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Addition of a Third of a Period to the Argument of the Elliptic Function

Published online by Cambridge University Press:  20 January 2009

D. G. Taylor
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1. If I is an inflexion on a non-singular plane cubic curve, a variable line IPP′ establishes a (1, 1) correspondence between points P, P′ on the curve. This correspondence defines a perspective transformation of the whole plane, with I for pole, and the harmonic polar of I for axis, of perspective; for, when I is projected to infinity on the y-axis, and its harmonic polar taken for x-axis, the resulting equation

indicates a curve symmetrical with respect to the latter.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , February 1920 , pp. 63 - 67
Copyright
Copyright © Edinburgh Mathematical Society 1920

References

* Cf. Baker, , B. A. Report 1910 (Sheffield), p. 528.Google Scholar