In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line...
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Parallel postulate (redirect from Playfair's)
fifth postulate (Playfair's axiom). Although known from the time of Proclus, this became known as Playfair's Axiom after John Playfair wrote a famous commentary...
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succeeded by Hymn Playfair Project TS Playfair, a Canadian sail training vessel Playfair's axiom named after John Playfair Playfair cipher, a manual encryption...
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wide audience. Playfair's textbook Elements of Geometry made a brief expression of Euclid's parallel postulate known now as Playfair's axiom. In 1783 he...
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postulate: The sum of the angles of a triangle is two right angles. Playfair's axiom: Given a straight line and a point not on the line, exactly one straight...
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Foundations of geometry (section Hilbert's axioms)
is given by Playfair's axiom and Euclid I.30 (see Playfair's axiom#Transitivity of parallelism). For instance, Hilbert uses Playfair's axiom while Birkhoff...
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the axioms, an affine plane is an object of study belonging to incidence geometry. They are non-degenerate linear spaces satisfying Playfair's axiom. The...
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Affine geometry (section Systems of axioms)
to which is associated a set of lines, which satisfy some axioms (such as Playfair's axiom). Affine geometry can also be developed on the basis of linear...
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geometries". These theorems along with their alternative postulates, such as Playfair's axiom, played an important role in the later development of non-Euclidean...
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however, modern treatments of geometry use Playfair's axiom instead. To prove proposition 29 assuming Playfair's axiom, let a transversal cross two parallel...
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