mentioned. Honein ben Ishak (died A. D. 873) published an edition which was afterwards cor- rected by Thabet ben Corrah, a well-known astro- nomer. After him, according to D'Herbelot, Othraan of Damascus (of uncertain date, but before the thirteenth century) saw at Rome a Greek ma- nuscript containing many more propositions than he had been accustomed to find: he had been used to 1 90 diagrams, and the manuscript contained 40 more. If these numbers be correct, Honein could only have had the first six books; and the new translation which Othman immediately made must have been afterwards augmented. A little after A. D. 1260, the astronomer Nasireddin gave an- other edition, which is now accessible, having been printed in Arabic at Rome in 1594. It is tolera- bly complete, but yet it is not the edition from which the earliest European translation was made, as Peyrard found by comparing the same proposi- tion in the two.
The first European who found Euclid in Arabic, and translated the Elements into Latin, was Athe- lard or Adelard, of Bath, who was certainly alive in 11 30. (See "Adelard," in the Biofir. bid. of the Soc. D. U. K.) This writer probably obtained his original in Spain: and his translation is the one which became current in Europe, and is the first which was printed, though under the name of Campanus. Till ver}' lately, Campanus was supposed to have been the translator. Tiraboschi takes it to have been Adelard, as a matter of course; Libri pronounces the same opinion after inquiry; and Scheibel states that in his copy of Campanus the authorship of Adelard was asserted in a hand- writing as old as the work itself, (a. d. 1482.) Some of the manuscripts which bear the name of Adelard have that of Campanus attached to the commentary. There are several of these manu- scripts in existence; and a comparison of any one of them with the printed book which was attributed to Campanus would settle the question.
The seed thus brought by Adelard into Europe was sown with good effect. In the next century Roger Bacon quotes Euclid, and when he cites Boe- thius, it is not for his geometry. Up to the time of printing, there was at least as much dispersion of the Elements as of any other book: after this period, Euclid was, as we shall see, an early and frequent product of the press. Where science flourished, Euclid was found; and wherever he was found, science flourished more or less according as more or less attention was paid to his Elements. As to writing another work on geometry, the middle ages would as soon have thought of composing another New Testament: not only did Euclid preserve his right to the title of Kvpios (rroix^iwri^s down to the end of the seventeenth century, and that in so ab- solute a manner, that then, as sometimes now, the young beginner imagined the name of the man to be a synonyme for the science; but his order of demonstration was thought to be necessary, and founded in the nature of our minds. Tartaglia, whose bias we might suppose would have been shaken by his knowledge of Indian arithmetic and algebra, calls Euclid solo introduttore deiie scietitie mathematice: and algebra was not at that time con- sidered as entitled to the name of a science by those who had been formed on the Greek model; " arfe maggiore " was its designation. The siory about Pascal's discovery of geometry in his boy- hood (a. d. 1635) contains the statement that he had got " as far as the 32nd proposition of the first book" before he was detected, the exaggeratora (for much exaggerated this very circumstance sliewa the truth must have been) not having the slightest idea that a new invented system could proceed iu any other order than that of Euclid.
The vernacular translations of the Elements date from the middle of the sixteenth century,from which. time the history of mathematical science divides itself into that of the several countries v/here it flourished. By slow steps, the continent of Europe has almost entirely abandoned the ancient Ele- ments, and substituted systems of geometry more in accordance with the tastes which algebra has introduced: but in England, down to the present time, Euclid has held his ground. There is not in our country any system of geometry twenty years old, which has pretensions to anything like cur- rency, but it is either Euclid, or something so fashioned upon Euclid that the resemblance is as close as that of some of his professed editors. We cannot here go into the reasons of our opinion; but we have no doubt that the love of accuracy in ma- thematical reasoning has declined wherever Euclid has been abandoned. We are not so much of the old opinion as to say that this nmst necessarily have happened; but, feeling quite sure that all the al- terations have had their origin in the desire for more facility than could be obtained by rigorous deduction from postulates both true and evident, we see what has happened, and why, without be- ing at all inclined to dispute that a disposition to depart from the letter, carrying off the spirit, would have been attended with very different results. Of the two best foreign books of geometry which we know, and which are not Euclidean, one demands a right to "imagine" a thing which the writer himself knew perfectly well was not true; and the other is content to shew that the theorems are so nearly true that their error, if any, is imperceptible to the senses. It must be admitted that both these absurdities are committed to avoid the fifth book, and that English teachers have, of late years, been much inclined to do something of the same sort, less openly. But here, at least, writers have left it to teachers to shirk[1] truth, if they like, without being wilful accomplices before the fact. In an English translation of one of the preceding works, the means of correcting the error were given: and the original work of most note, not Euclidean, which has appeared of late years, does not attempt to get over the difticulty by any false assumption.
At the time of the invention of printing, two errors were current with respect to Euclid person- ally. The first was that he was Euclid of Megara, a totally different person. This confusion has been said to take its rise from a passage in Plutarch, but we cannot find the reference. Boethius per- petuated it. The second was that Theon was the demonstrator of all the propositions, and that Euclid
only left the definitions, postulates, &.C., with the
- ↑ We must not be understood as objecting to the teacher's right to make his pupil assume anything he likes, provided only that the latter knows what he is about. Our contemptuous expression (for such we mean it to be) is directed against those who substitute assumption for demonstration, or the particular for the general, and leave the student in ignorance of what has been done.
