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Orthologic Desargues' figure

Part of: Linear incidence geometry Geometry

Published online by Cambridge University Press:  09 April 2009

Sahib Ram Mandan
Sahib Ram Mandan
Affiliation:
Flat 19, “Vitaya”, Chhedanagar, Bombay-400089, India
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Abstract

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In 1894 Sondat published a theorem that the centre of perspectivity and the 2 orthologic centres of any 2 bilogic (perspective as well as orthologic) triangles lie on a line perpendicular to their axis of perspectivity. Thébault (1952) gave an elementary proof of this theorem. Here we give two new proofs, one synthetic and the other analytic, and then deduce the existence of an orthologic Desargues' figure where all the 10 pairs of perspective triangles in it are orthologic. Consequently we arrive at an orthologic Veronese configuration of 15 points and 10 pairs of perpendicular lines studied in 5 different ways.

MSC classification

Secondary: 51A20: Configuration theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 295 - 302
Copyright
Copyright © Australian Mathematical Society 1979

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