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Mathematical Sciences Library QPR 1? PA PI? orKMAU ti, Lobachevski was the first man ever to publish a non-E uclidean geometry. Of the immortal essay now first appearing in English Gauss said, The author has treated the matter with a master-hand and in the true geometers spirit. I think I ought to call your attention to this book, whose perusal can not fail to give you the most vivid pleasure. Clifford says, It is quite simple, merely Euclid without the vicious assumption, but the way things come out of one another is quite lovely. What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobachevski to Euclid. Says Sylvester, In Quaternions the example has been given of Algebra released from the yoke of the commutative principle of multiplication an emancipation somewhat akin to Lobachevski sof Geometry from Euclid snoted empirical axiom. Cayley says, It is well known that Euclid stwelfth axiom, even in Playfair sform of it, has been considered as needing demonstration; and that Lobachevski constructed a perfectly consistent theory, wherein this axiom was assumed not to hold good, or say a system of non Euclidean plane geometry. There is a like system of non-E uclidean solid geometry. GEORGE BRUCE HALSTED. 2407 San Marcos Street, A ustin, Texas. May 1, 1891.
(Typographical errors above are due to OCR software and don't occur in the book.)
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