The statement is as follows:
Pasch's theorem — Given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d).
[Here, for example, (a, b, c) means that point b lies between points a and c.]
- Coxeter, H.S.M. (1969), Introduction to geometry (2nd ed.), John Wiley and Sons, ISBN 978-0-471-18283-2, Zbl 0181.48101
- Pasch, Moritz (1912) [first edition 1882], Vorlesungen uber neuere Geometrie (in German) (2nd ed.), Leipzig: B.G. Teubner