Proceedings of the Cambridge Philosophical Society: Mathematical and physical sciences, Volume 19Cambridge Philosophical Society, 1920 |
Autres éditions - Tout afficher
Proceedings of the Cambridge Philosophical Society ..., Volumes 18 à 19 Cambridge Philosophical Society Affichage du livre entier - 1916 |
Proceedings of the Cambridge Philosophical Society: Mathematical ..., Volume 15 Cambridge Philosophical Society Affichage du livre entier - 1910 |
Proceedings of the Cambridge Philosophical Society: Mathematical ..., Volume 23 Cambridge Philosophical Society Affichage du livre entier - 1927 |
Expressions et termes fréquents
Abel's Abel's Theorem am,n appear bounded variation Bromwich Cambridge colourimeter Common Earwig Communicated by Professor complex condition constant convergent throughout coordinates cosh definition deposits earwigs elementary propositions equation expressed finite number follows formula G. H. HARDY G. N. WATSON given gravels gravitation Hence hydrogen ion concentration hyperparasite infinity integral interval J. E. Littlewood lamp Lemma limit logic Madreporarian Math motion Neon observed obtained paper positive prime primitive propositions Prof proof prove quadric Ramanujan rays recorded result Rodrigues sinh solution species spicules St John's College Stokes suppose surface t₁ t₂ tan³ tanh tanha theorem theory Trinity College tx+1 uniform convergence unity values w₁ w₂ wasp zero
Fréquemment cités
Page 312 - And to shew that I do not take Gravity for an essential Property of Bodies, I have added one Question concerning its Cause, chusing to propose it by way of a Question, because I am not yet satisfied about it for want of Experiments.
Page 177 - President, in the chair. The following were elected Fellows of the Society : — Mr.
Page 333 - Experiments were described with a mercury voltameter, in which one elctrode consists of a sphere of mercury deposited on the end of a fine platinum wire and measured by means of a microscope. Quantities of electricity varying from a few hundred electrostatic units to about one coulomb may be measured by it. The almost instantaneous change of size of the drop when a capacity of one tenth of a microfarad, charged to 1 volt, is discharged through the instrument is easily observed.
Page 113 - PRESIDENT, IN THE CHAIR. The following were elected Officers for the ensuing year: President: Mr GU Yule.
Page 81 - On Convergence Factors in Double Series and the Double Fourier's Series', Trans.
Page 139 - Proc. London Math. Soc., ser. 2, vol. 6, 1907, pp. 29-51. Young, in his paper already quoted, by means of the Heine-Borel Theorem*; and it plainly includes, as a particular case, Weierstrass's theorem referred to above. 5. It seems to me that the definition given by Stokes is not any one of A 1 , A 2, A 3 ; and that, if we are to understand him rightly, we must consider another parallel group of definitions. These definitions differ from those given above...
Page 14 - If p is an elementary proposition, ~ p is an elementary proposition. Dem. Axiom 2 gives us 'pAp' elementary when p is elementary; is ~ p, by Definition of Negation. Hence the theorem. This is a proof of Mr Russell's primitive proposition *1.7 given above. THEOREM 2 If p and q are elementary propositions, ' pvq ' is an elementary proposition. Dem. By Theorem 1, if p and q are elementary so also are ~j9 and ~ q.
Page 143 - ... than a given quantity e, which may be as small as we please, n increases beyond all limit as h decreases beyond all limit. 'DEMONSTRATION. If the convergency do not become infinitely slow it will be possible to find a number n, so great that for the value of h we begin with and for all inferior values greater than zero the sum of the neglected terms shall be numerically less than e....
Page 141 - Bl: a series quasi-uniformly convergent at every point of an interval (or in the neighbourhood of every such point) is not necessarily quasiuniformly convergent throughout the interval. We can apply the Heine-Borel Theorem in the manner indicated in the first sentences of...
Page 143 - ... numerically less than a given quantity e which may be as small as we please, n increases beyond all limit as h decreases beyond all limit.