"Each of five men—Lobachewsky, Bolyai, Plücker, Riemann, Lie—invented as part of his lifework as much (or more) new ge…"

"The chemist smiles at the childish efforts of alchemists but the mathematician finds the geometry of the Greeks and t…"

"When the value of mathematical training is called in question, quote the inscription over the entrance into the acade…"

"Students in analytical geometry should know something of Descartes, and, after taking up the differential and integra…"

"The Egyptians carried geometry no further than was absolutely necessary for their practical wants. The Greeks, on the…"

"Aristotle (384-322 B.C.), the systematiser of deductive logic, though not a professed mathematician, promoted the sci…"

"When Ptolemy once asked Euclid if geometry could not be mastered by an easier process than by studying the Elements, …"

"It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are …"

"I would myself say that the purely imaginary objects are the only realities, the ὂντως ὂντα, in regard to which the c…"

"The classic example of an is that of plane geometry formulated by Euclid... It forms the model of all rigorous mathem…"