Proceedings of the Edinburgh Mathematical Society, Volume 16Scottish Academic Press, 1898 - Electronic journals |
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... Proportion in Elementary Geometry , 99 GIBSON , Prof. , and MACDONALD , W. J. Discussion on Euclid's Definition of Proportion [ Title ] , 48 GUIMARÃES , R. On a Geometrical Problem , 47 iv JACK , Professor . INDEX . A New Proof.
... Proportion in Elementary Geometry , 99 GIBSON , Prof. , and MACDONALD , W. J. Discussion on Euclid's Definition of Proportion [ Title ] , 48 GUIMARÃES , R. On a Geometrical Problem , 47 iv JACK , Professor . INDEX . A New Proof.
Page 48
... Fig.15 , we have Power of A AD . AF Power of B BD . BE AD2 CA = BD2 CB Discussion on Euclid's Definition of Proportion . Papers by Prof. GIBSON and Mr W. J. MACDONALD . Fifth Meeting , March 11th , 1898 . Dr MORGAN 48.
... Fig.15 , we have Power of A AD . AF Power of B BD . BE AD2 CA = BD2 CB Discussion on Euclid's Definition of Proportion . Papers by Prof. GIBSON and Mr W. J. MACDONALD . Fifth Meeting , March 11th , 1898 . Dr MORGAN 48.
Page 99
... Euclid's Elements appears in all editions of Euclid , I know of no school or college where it is read ; I know of no examination for which it is prescribed , and I have never seen an examination paper which contained a question based ...
... Euclid's Elements appears in all editions of Euclid , I know of no school or college where it is read ; I know of no examination for which it is prescribed , and I have never seen an examination paper which contained a question based ...
Page 100
... Euclid's method has broken down . The current practice of using only his definitions seems to me a very unsatisfactory makeshift , especially because I believe that we have ready to our hand an equally rigorous method , that is free ...
... Euclid's method has broken down . The current practice of using only his definitions seems to me a very unsatisfactory makeshift , especially because I believe that we have ready to our hand an equally rigorous method , that is free ...
Page 104
... Euclid any further ; but I have discussed Euclid's definition of ratio at considerable length in order to show that when we approach the consideration of ratio from his standpoint , we have to put out of sight altogether the ...
... Euclid any further ; but I have discussed Euclid's definition of ratio at considerable length in order to show that when we approach the consideration of ratio from his standpoint , we have to put out of sight altogether the ...
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Common terms and phrases
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.