## Proceedings of the Edinburgh Mathematical Society, Volume 3 |

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ABCD arbelos asymptotes axes bisects bx")pdx centre of similitude circle ABC circumference circumscribed circle collinear concyclic points cone confocal conicoid constant contour lines contours corresponding points curve cylinder D(ABC denote determined diagonal diameter displacement distance drawn EDINBURGH MATHEMATICAL SOCIETY equal equation Eutocius figure finite four points Fourier's George Thom gives Hence hyperbola inscribed integral limit line joining Mathematical mean proportionals meet method middle point minimum circle nine-point circle orthocentre paper parabola parallel parallelogram pass perpendicular points of intersection polygon position projection quadric quadrilateral radical axis radius ratio rectangle respectively result right angles roller rotation segment semicircle sides Simson lines sphere square suppose surface tangent planes theorem Thomas Muir tion touch triangle vertex vertices vibration xm(a

### Popular passages

Page 83 - ... une est indépendante de la position du point B, et V autre 2 dépend de la position de ce point. Chercher ce que devient la surface 2 quand, dans la construction qui donne les points de cette surface, on fait jouer au point A le rôle du point B, et inversement. 3°. Le point A restant fixe, déterminer les positions occupées par le point B quand la surface 2 n' a pas un centre unique à distance finie.

Page 78 - ... the sides of the triangle formed by joining the middle points of the sides of the original triangle...

Page 8 - If two circles touch each other, and also touch a given straight line, the part of the straight line between the points of contact is a mean proportional between the diameters of the circles.

Page 34 - Enler's and Lexell's memoirs of 1775. 211. The following properties are also given, viz., considering two similar solid bodies (or in particular any two positions of a solid body) and joining the corresponding points, the lines which pass through one and the same point form a cone of the second order ; and the points of either body form on this cone a curve of the third order (skew cubic). And, reciprocally...

Page 67 - ... equal to the axis-major of the surface. This theorem, due to Prof. Mac Cullagh, is analogous to the theorem for plane curves, that a line through the centre parallel to a tangent to an ellipse cuts off on the focal radii portions equal to the axis-major. 192. M. Chasles has used the...

Page 65 - The rectangle contained by the side of a cone -of revolution enveloping an ellipsoid, intercepted between the vertex and point of contact, and the perpendicular from the centre upon the tangent plane at that point, is constant.

Page 6 - A6 between which it is required to find two mean proportionals in continued proportion...

Page 106 - How I wish I could recollect of circle round The exact relation Archimede unwound! The " relation Archimede unwound...

Page 19 - The series which defines the function may be looked on as a sum of terms, each of which is a product of...