The Messenger of Mathematics, Volume 21Macmillan and Company, 1892 |
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Expressions et termes fréquents
arithmetical series asymptotic limits B₁ Brocard point Cambridge centre of gravity centre of pressure circle circum-circle coefficients congruence conic constant contain corresponding curve denote determinant divisors double points E₁ equation Euler expressed factors formula functions given gives h₁ h₂ harmonic scheme Hence inequality integral intersection J. W. L. GLAISHER linear logn Mersenne's MESSENGER OF MATHEMATICS modulus nine-points circle normal form number of primes number of representations obtained P₁ P₂ pairs plane powers prime numbers Prof quadratic quadratic functions quadric quantities quartic relation respectively rows satisfied sequence Serret square number square roots stigmatic multiplier stigmatic series substitution surface tangents theorem three squares triangle triangular number u₁ unity values vanish W. W. Rouse Ball x₁ Y₁ Y₂ zero μω ди
Fréquemment cités
Page 7 - ... (m +1) (m + 2) (m + 3) (m + 4) (m + 5) (m + 6) (m + 7) > 1.2.3.4.5.6.7.8.9.10.11.12.13, which is easily seen to be satisfied when m = or > 100.
Page 6 - M- 1 M- 2 M- 3 M- 4 M- 5 M- 6 M- 7 M- 8 M- 9 M- 10 M- 11 M- 12 M...
Page 22 - ... but a medium plus the invisible order of things, so that when the motions of the visible universe are transferred into ether, part of them are conveyed as by a bridge into the invisible universe, and are there made use of or stored up. Nay, is it even necessary to retain the conception of a bridge ? May we not at once say that when energy is carried from matter into ether it is carried from the visible into the invisible; and that when it is carried from ether to matter it is carried from the...
Page 74 - An octagonal plate is immersed in a fluid, so that one of its sides is upon the surface ; find the distance of the centre of pressure from the centre of the plate.
Page 22 - In fine, what we generally call ether may be not a ' mere medium, but a medium plus the invisible order of things, so that when the motions of the visible universe are transferred into ether, part of them are conveyed as by a bridge into the invisible universe, and are there made use of or stored up.
Page 34 - Mersenne published, in effect, the statement that the only values of p not greater than 257 which make Mp prime are 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257.
Page 126 - Consequently 12E (n) is the number of representations of n as a sum of three squares ; for, assuming that this is so for 1 , 2, 3, ...,.«— 1, we may infer from the formula X.
Page 95 - In the text we have set ont the outstanding group and the first period, the other periods will be formed from this one by adding to each denominator in it successive multiples of 210. each of which is equal to zero or a positive quantity. So the eighth group of the second arrangement is resoluble into the pairs each of which is zero or a negative quantity. It may be as well to notice in this place that the sum of the coefficients, reckoning from the first term of the outstanding group to the term...
Page 40 - ... important problem of Physical Astronomy. In the History of the Mathematical Theories of Attraction and of the Figure of the Earth will be found an account of the origin and early progress of the branch of analysis which we are now about to expound. 2. Suppose that the expression (1 — 2oa; + a 2 )^ is expanded in a series of ascending powers of a.; the coefficient of a...