Analysis of information sources in references of the Wikipedia article "Parallel postulate" in English language version.
Katz, Victor J. (1998), History of Mathematics: An Introduction, Addison-Wesley, ISBN 0-321-01618-1, OCLC 38199387In effect, this method characterized parallel lines as lines always equidistant from one another and also introduced the concept of motion into geometry.
Katz, Victor J. (1998), History of Mathematics: An Introduction, Addison-Wesley, ISBN 0-321-01618-1, OCLC 38199387"But in a manuscript probably written by his son Sadr al-Din in 1298, based on Nasir al-Din's later thoughts on the subject, there is a new argument based on another hypothesis, also equivalent to Euclid's, [...] The importance of this latter work is that it was published in Rome in 1594 and was studied by European geometers. In particular, it became the starting point for the work of Saccheri and ultimately for the discovery of non-Euclidean geometry."
The parallel postulate is equivalent to the Equidistance postulate, Playfair axiom, Proclus axiom, the Triangle postulate and the Pythagorean theorem.
We could include...the parallel postulate and derive the Pythagorean theorem. Or we could instead make the Pythagorean theorem among the other axioms and derive the parallel postulate.
Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
{{cite book}}: CS1 maint: multiple names: authors list (link)Katz, Victor J. (1998), History of Mathematics: An Introduction, Addison-Wesley, ISBN 0-321-01618-1, OCLC 38199387In effect, this method characterized parallel lines as lines always equidistant from one another and also introduced the concept of motion into geometry.
Katz, Victor J. (1998), History of Mathematics: An Introduction, Addison-Wesley, ISBN 0-321-01618-1, OCLC 38199387"But in a manuscript probably written by his son Sadr al-Din in 1298, based on Nasir al-Din's later thoughts on the subject, there is a new argument based on another hypothesis, also equivalent to Euclid's, [...] The importance of this latter work is that it was published in Rome in 1594 and was studied by European geometers. In particular, it became the starting point for the work of Saccheri and ultimately for the discovery of non-Euclidean geometry."