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 AB is any 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
-
(3)
no straight line through P entering LYPX is parallel to AB. (See figure 146).
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Notes
upper limit for the areas of triangles. Remember Gauss’ Postulate (p. 128)?
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© 2001 Birkhäuser Boston
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Trudeau, R.J. (2001). Hyperbolic Geometry. In: The Non-Euclidean Revolution. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2102-9_6
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DOI: https://doi.org/10.1007/978-1-4612-2102-9_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4237-2
Online ISBN: 978-1-4612-2102-9
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