Excerpt from Theories of Parallelism: An Historical Critique
Haec hactenus... Some years ago I made use of this expression incidentally in the course of my annotated edition of the First Book of Euclid's Elements, with reference to an historical sketch of the Theory of Parallelism. After much hesitation and with much diffidence, somewhat augmented by the appearance (after the first draft of this little volume had been prepared) of Dr Heath's most learned and elaborate Thirteen Books of Euclid's Elements, I have here tried to disburden conscience and memory by drawing up in chronological order my notes on the treatment of parallelism by about 40 Geometers of rank. Except for the last generation, I believe that these 40 names are the most noteworthy throughout twenty-two centuries in this connexion. As is well known, any theory of parallelism is not an isolated fragment of geometrical research, but must be capable of supporting the whole superstructure of the Science of Space. And the historical study of this matter is interesting, not least because it displays, in a manner partly amusing and partly pathetic, the dulnesses, limitations, prejudices and aberrations of professedly logical minds. Frail and imperfect demonstrations were once viewed with considerable complacency. Up to the middle of last century the treatment of parallelism was a favourite lurking-place for paralogisms. Wonderful indeed is the serene illumination of Truth by which the student works in this twentieth century. Compared with it, the Renascence was only a stirring and awakening out of sleep in the dim twilight of the early dawn. If it is not impertinent in me to suggest it, we seem to be finding the Balance of Truth.
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