A New Attempt to Prove the Parallel Postulate

Extract

Periodically until the end of time there will appear published works purporting to prove the parallel postulate, and it has fallen to the writer's lot to read what is perhaps the most recent of these. While the exact mathematical value of such attempts can always be gauged a priori, it is useful to put on record any new method followed, if only to warn future generations of parallel-postulate-provers against trying it. But such attempts are not without all value , some readers may find it a congenial occupation to spend a little time in discovering the inherent fallacy , alternatively, the task may be given to a student as a profitable and novel exercise in geometry

For these reasons, then, the following résumé of this most recent attempt is given here. And in order that the full interest of discovering the fallacy may not be denied to the reader or the luckless student to whom he delegates the task, it has been thought better to give only the proof as the author gives it, and not to point out where the fallacy lies. The writer has, however, allowed himself to make one or two comments on certain noteworthy points.