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# Peacock Tail

The eighth proposition in the third book of the Elements is one of Euclid's most complex propositions. It shows that a segment through an outside point and a circle is shortest when it lies on the line passing through the center , as illustrated above. Euclid also describes the near and far halves of the circumference.

According to Billingsley (1570), the proposition "is called commonly, in old books amongst the barbarous, the Peacock Tail."

Bride's Chair, Windmill

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## References

Billingsley, H. "Peacock Tail." §III.8 in The Elements of Geometry of Euclid. 1570.Joyce, D. E. "Euclid's Elements." http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII8a.gif.Simpson, J. A. and Weiner, E. S. C. (Preparers). The Compact Oxford English Dictionary, 2nd ed. Oxford, England: Clarendon Press, p. 1293, 1992.

Peacock Tail

## Cite this as:

Weisstein, Eric W. "Peacock Tail." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PeacockTail.html