## Proceedings of the Edinburgh Mathematical Society, Volume 16 |

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algebraic algorithme angles applied Archimedes axes axis B.Sc base Book centre circle College common complete condition conic consider constants containing continuous corresponding COSC definition denote deux difference direction displacements Edinburgh equal equation équations Euclid's exist expressed factors figure fonction force geometry George given gives Glasgow Hence inequalities integral JOHN l'équation l'on limit lines magnitudes Mathematics meaning Meeting method multiples Note ordonnée parallel peut plane position present produced Professor proof proportion proposition prove puissance quantity racines ratio referred relation respect School sides similar simple solid space square substitution suppose surface symbole theorem theory tractions transformation unit University valeur volume w₁

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Page 64 - ... 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 39 - 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 100 - 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 47 - 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 81 - ... 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 53 - ... 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.