ; but he knows this as of Here and Now ; beyond his range is a There and Then of...
Pàgina xxviii - CLIFFORD — THE ELEMENTS OF DYNAMIC. An Introduction to the Study of Motion and Rest in Solid and Fluid Bodies.
Pàgina 20 - Similarly although the axioms of solid geometry are true within the limits of experiment for finite portions of our space, yet we have no reason to conclude that they are true for very small portions ; and if any help can be got thereby for the explanation of physical phenomena, we may have reason to conclude that they are not true for very small portions of space" (see Clifford's ' Mathematical Papers,
Pàgina xlvi - ... but if we suppose it approximately uniform to the limit of telescopic reach, it will be restricted to very much narrower limits. I cannot perhaps do better than conclude by describing to you as well as I can what is the nature of things on the supposition that the curvature of all space is nearly uniform and positive. In this case the Universe, as known, becomes again a valid conception; for the extent of space is a finite number of cubic miles.4 And this comes about in a curious way.
Pàgina 56 - But hence flows as a necessary consequence that the propositions of Geometry cannot be derived from general notions of magnitude, but that the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience. Thus arises the problem to discover the simplest matters of fact from which the measure-relations of space may be determined ; a problem which from the nature of the case is not completely determinate, since there may be several systems...
Pàgina xlvi - In fact, I do not mind confessing that I personally have often found relief from the dreary infinites of homaloidal space in the consoling hope that, after all, this other may be the true state of things.
Pàgina xliv - What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobatchewsky to Euclid. There is, indeed, a somewhat instructive parallel between the last two cases. Copernicus and Lobatchewsky were both of Slavic origin. Each of them has brought about a revolution in scientific ideas so great that it can only be compared with that wrought by the other.