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Extension of the “Medial Section” Problem (Euclid II :11, VI: 30, etc.) and derivation of a Hyperbolic Graph

Published online by Cambridge University Press:  20 January 2009

R. E. Anderson
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Extract

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To divide the straight line AB (containing a units) at C so that

By algebra, taking the positive root,

The number p may therefore have any positive value, integral or fractional, and when negative cannot exceed ¼. Secondly, AC and AB are incommensurable except when 4p +1 is a square:– e.g., if 4p = (q – l)(q +1) or if p = q(q+l), q being any positive integer or fraction.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , February 1896 , pp. 65 - 69
Copyright
Copyright © Edinburgh Mathematical Society 1896

References

page 66 note * In the diagrams M is the mid-point of AB and in Figs. 1, 2, 3, SAK is LAB.