Proceedings of the Edinburgh Mathematical Society Volume 18-20 (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1900 Excerpt: ... of the A' group at a vertex of a triangle of the T' group inscribed in it, is parallel to the opposite side of the triangle. From this we infer the truth of Proposition (2). Another important inference from the same result is that every triangle of the T' group is an inscribed triangle of maximum area in the ellipse of the J2' group in which it is inscribed. Otherwise: Every conic of the 12' group is the Steiner ellipse of every triangle of the T' group inscribed in it. This form of statement makes it clear that any triangle of either the T' or the T group may be taken as the triangle of reference without any alteration in the general form of the equation for the associated group of conies. It is well known that the group of triangles of maximum area inscribed in an ellipse are circumscribed to a concentric, similar and similarly situated ellipse; that the lines joining the points where the latter ellipse touches their sides, to the opposite vertices, cointersect in the centre of the ellipses; and that this point is the centroid of all the triangles. Applying these statements to the triangles of the T' group and extending them to those of the T group, we obtain Propositions (3), (4) and (5). f The coordinates of the vertices of any triangle of the T' group, with reference to any other triangle of the group, are of the form (K ft v), (p, v, A), (v, A, fi). See "Resume des propriete concernant lea triangles d'aire maximum inscrits dans 1'ellipse," by M. E. N. Barisien, Mathesis, 2nd series, Vol. V., p. 42. t Of the many properties that may be deduced from the fact that the T" group consists of triangles of maximum area inscribed in concentric, similar and similarly situated ellipses, one of the most interesting is that all the triangles of the...