Proceedings of the Edinburgh Mathematical Society, Volume 16Scottish Academic Press, 1898 - Electronic journals |
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Page 7
... factors whose sum was a would lead to the squaring of the n - 1 values b + 1 , c + k , etc. The actual demonstration given by Archimedes is no doubt quite different , but the artificiality of the transformation referred to above leads ...
... factors whose sum was a would lead to the squaring of the n - 1 values b + 1 , c + k , etc. The actual demonstration given by Archimedes is no doubt quite different , but the artificiality of the transformation referred to above leads ...
Page 57
... + - -- a1 - + + a2 .. ar - a pu = ar * " On the Factors of the Solutions in Finite Terms of Lamé's Equation , " Quarterly Journal of Pure and Applied Mathematics , No. 114 , 1897 . By differentiation of we find u du du ( pu 57.
... + - -- a1 - + + a2 .. ar - a pu = ar * " On the Factors of the Solutions in Finite Terms of Lamé's Equation , " Quarterly Journal of Pure and Applied Mathematics , No. 114 , 1897 . By differentiation of we find u du du ( pu 57.
Page 59
... factor √pu - e . Then if n = 2m + 1 , U1 = √pu - e ( pu - a ) ( pua ) ... ( pu - am ) , where all the a's are real and different and no one coincides with an e , as I have proved in the former paper already referred to . n du 。( pu ...
... factor √pu - e . Then if n = 2m + 1 , U1 = √pu - e ( pu - a ) ( pua ) ... ( pu - am ) , where all the a's are real and different and no one coincides with an e , as I have proved in the former paper already referred to . n du 。( pu ...
Page 60
... factor or one , and when n is odd , ( n − 1 ) / 2 or ( n − 3 ) / 2 , according as U1 has an irrational factor √pue or the factors √ ( pu − e ) ( pu − e ) ( pu – eç ) , g ( pu ) is the irrational factor , if any , in Un , and C , D ...
... factor or one , and when n is odd , ( n − 1 ) / 2 or ( n − 3 ) / 2 , according as U1 has an irrational factor √pue or the factors √ ( pu − e ) ( pu − e ) ( pu – eç ) , g ( pu ) is the irrational factor , if any , in Un , and C , D ...
Page 66
... factor in brackets is ( 3 ) which gave the solution ( II . ) y'2 = 0 gives y = D - ( III . ) which on trial is found to be a solution of the equation , and is thus a second family of singular solutions . It is to be noticed , however ...
... factor in brackets is ( 3 ) which gave the solution ( II . ) y'2 = 0 gives y = D - ( III . ) which on trial is found to be a solution of the equation , and is thus a second family of singular solutions . It is to be noticed , however ...
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abscisses algebraic algorithmes naturels angles Archimedes axes axis B.Sc b₁ Betti's Theorem centre College common difference Conformal Transformation conic constants corresponding COSC courbe D.Sc d'une d²r denote deux racines displacements dy dz Edinburgh égale equal equation équations Euclid's definition exemple fonction force parallel geometry George Heriot's School George Watson's College given Glasgow Hence hyperlogarithmes inequalities integral irrational number l'algorithme l'autre l'équation l'expression l'on LAWRENCE CRAWFORD LL.D logarithme magnitudes Mathematics membre method moyen des algorithmes nombre ordonnée peut plane pourra premier Professor proportion proposition puissance qu'on quadratic space quantuplicity racines réelles ratio rational numbers relation représenter RITCHIE SCOTT School segment singular solutions solid Stewart's theorem suppose surface tractions surpuissance symbole théorème theory triangle U₁ unaltered unit force v₁ valeur w₁
Popular passages
Page 62 - ... EDINBURGH. Mathematical Society, May 13. — Mr. JB Clark, President in the chair. — The following papers were read :— On the second solutions of Lame's equation, by Mr. Lawrence Crawford (communicated by Mr. JW Butters); on the insolation of a sun of sensible magnitude, by Mr. A. Ritchie Scott; the singular solutions of a certain differential equation of the second order, by Mr. Hugh Mitchell. PARIS. Academy of Sciences, June 6. — M. Wolf in the chair. — New photographic studies of the...
Page 37 - In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them.
Page 98 - II. A greater magnitude is said to be a multiple of a less, when the greater is measured by the less, that is, ' when the greater contains the less a certain number of times exactly.' III. " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity.
Page 45 - Stewart's theorem enables us to resolve easily the following problem : " To draw a circle touching another given circle and passing through two given points.
Page 79 - ... produced. The proposition, however, is equally true for both figures. By adopting the suggested convention we get rid both of the difficulty of drawing the figure and of the implication that the truth of the proposition is limited to the case where the perpendiculars lie on opposite sides of BC. (c) " AB, BC are equal arcs of a circle and P is a point on the arc BC, show that BP bisects the angle contained by AP and CP produced.
Page 51 - ... methods conducted to the same result. Object of the present paper is the analytical demonstration and the extension to «-dimensional space of a third mode of generation, equally due to Mannheim, according to which the wave-surface is the locus of the point that admits with respect to a given ellipsoid an enveloping cone , one of the principal sections of which is a right angle. This generalisation however does not conduct to the same « — 1-dimensional figure as before (p.