Latin version from the Greek; containing the elements, data, and other writings, in Latin, with critical notes. The elements out of this edition, the notes excepted, were reprinted by Henry Stephens, at Paris, in 1516, together with the Latin of Adelard: so that five folio editions of Euclid were published within little more than half a century after the invention of printing. This text of Zamberti shows what root the notion of Theon's editorship had taken. The proposition is always headed "Euclid," the demonstration "Theon:" and in the edition of 1516, Euclid is again the author of the proposition; the demonstration from the Greek is called Theon's commentary, and that from the Arabic Campanus's commentary: while in the two last books, the demonstration is Hypsicles' commentary.

We now come to the Greek text, and may here explain our particular object in writing this article. The Greek text of Peyrard, in three volumes quarto, which will presently be more particularly described, has been hitherto a scarce book in England, and even in France it seems to have gone out of notice. A little time ago, however, we were surprised by procuring a very new-looking copy, and by finding that it could be got both in England and France. We have no great difficulty in explaining this: there is a tide in the affairs of books, which taken at the flood, leads on to the second-hand shops, and empties the publisher's warehouse. But if the book be too heavy for this tide to float it, and yet too valuable to come in a short time to wrap up figs and sugar, it remains in the publisher's hands, and is called stock; not that it pays any interest, but because it stands stock-still. When once a book is well abroad in the world, and comes to be known of the second-hand booksellers, the true preservers of books, it never goes out again; but a book may remain publisher's stock for many a year, as we very well know. Dodson's Mathematical Repository, published in 1743, was let out of somebody's stock a few years ago, and, all of a sudden, the second-hand shops all had copies, uncut. Barlow's tables remained in the publisher's stock long after the second-hand booksellers had begun to mark it "scarce ": Sir J. Herschel's edition of Spence's writings was snug in Edinburgh for twenty years, while the second-hand booksellers wondered they had never seen a copy, and almost considered it a supposititious publication: the translation of Nassireddin, already noticed as published in 1594, was, according to Brunet, in stock at Florence in 1810. When, therefore, we saw Peyrard, as

good as new, uncut, and with a paper cover as fresh as if Bachelier had just announced it, we knew that the chain was broken somewhere, and that it would begin to make its appearance like a new work: we did not remember having seen it reviewed, and we considered that the subject would possess interest in a country which has, more than any other, adhered to Euclid.

The first Greek text (containing the Elements in fifteen books, and the Commentary of Proclus) was published at Basle, in 1533, by Hervagius, under the editorship of Simon Grynous, dedicated to Cuthbert Tonstall, bishop of Winchester and London, well known to mathematical antiquaries for his treatise De arte supputandi, and to theological historians for his resistance to Henry's divorce. Two manuscripts were employed, furnished by private friends, and one of Proclus, which was procured from Oxford. Various editions followed, which it is unnecessary to cite, because they were all taken, as to text, from the Basle edition. It may be necessary, however, to remind the reader that in this century there was a fashion of publishing Greek mathematicians with the enunciations only in Greek and Latin, and all the rest in Latin: a practice, no doubt, arising out of the notion already alluded to, that nothing but the enunciation was Euclid's. But it was imitated in editing other writers, Archimedes for instance and a Greek and Latin title-page made bibliographers (those men of title-pages) slip down "Gr. Lat." in their lists. In this way it would cost nothing but an overhauling of catalogues to furnish out a dozen Greek Euclids of the sixteenth century; particularly if we followed the catalogists in another of their errors. Our readers ought to know, or, not knowing, ought now to laugh at, the story of the nouveau riche who would be learned, and bought books in large numbers, but after a time wrote to his bookseller complaining that if he must have nothing but Operas, he would rather they were not all written by Tom. A great many titles, as they stand in catalogues, are really Tom's Operas: there are So-and-so's Works, containing &c. &c. (one or two of them); the catalogue maker has down Mr. So-and-so in a moment for a complete edition, looks at the bottom of the page, writes down a place and date (a wrong one, maybe) and passes on.

:

The next original Greek text was that published at Oxford in 1703, containing all the works of Euclid, certain or reputed, and edited by David Gregory, then Savilian professor.

The University of Oxford has the honour of having published the best editions of the three great geometers, Euclid, Apollonius, and Archimedes. In mentioning the first it may be worth while to give a slight account of all. The design of printing Greek mathematics on a large scale originated with Dr. Edward Bernard (died 1697), who preferred the Savilian chair to preferment in the Church, that he might organize a large system of recovering and combining mathematical antiquities. Henry Savile himself, the founder of the chair, was a diligent collector and collator of manuscripts, and possessed several of Euclid, which he bequeathed to the university. And he did not abandon his chair to its first professor, until he had filled it himself time enough to deliver thirteen lectures on the foundation of Euclid's elements, which were published the following year, in 1621. Dr. Bernard did not complete any of his design, but only left behind him a synopsis of it, describing the contents of fourteen intended bulky volumes; to wit: 1. Euclid; 2. Apollonius; 3. Archimedes; 4. Pappus and Hero; 5. Athenæus; 6. Diophantus; 7. Theodosius, Autolycus, Menelaus, Aristarchus, Hypsicles; 8-14. Ptolemy. Quantus Scriptor! he adds, and well he may. These volumes were to contain commentaries, selections from the moderns, &c. It is singular enough that the three first volumes (the commentaries, &c. excepted) have been published, and that in the order proposed by Bernard. And now we are to ask, when is the Oxford edition of Pappus and Hero to appear? There is no writer who more requires the publication of an edition than Pappus; and as the Archimedes was executed by a foreigner, and published by the university, we shall be curious to see which takes place first; the preparation of a good edition by an Oxonian, or the presentation of one from abroad. It can hardly be doubted that, if it were worthily done, Oxford would feel it an hereditary duty to defray the publication. "Neque gravata est Acad. Oxon. in patrocinium suum recipere quod Euclidi et Apollonio suo velut cognationis jure tertium Opus accederet," says Robertson in the preface to the Archimedes.

