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
YPX is not a single straight line
YPZ and WPX are each parallel to AB, and
no straight line through P entering ∠ YPX is parallel to AB. (See Figure 146.)
KeywordsAcute Angle Euclidean Geometry Hyperbolic Geometry Small Triangle Equal Angle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
© Birkhäuser Boston 2008