shall have to present for the contemplation of our readers a probably unique picture of a man, leading a humble and obscure life, yet in subsequent ages exercising a mighty influence over the thoughts and lives and destinies of mankind,-an influence the more remarkable because it acts not on the passions and affections, nor directly on the interests, of men, but on their minds as distinguished from their hearts; and operates on these minds not with a stimulant, but rather with a sedative power. Even so, for "God hath chosen things which are not, to bring to nought things that are." Migara II WHO was Euclid? We do not know. No one knows. We do know, however, and ought to state, that he was not Euclid of Megaera, with whom he has been disastrously confounded. Euclid of Megaera was a disciple of Socrates, after whose death, in 399 B.C., he left Athens and founded a school at Megaera. He was therefore, probably, a century prior to our Euclid. If the same question were put respecting any other man, substantially the same answer might be given, and would be true in a certain sense. For not only of the men who lived long ago, and of those who lived. recently, or are living now, in lands far off and little known, but even of those whose doings are chronicled in our newspapers and magazines; yea, of those with whom we are maintaining constant and intimate intercourse, it is true that we know them only in part, and that, in many cases,-probably in all,-the part which we know is insignificant in comparison with that which is beyond our ken. But it is not merely in this sense that we are compelled to give the answer which is here given when the question is put concerning Euclid. For we know neither the place nor, except within rather broad limits, the time of his birth. We know nothing of his parentage or ancestry, or of the influences which, in his early years, acted on the development of his mind and the formation of his character. Very little is known of the events of his life or of his habits, and simply nothing of his physical and moral characteristics; while even his mental and intellectual powers can only be inferred from his writings. Then, as to the writings imputed to him, it is not known concerning some of them whether they are his or not; while, even respecting those of undoubted authenticity, it is uncertain whether he was their author, in a strict sense, or only their compiler. All that we can do, therefore, towards answering the question which introduces this section, is to summarise the scanty records which have come down to us, none of which are contemporaneous, while some contain statements which are certainly inaccurate. Homer and Euclid are both dead. In this respect there is entire accord between the fates which have befallen the father of poetry and the father of geometry respectively. But here the accordance ends. Seven cities have contended for the honour of having given birth to the poet; whereas it does not appear that any city, town, village, hamlet, villa, or cottage has advanced any pretence to stand in that relation to the geometer. A thorough-going mythist might even doubt, and consequently deny,for, with the proper mythist, a very small measure of doubt warrants a very decided denial,—that Euclid was ever born, or ever existed as a man at all. The argument might stand in some such fashion as this. Manifestly the name Eukleides is compounded of the two words eu="well," and kleis, kleidos="a key." Now what name could have been given more appropriately to the science of geometry than the happy key? Or to what could the name have been more appropriately given? Did not Plato virtually give the name to the science when he proclaimed · Πρὸ τῶν προθύρων αὑτοῦ γράψας ὑπῆρχε Πλάτων, that the want of it made entrance into the abode of knowledge impossible? Could any language have expressed more emphatically the conviction that geometry was the key, the only key, the auspicious key, before whose potent touch the portals of the temple of knowledge would roll back, and disclose a patent access to the sacred shrine? And then, was it not in accordance with all ancient usage that this science-key should be personified; that the science should become a man; and that in the course of time innumerable legends should cluster around his name? If this reasoning (!) be not sound and conclusive, then a great amount of precisely parallel or virtually identical reasoning, which has been used by some and accepted as valid by many, with reference to other persons and things, is inconclusive and unsound. What is the use of living in the twentieth century if we are to be bound by the traditionary beliefs of the centuries which were notoriously uncritical? 2 1 It is true that for this inscription on the gates of the "olive-groves of Academe" we have no earlier authority than a monk of the twelfth century. The question of its genuineness is therefore simply a weighing of probabilities: whether it is likelier that it had come down through channels of tradition which have now disappeared, or that this monk invented it. 2 Since this was written, we have found that what we wrote as an extravagant burlesque is, almost to the letter, descriptive of what was actually done long ago. The following is an extract from Mr. Ball's Short History of Mathematics :-"Some of the medieval writers went so far as to deny his existence, and, with the ingenuity of philologists, There is no reasonable doubt that Euclid was a Greek by birth, though it has been said by some that he was a native of Tyre; and there is considerable probability that he was an Athenian, or, at all events, an Attican. He was born about 330, and died about 275 B.C. If we assume these approximate dates to be the actual ones, it will appear that he was fully a century later than Plato (429-348 B.C.). He was contemporary with Aristotle (384-322 B.C.), having been born fifty-four years later, and having died fortyseven years later than the Stagyrite. Thus Euclid was about eight years old when Aristotle died. It may help the reader to "locate" Euclid in the history of Greece, if it be stated that the year which is given as that of his birth was seven years before the death of Alexander the Great, who survived his famous tutor by a year. Archimedes also was contemporary with Euclid, having been born thirty-three years later, and survived him by sixty-three years (297-212 B.C.). All they explained that the term was only a corruption of ukli="a key," and dis="geometry." The former word was presumably derived from kleis. I can only explain the meaning assigned to dis by the conjecture that, as the Pythagoreans said that the number two symbolised a line, possibly a Schoolman may have thought that it could be taken as indicative of geometry.' With all humility, we submit that our theory is better than that of the medieval writers referred to, and our explanation better than Mr. Ball's. For, first, the name is not Ukleidis, but Eukleides. Secondly, there is no such word as ukli; but there are two such words as eu and kleis. Thirdly, d is part of the root of the word of which kleis is the nominative; and es is merely a termination necessary in order to give the word a Greek form. Some may reckon it curious to note that Euclid received at the hand of these medieval writers precisely the same treatment that Homer afterwards received from Wolf, and that various persons of antiquity are now receiving at the hands of the "higher critics"; the latest victim being the prophet Malachi. |