David Gregory, the successor of Dr. Bernard, used in his edition (folio, Greek and Latin, with hardly any notes or various readings) the manuscripts which Savile had left, “in hunc ipsissimum usum," his notes on the Basle edition, &c.; and those of Dr. Bernard. A very careful collation was made by Dr. Hudson, the Bodleian librarian. The best testimony to this edition is the smallness of the number of what Peyrard

calls its "mendæ crassisimæ," one hundred and fifty-one in the whole of fifteen books of the Elements. The French editor had some reason (as we shall see) to feel a little galled; and the feeling must have been strong when he paraded under such a title (we take some consecutive ones from the commencement that Gregory had let pass ἀνίσας for άνισες; ΓΗΘ for ὁ ΓΗΘ; τῷ ἐλάσσονι τὸ μεῖζον for τὸ ἐλάσσον τῷ μείζονι ; τῶν for τῆς; τοῦ for τοῦ ἀπὸ τοῦ; τῆς for τοῦ; ἡ for τοῦ; &c. We shall by and by examine M. Peyrard himself on such points.

The edition of Apollonius appeared in 1710, under the care of Halley, the successor of David Gregory; and even Peyrard would be obliged to admit it to be the best printed Greek text, for it is the only one: but it would not be easy to edite another with more care and success. The Archimedes was not published till 1792. Joseph Torelli of Verona had prepared every thing for press with great care, and the University of Oxford, through Earl Stanhope, had negotiated for being allowed to print it. Torelli refused, during his life, to let the superintendence pass out of his own hands; but he having died, his executors saw no other way of procuring publication than by renewing the old negotiation, which succeeded.

M. Peyrard was a scholar, and an admirer of Euclid, who published in 1804 a French translation of the first four, the sixth, eleventh, and twelfth books of the elements, leaving out the fifth book! and a translation of Archimedes (a very good one) in 1808. He undertook to publish the complete text of Euclid, Archimedes, and Apollonius; and, beginning with the former, proceeded to examine the manuscripts of the elements, which are in the Royal Library at Paris, 23 in number. He soon found one, marked No. 190, which appeared more complete in some parts, and less redundant in others, than any of the rest. It also had much the advantage in antiquity, having all the characters of manuscripts at the end of the ninth century. This manuscript had lain in the Vatican Library long enough, said the French, who paid a visit to Rome some time or other in the last century, and found plenty of things which they thought the Pope could do without. Monge, who has so many better titles to fame, was searching the city with the eye of a hawk and the nose of a greyhound for spoil, and found out the manuscript in question, which, with others, was sent to Paris. We know how Peyrard styles such a transaction both in Latin and French (his preface is in both languages): "il fut envoyé

de Rome à Paris." "à Româ Lutetiam fuit missus." This is very bad scholarship; missus in Latin never bore the sense in which the French then used the word envoyé. When the time came for restitution, permission was obtained for this manuscript to remain in the hands of Peyrard until his edition was completed, one volume only having then been published (in 1814). Two more followed in 1816 and 1818, and here the work closes; having been originally intended to include all the writings of Euclid. It contains the thirteen undoubted books of the Elements; the two of Hypsicles; and the Data: the first and third of which M. Peyrard considers as the only writings of Euclid, without giving any reasons for the rejection of the others. This is a convenient plan enough, but one which tends to destroy confidence in the follower of it. To take issue on a single point;-Pappus, in the commencement of his sixth book, refers to the second proposition of Euclid's Phoenomena: on looking into the book of Phoenomena which has come down to us under the name of Euclid, we find the second proposition of that book to contain the matter of Pappus's reference. Now the latter has always been considered as very good authority on the mathematical writings of the ancients: we do not say M. Peyrard was bound to follow him; but, if only out of decent respect to the whole of the learned world, and to avoid being thought to have practised a mere evasion, he ought to have favoured his readers with some reason for rejecting such testimony as that of Pappus. M. Peyrard has added the various readings of the Oxford edition, and of the twenty-two manuscripts which lawfully belonged to the Royal Library at Paris: having himself generally followed the one marked No. 190, which, as above explained, was "sent" to Paris. Before we enter further on this work, we mention one more new text which has appeared since that of Peyrard.

This is an unassuming octavo volume published at Berlin in 1826, by Ernest Ferdinard August. It contains the Greek text of the thirteen books of the Elements (without Latin), some historical notes, various readings, mostly from Proclus, Peyrard, and Gregory, with some from three manuscripts belonging to the Library at Munich. It appears to us to be very judiciously done, and very correctly printed, as to the Greek. Not but that we entered upon it with a little bias against the author, when we saw in the first page of the preface that Tonstall was printed Constall, and in the second, that Bart. Zamberti of Venice, and Candalla, two very distinct