read in this place εν δωδεκάτω τωνδε των τοιχείων, and the text was most probably the same in the MS. used by Commandine, "solertissimo mathematico," as Meibomius remarks, "Græcæ linguæ mediocriter perito;" but Halley rejects raids altogether, and, if we admit it to be an interpolation, there will remain no reason for supposing that Pappus meant to refer to his own work. Ta raxua is the well known expression for the Elements of Euclid ; Pappus himself talks of Ευκλείδει τα τοιχείωτε ; the title uniformly given to each of his own books is ouaywyn, and at the end of Jos. Scaliger's MS., which is now at Leyden, the whole is closed by των συναγωγών Πάππε τελός.

Of these eight books, it is very probable that no entire copy is at present in existence: certainly there is none in our own country. In the Catalogus Librorum MSS., Angliæ et Hiberniæ, published at Oxford in 1698, there is mention made of two manuscripts in the Savilian Library in that University. They are marked 6550: 3, and 6556: 9, the larger numbers referring to the general enumeration, and the smaller (3. and 9.) to that of the Savilian Manuscripts. These have been about 200 years in Oxford; for they appear in the original "Catalogue indented betweene the Universitye and Sir Henrie Savile, contayning the names of such bookes as the said Sir Henrye Savile hath bequeathed to the University, for the use chiefly of the mathematical readers." This catalogue is signed by Sir H. Savile himself, and there can therefore be no doubt of the manuscripts being older at least than 1620. This is indeed a late date, but neither of the books bears any marks of high antiquity.

No. 3. is very well written on paper, and the ink is clear throughout; the volume is in excellent preservation, and in the original binding. It contains the Greek text of the 3d, 4th, 5th, 6th, 7th and 8th Books of the Mathematical Collections, with the diagrams for these books, very neatly drawn, after which are inserted some works of Theodosius and Autolycus. The whole is written undoubtedly by the same hand: each line is regular, each page is bounded by an ample margin, and the extremities of the writing are as even as if they had been set off with a ruler. The titles of the several books, those of the leading divisions of the work, many of the initial letters, and the numbers of the propositions in the margin, are written with red ink.

The book is in folio, the paper is all of the same texture, although the water-marks are not all the same: no date, however, appears, and there is no notice, in any part of the volume, of when or by whom it was written; there is no memorandum in it of any one, to whom it has ever belonged; nor are there any traces of where it was procured by Sir H. Savile. There is in the same library a volume containing some works of Ptolemy, Theon and Aristides Quintilianus, which is evidently by the same transcriber; and his hand again appears in a copy of Simplicius's Commentary of the second of Aristotle's books wię reavor, but no further light can be collected from any of them. In No. 3., many of the passages, which were originally deficient, have been filled up in pencil; there are likewise many memoranda written in the margin in pencil; there are some also in ink in a smaller hand, which are most numerous in the beginning of the 4th book.

περι

No. 9. is not by any means so well written as No. 3. The mathematical collections occupy the latter part of this volume: they are entirely written on separate half sheets of folio paper, which have afterwards been pasted on guards, in order that they might be bound up with the other manuscripts. The book is described in the Catalogus Librorum MSS. above mentioned, as "Pappi Alexandrini Coll. Math. deest. liber 1. et septimus et initium 2." This is copied by Harles in his edition of Bibliotheca Græca, and he probably had not the means, even if he had suspected the inaccuracy, of correcting it; but it is extraordinary that a great mistake should have been made in this description. The catalogue of the Savilian Library was drawn up for this 'collection by Caswell, who published a short treatise on trigonometry at the end of Wallis's Algebra, and who became Sayilian Professor of Astronomy in 1709; but he did his work most incorrectly. In the present instance the error is remarkable. If he had overlooked any deficiency, it might easily have been accounted for ; but that he should have gone out of his way to mark a deficiency, which never existed, is very extraordinary. The manuscript does not want the seventh book; neither has that book been inserted at any time subsequent to the formation of the catalogue. The writing of it agrees exactly with that of the rest of the work; and Wallis in 1688 describes this MSS. as one 66 qui continet

