I HAVE read the passage referred to, but for many reasons cannot admit that the argument is conclusive. In the first place, the quotation from Aristotle's “Ethics” has no authority whatever; it has no ...

I HAVE long thought that by the words, commonly translated evenly, Euclid means symmetrically. The symmetry can be tested by turning the line over; for in stance, the edge of a flat ruler is straight ...

The Straight Line Euclid's definition of it is worthless, but his axioms remain basically sound. His successors in mathematics have extended his ideas to the curved line and a clearer concept of ...