Non-Euclidean Geometry: A Critical and Historical Study of Its Development (Classic Reprint) - Tapa blanda

Excerpt from Non-Euclidean Geometry: A Critical and Historical Study of Its Development

The admirable simplicity of the author's treatment, the elementary character of the constructions he employs, the sense of harmony which dominates every part of this little work, are in accordance, not only with the artistic temperament and broad education of the author, but also with the lasting devotion which he bestowed on the Theory of non-euclidean Geometry from the very beginning of his scientific career. May his devotion stimulate others to pursue with ideals equally lofty the path of historical and philosophical criticism of the principles of science! Such efforts may be regarded as the most fitting introduction to the study of the high problems of philosophy in general, and subsequently of the theory of the understanding, in the most genuine and profound signification of the term, following the great tradition which was interrupted by the romantic movement of the nineteenth century.

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I ntroduction. The translator of this little volume has done me the honour to ask me to write a few lines of introduction. And 1do this willingly, not only that I may render homage to the memory of a friend, prematurely torn from life and from science, but also because I am convinced that the work of ROBERTO BONOLA deserves all the interest of the studious. In it, in fact, the young mathematician will find not only a clear exposition of the principles of a theory now classical, but also a critical account of the developments which led to the foundation of the theory in question. It seems to me that this account, although concerned with a particular field only, might well serve as a model for a history of science, in respect of its accuracy and its breadth of information, and, above all, the sound philo sophic spirit that permeates it. The various attempts of successive writers are all duly rated according to their relative importance, and are presented in such a way as to bring out the continuity of the progress of science, and the mode in which the human mind is led through the tangle of partial error to a broader and broader view of truth. This progress does not consist only in the acquisition of fresh knowledge, the prominent place is taken by the clearing up of ideas which it has involved; and it is remarkable with what skill the author of this treatise has elucidated the obscure concepts which have at particular periods of time presented themselves to the eyes of the investigator as obstacles, or causes of confusion.
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