# Proceedings of the Edinburgh Mathematical Society, Volume 7

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### Contents

 Section 1 1 Section 2 2 Section 3 4 Section 4 5
 Section 5 6 Section 6 30 Section 7

### Popular passages

Page 46 - ... the straight line AB. Bisect AB in D, and if the square upon AD be equal to the square upon C, the thing required is done : but if it be not equal to it, AD must be greater than C, according to the determination : draw DE at right angles to AB, and make it equal to C; produce ED to F, so that EF be equal to AD or DB, and from the centre E, at the distance EF, describe a circle meeting AB in G...
Page 63 - G sur une conique S, et un point D sur une droite L. Soient a, /3, y les points d'intersection des droites BC, ÇA et AB avec la droite L, et A', B', C' les seconds points de rencontre des droites AD, BD, CD avec la conique S.
Page 63 - L, correspond un point .I parfaitement determiné de la conique. Si donc inversement au lieu de se donner la droite L, on se donne le point I, la droite L sera parfaitement déterminée, et passera par les quatre points a, /3, y et D. On pent donc énoncer le théorème suivant : Théorème : Par un point D du plan d'une conique, on mène trois sécantes AA', BB', CC', et l'on prend un point I sur /a courbe. Si l'on prolonge chacun des côtés du triangle ABC jusqu...
Page 2 - A, (4) be a pair of sets of curves possessing the required property, we obtain at once another pair by substituting for x and y their values in terms of £, ?/. These may now be written as x, y, and the process again applied, and so on. Thus, let the values of the pairs of equal quantities in (2) be 1, 0, respectively (which is obviously lawful), we have...
Page 3 - If there is inversion, all that is necessary is to substitute p-1 for p, or — p-1dpp-1 for dp. But the necessity for this may be avoided by substituting for any pair of systems which satisfy the condition their electric image, which also satisfies it, and which introduces the required inversion. The solution of this problem without the help of quaternions is interesting. Keeping as far as possible to the notation above, it will be seen that the conditions of the problem require that...
Page 44 - ... hexagonal figure thus formed is equal to four times the sum of the squares on the sides of the triangle. VII. 54. Find the side of a square equal to a given equilateral triangle. 55. Find a square which shall be equal to the sum of two given rectilineal figures. 56. To divide a given straight line so that the rectangle under its segments may be equal to a given rectangle. 57. Construct a rectangle equal to a given square and having the difference of its sides equal to a given straight line.
Page 2 - W represent associated series of equipotential, and current, lines in two dimensions. Assuming any lawful values for the members of (2) we obtain u and <f>, and thence, by integration of (1), <r is given in terms of p. Thus <r = i£ +JT], where £ and T; are known functions of x and y.
Page 47 - AA' and BB'. Now, of these double points, one lies to the right, and the other to the left of the centre of the involution, and, to give effect to this distinction, we may indicate the former by naming our four points from left to right, say ABB' A', and the latter by naming them from right to left, AA'B'B, or A'B'BA.
Page 64 - ... Salmon sur les sections coniques. Mais toutes ces recherches ont pour point de départ la figure formée par six points déterminés de la courbe et six seulement. Nous n'y voyons pas de conséquences, au moins immédiates, relatives à ce septième point de la conique, dont l'introduction constitue en quelque sorte le caractère du théorème précédent. Toutefois, il est facile d'obtenir ce théorème par l'application répétée du théorème de Pascal à différents hexagones ayant pour...
Page 61 - Nous pouvons en effet définir tous les cercles <r au moyen d'un troisième point qui décrirait la circonférence s. Or, quelle que soit la position c...