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Proceedings of the Edinburgh Mathematical Society Volume 9 (Paperback) Loot Price: R258
Discovery Miles 2 580

# Proceedings of the Edinburgh Mathematical Society Volume 9 (Paperback)

## Edinburgh Mathematical Society

Loot Price R258 Discovery Miles 2 580

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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. 1891 Excerpt: ...line of a triangle and theorems connected with it. By George A. Gibson, M.A Most of the following theorems occur in a more or less explicit form in text-books on the geometry of the parabola; but it will not, I hope, be without interest and value to consider them independently, and to prove them by using only the propositions of Euclid. 1. If the perpendiculars AD, BE, CF of a triangle ABC are produced to meet the circumcircle of the triangle in X, Y, Z respec tively; and if through the orthocentre 0 any line be drawn meeting the sides BC, OA, AB in U, V, W respectively, then XU, YV, ZW intersect the circumcircle at the same point S, the pedal of which is parallel to the line through O and is midway between S and that line. From the orthocentre O (fig. 26) draw any line OU cutting BC at XJ and let XU meet the circumcircle at S. Draw SL perpendicular to BC, meeting OU at P. Assume the property that OD is equal to DX. Then since the triangle ODU, XDU are congruent, so are the triangles SLU, PLU and therefore SL = LP. Also UOX= uxo= SCA. Similarly it may be shown that if SY meet CA in V and if SM be drawn perpendicular to CA and produced to meet OV at Q, then SM = MQand z.VOY=SCB. Hence Z.UOX+ Lvoy = L ACB = supplement of Z.XOY. Therefore OU and OV are in the same straight line. Similarly it may be shown that ZS meets AB at W, the point of intersection of UO and AB, and that if SN be drawn perpendicular to AB and produced to meet UW at R, then SN = NR. L, M, N being the middle points of SP, SQ, SR respectively, are therefore collinear, and obviously LM bisects SO. 2. If on the pedal line a point G be taken (fig. 27) and if through G a line be drawn perpendicular to SG meeting the sides BC, CA, AB in A', B', C respectively, then SA', SB', SC make equal angles w...

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 Imprint: Rarebooksclub.com Country of origin: United States Release date: March 2012 First published: March 2012 Authors: Edinburgh Mathematical Society Dimensions: 246 x 189 x 1mm (L x W x T) Format: Paperback - Trade Pages: 26 ISBN-13: 978-1-130-36779-9 Barcode: 9781130367799 Categories: Promotions Books > Humanities > History Books > Humanities > History > General Books > History > General LSN: 1-130-36779-7

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