Abstract
In elementary books (like this one) the development of hyperbolic geometry is often based on a stronger version of ∼ Playfair’s Postulate: Postulate H. If P is any point and A B is any straight line not passing through P (even if produced), then through P there are straight lines YPZ and WPX such that
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(1)
YPX is not a single straight line
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(2)
YPZ and WPX are each parallel to AB, and
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(3)
no straight line through P entering ∠ YPX is parallel to AB. (See Figure 146.)
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© 2008 Birkhäuser Boston
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(2008). Hyperbolic Geometry. In: The Non-Euclidean Revolution. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4783-4_6
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DOI: https://doi.org/10.1007/978-0-8176-4783-4_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4782-7
Online ISBN: 978-0-8176-4783-4
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