Proceedings of the Edinburgh Mathematical Society, Volume 16Scottish Academic Press, 1898 - Electronic journals |
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... Angle , On the Second Solutions of Lamé's Equation DOUGALL , J. 42 d'U du2 √2 = U { n ( n + 1 ) pu + B U { n ( n + B } 57 Note on the Centre of Gravity of a Circular Arc , A General Method of Solving the Equations of 49 Elasticity ...
... Angle , On the Second Solutions of Lamé's Equation DOUGALL , J. 42 d'U du2 √2 = U { n ( n + 1 ) pu + B U { n ( n + B } 57 Note on the Centre of Gravity of a Circular Arc , A General Method of Solving the Equations of 49 Elasticity ...
Page 9
... angles to the axis at distance a from the vertex ; let the distance a be divided into n equal parts , the distances from the vertex of the points of section forming the A.P. a , b , ... l , and let the figures described in §4 be ...
... angles to the axis at distance a from the vertex ; let the distance a be divided into n equal parts , the distances from the vertex of the points of section forming the A.P. a , b , ... l , and let the figures described in §4 be ...
Page 13
... angle que fait avec OX la tangente en M soit en raison inverse de la sous - tangente en M ' . En posant y + Ayy1 , l'équation peut s'écrire ( 1 ) y ' = cy1y ' Considérons l'équation générale ( 2 ) yi yı1 = cy ' qui se réduit à la ...
... angle que fait avec OX la tangente en M soit en raison inverse de la sous - tangente en M ' . En posant y + Ayy1 , l'équation peut s'écrire ( 1 ) y ' = cy1y ' Considérons l'équation générale ( 2 ) yi yı1 = cy ' qui se réduit à la ...
Page 39
... angles . ACB ( Fig . 9 ) is a spherical A , with C a right angle . = π 2 ' Produce AC , AB to D and E so that AD = AE : Draw the great ○ DEF and produce CB to meet it in F. Then F is the pole of AD and A the pole of DF . Then sides and ...
... angles . ACB ( Fig . 9 ) is a spherical A , with C a right angle . = π 2 ' Produce AC , AB to D and E so that AD = AE : Draw the great ○ DEF and produce CB to meet it in F. Then F is the pole of AD and A the pole of DF . Then sides and ...
Page 40
... 2 3 4 5 where the mid - column contains the hypotenuse , the two next to it contain the angles , and the extreme columns the sides of the several right - angled triangles . Now assume cos hypotenuse = product of cosines of sides 40.
... 2 3 4 5 where the mid - column contains the hypotenuse , the two next to it contain the angles , and the extreme columns the sides of the several right - angled triangles . Now assume cos hypotenuse = product of cosines of sides 40.
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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.