Playfair's axiom
id:
playfair-s-axiom-275-5195557
title:
Playfair's axiom
text:
In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid: It is equivalent to Euclid's parallel postulate in the context of Euclidean geometry and was named after the Scottish mathematician John Playfair. The "at most" clause is all that is needed since it can be proved from the first four axioms that at least one parallel line exists given a line L and a point P not on L, as follows: Construct a perpendicular: Using the axioms and previously establishe
brand slug:
wiki
category slug:
encyclopedia
description:
Modern formulation of Euclid's parallel postulate
original url:
https://en.wikipedia.org/wiki/Playfair%27s_axiom
date created:
date modified:
2023-11-08T23:50:44Z
main entity:
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image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/4/47/Point_and_line.png","width":208,"height":156}
fields total:
13
integrity:
15