non tantum Pappi librum tertium cum sequentibus, sed secundum etiam, non quidem integrum, sed ipsius partem non contemnendum." Halley likewise specifically says, in the preface to his edition of the Conics, " singulis Apollonii libi is Pappi Lemmata præfixa dedimus, e duobus codd. MSS. Savilianis desumpta;" and these lemmata are all in the seventh book, comprising Prop. 165-234. of Commandine's translation. Halley also prefixed to his edition of Apollonius de sectione rationis, the Greek text of the preface to the seventh book, " pristina integritati, quoad ejus fieri potuit, restitutum e duobus codd. MSS. Bibliothecæ Savilianæ." Now, these two works of Halley were published in 1710 and 1706, and the date of the catalogue is 1698; if, therefore, we had no other ground of argument, we could hardly imagine that he would have derived his authority without any notice, from so recent a manuscript as that of the seventh book must have been, if it had been inserted subsequent to Caswell's publication. The several books, however, in No. 9. are not arranged in their natural order; which, though not sufficient to account for the assertion of the defect, may have prevented the blunder from being immediately detected. In the beginning we have " Pappi Alexandrini συναγώγη . . . λειπει το πρώτον και η αρχή του δευτερο ;” the first words of the text are γαρ αυτους ελασσονας μεν είναι εκατοναδας, which is the middle of the enunciation of the 15th proposition; and then follows the end of the second book, as published by Dr Wallis. The other six books then come in the following order, 3, 7, 5, 6, 8, 4. The beginning of the 8th book is written on the back of the leaf, which contains the end of the 6th; it is not therefore improbable that the MS. was originally copied from one which wanted the 7th and possibly the 4th book, and that these were afterwards supplied and misplaced; but the whole is clearly of the same age, and written by the same persons. After a careful examination, there seem really not to be more than four or five; but their several hands are so mixed together, often two, and sometimes more, occurring in the same page, that there appears, at first sight, to be a larger number. The best of these writers executed the greater part; of his coadjutors one writes arroyiar zaggœλanλov, and, although these blunders are generally corrected, and are, for the most part, confined to the beginning of his work,

still they shew the man not to have been familiar with Greek. Another, who certainly writes a more practised hand, fills his parts with contractions: these are not only literal but verbal; we have formes, ▲ for tyver, &c. &c.; again, Pavegov is por, ελάχισος is έλαδος, and ags occurs where we can only determine from the context whether it is intended for agiluntians or agμoviens. What the arrangement was which these scribes made among themselves, is not easy to conjecture; but it seems to have been such, that they might all, at least in some parts, have been working at the same time; for the pages are hardly any of them full, some having more and some less vacant spaces left at the bottom of them, and the last lines of the pages are very seldom, if ever, complete, although the change to the next page may be in the middle of a sentence, or even of a word. All this may have been occasioned by the copy's being made to contain exactly what was found on each page of that from which it was taken; and as the diagrams are in general omitted, this alone, if we suppose them to have been annexed to the several propositions in the original, will account for inequalities in the length of the pages in the transcript. The plan of several copying different parts at the same time, may account for a very singular confusion which occurs in the 4th, 5th, and 8th books, in which some of the pages are divided into two, while the upper and lower halves do not make parts of the same passages, neither does the text in the successive pages follow any regular order.

The volume is put together in a parchment cover, without any boards, and is, upon the whole, in as good condition as could be expected; but the lines generally reach both ways to the edges of the paper, so that letters are sometimes lost on one side by the pasting of the leaf on the guard, and, on the other, by the outer margin's being worn. There is no memorandum of the age of the manuscript, nor of the persons who were employed to copy it. In Sir H. Savile's own catalogue, the Pappus is mentioned by itself, so that the other books were probably bound up with it at a subsequent period. There is the following memorandum written against the Pappus: ❝m. script. "Argentorati," and as Dr Trail speaks of a MS. in the Strasburg Library which is not noticed by Harles, it is possible that there may be some connection between the books. In the 24th,

and some other pages, there are references to Commandine, which appear to be written with the same ink as the manuscript; the difference of the Greek character from the Latin, in which these references are written, making it impossible to form any opinion from the handwriting; but whether they are or are not by the original transcribers, the manuscript is probably not older than 1588, when the Latin was first published.

There are no red letters or ornaments of any kind; the lines are uneven, the margins are rugged, the ink is faded in many parts, and in others remains much blacker in some words than in the rest. There are frequent erasures, from the words having in haste been written wrong, and the pen's having been dashed through it, which is not the case in No. 3. The text, likewise, has been corrected in many other places; in some instances this seems to have been done by the transcriber, who has been mentioned as more accurate than his associates; but many altera tions have been made by later hands, particularly in the beginning of the 3d book, where the old writing is in some instances absolutely effaced by the corrections, and at p. 15. we find "hactenus recensuit Wallisius."

......

Halley says, "Græca Pappi in hisce codicibus sæpiuscule luxata sunt et depravata." This is not, indeed, peculiar to the Oxford MSS.; Dr Trail says, that all " which have been examined are mutilated, and contain many errors, from the ignorance or carelessness of transcribers ;" and he quotes from Dr Simson, 66 non pauca in eo codice (Parisiensi Regio sc.) vitiata sunt, ut in omnibus fere Pappi propositionibus, et, ut videtur, in omnibus manuscriptis." Wallis says more specifically of the Savilian Manuscripts, " qui elegantius scribitur, est mendosior; quique festinantius et minus eleganter scribitur est emendatior; ex quo alterum fuisse descriptum conjicio." Now if No, 9. is in some respects more accurate than No. 3., the cause must be found in its having been taken from a more correct original, for it certainly is not from the merits of the transcribers; and the conjecture of the one's being only a fair copy of the other is manifestly erroneous. There are indeed many remarkable points of coincidence; the same errors, the same repetitions of words and sentences, and the same lacunæ occur in innumerable instances; but after a complete and careful colla