Greek Geometry from Thales to Euclid

Abstract

THE subject-matter of this work has at different times been brought under the notice of the readers of NATURE, for it is very little more than a collected and corrected reproduction of papers which have at varying intervals appeared during the last eleven years in Hermathena. In all our previous notices, we believe, we strongly insisted upon the desirability of Dr. Allman's giving a permanent form to his labours, which should render his brilliant achievements the more readily accessible to mathematical and, we may say also, to general readers. Hitherto all the original investigation in this direction has been carried on by German, French, and Danish writers, for Mr. Gow's “Short History of Greek Mathematics,” interesting though it is, is confessedly not founded upon independent research, nor does Mr, Heath's “Diophantus,” concerned as it is with Greek algebra, form exception to our statement. In the historical domain of mathematics, Montucla held sway until quite recently, and even the latest French work, by M. Marie, the outcome of forty years' travail, holds fast by him, so that Heiberg (quoted by our author) writes: “The author [Marie] has been engaged with his book for forty years: one would have thought rather that the book was written forty years ago.” Far different is the case with Dr. Allman: all along the line of his labours he has consulted the original Greek authorities, and fought every inch of the ground with such experts as Heiberg, Bretschneider, Cantor, Tannery, and several other writers we could name, many times adopting their results, but in nearly as many cases putting forward and convincingly maintaining views of his own. In evidence that the views we have all along held of the importance of this contribution to our knowledge of the early Greek geometers was not a singular one, we have now the confirmation of the favourable reception the papers in their original form met with from many competent authorities on the Continent and elsewhere, the outcome of which has been the present handy volume. Dr. Allman states that “it has been, throughout, my aim to state clearly the facts as known to us from the original sources, and to make a distinct separation between them and conjectures, however probable the latter might be.” This testimony is, we believe, true: certainly the reader is put in possession of the facts so far as they are at this date obtainable. Greek Geometry from Thales to Euclid. By Dr. G. J. Allman. (Dublin: Hodges, 1889.)