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The Pedal (3, 2) Correspondence
Published online by Cambridge University Press: 24 October 2008
Extract
This is a sequel to recent communications to the Society, on “The General (m, n) Correspondence” and “The (2, 1) Correspondence.” For convenience the reference numbers here adopted will be consecutive with what has preceded, so that the present work opens with § 6 as a direct consequence of previous results in earlier sections.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 6 , April 1927 , pp. 631 - 652
- Copyright
- Copyright © Cambridge Philosophical Society 1927
References
* Proc. Camb. Phil. Soc. xxiii (1926), pp. 109–119, 233–261.Google Scholar
* Thus the concurrency systems of all semi-pedal forma of αβγ are the same. 5·18 shews the sameness of the concurrency-systems for two particular semi-pedal forms, namely the pedal form and the defective polar form. The sameness of the concnrrenoy-syetems is also a direct consequence of 6·13. It follows from 1·1 and 6·11 that the second rank covariant of any semi-pedal form of αβγ is a binary cubic whose roots correspond to the vertices of the pedoperpendicolar equilateral triangle of αβγ.
* The theorem 7·23 may also be obtained by elementary geometry as a necessary consequence of 7·15.
* The word “prime” has been suggested by Professor Baker for denoting a flat (n − 1)-dimenuional space situated in a flat spare of n dimensions.
† Proc. Camb. Phil. Soc. xxii (1925), pp. 34–41.Google Scholar