EUCLID, the Mathematician, was born at Alexandria in Egypt, about 300 years before Christ. We have n9 certain information as to the precise period, either of his birth or death ; nor do we possess many particulars re specting his life. It would appear that he resided con stantly in his native city, and devoted himself to the stu dy of the mathematics, which he cultivated and taught with distinguished success. Among his scholars, he had the honour of reckoning Ptolemy Philadelphus, King of Egypt, of whom Proelus relates an anecdote, worthy of being preserved, not only as it shows the friendship and familiarity which Euclid enjoyed with his royal pupil, but as it is strikingly characteristic of an enthusiastic geometer, and the only one on record which brings him, as it were, personally before us. Ptolemy, fatigued with the long and unremitting attention necessary to compre hend the demonstrations of certain propositions, one day inquired of his teacher, whether he could not point out an easier method of investigation? " Aro, sire," replied the philosopher, ingenuously, " there is no royal road to geometry." The work by which Euclid is best known to us is his Elements ; a work which, to use the words of a learned critic, " has weathered the vicissitudes of opinion for two thousand years, and has been translated into all the lan guages, both ancient and modern, in which there is re finement enough for the expression of abstract truth." Various opinions, however, have been entertained with regard to the share which Euclid had in the composition of these Elements. While some maintain that he was the author of the whole, others assert that the demon strations only are his, and others that lie furnished the propositions alone. As in most disputes of this none of the contending parties are perfectly correct. Independent of the undeniable fact, that some particular propositions were furnished by others, as the 47th of the first book, by Pythagoras, it must be obvious, from the state of the mathematical sciences at the period in which Euclid wrote, that he could not be the author of the whole. Long before his time, mathematicians had been engaged in attempting to solve the famous problems of the duplication of the cube, and the trisection of an an gle, problems which they never could have attempted without the assistance of many propositions to be found in his Elements. On the other hand, it seems impossi ble to grant, what is universally allowed, that he was the first who arranged all the propositions then known into a system, without granting a great deal more. The mind
that was capable of putting such a system together, even though the materials had been ready furnished, could hardly fail to discover some room for improvement,— some defect to be supplied, or some weak link that re quired to be strengthened. Reasoning, then, from what we might naturally suppose to be the process of a mind accustomed to scientific investigation, we shall be led to conclude that Euclid must have been the author of no inconsiderable part of the Elements. This circumstance, however, is immaterial, and not at all necessary to enti tle him to the appellation of the Father of Geometry. Even supposing every proposition in the Elements to have been known and demonstrated, still they were but insulated truths, and, as such, of comparatively little va lue. The young mathematician, unless he possessed no ordinary portion of ingenuity, must have been guided in his studies in a great measure by accident—interrupted at every step of his progress, and obliged to go out of his way for the purpose of investigating a proposition of which he was not at first aware, but which was necessa ry for the demonstration of a more important truth. The length of time thus necessary, in the most favoura ble circumstances, for acquiring a knowledge of the fun damental propositions, and the difficulty of bringing them, after they were known, to bear on any particular point, so as to be useful in the investigation of new truths, must have presented obstacles of no ordinary magnitude even to the most skilful geometer, and rendered the fu ture progress of mathematical discovery both slow and uncertain. Every person who has studied geometry, or paid any attention to the nature of mathematical investi gation, will be ready to admit the truth of these remarks, and to acknowledge the extent of the obligations which he owes to Euclid ; nor have the admirers of that distin guished mathematician any reason to lament his being denied, in some instances, the merit of original invention, while it is admitted that, by the skilful arrangement of the discoveries of others, he has put into the hands of his successors an instrument which, at a comparatively trifling expense of time and labour, has enabled them to reap not a little of what is most valuable in the field of mathematical discovery.