problems. After having heard him with attention, Laplace, who had been his professor of mathematics at Brienne, said, "General, we expected a good deal of you, but not lessons in mathematics." This must have been the circular geometry' with which Bonaparte amused his staff on the way from Egypt.

Our limits will not permit our considering this work as an edition of Euclid; we can only say that the part which relates to nomenclature, the details of the propositions, and the scholia appended to many of them, are all excellent. If our author could tolerate an expressed axiom, he would be among the very best editors of Euclid; as it is, we think the work might be looked over with profit, as it certainly would be with interest, by every one who has studied geometry; as putting the reader in possession of the actual state of the controversy about the theory of parallels. But where the author departs from the old model, that is, does not like the avowed admission of the clearest physical truths on the evidence of the senses, he seems to us to substitute the tacit rejection of untruths from the same authority: if, then, he will not follow Euclid because the latter heads the school of axiomatic assumption, he himself must be looked upon, up to his fourth edition at least, as belonging to that of axiomatic denial.

BUTTMANN'S GREEK GRAMMAR.

Dr. Philip Buttmann's Intermediate or Larger Greek Grammar, translated from the German. By D. Boileau, Esq., &c. Edited, with a few Notes, by E. H. Barker, Esq. London: Black and Young. 1833.

We are glad to see anything that Buttmann has done presented to the English reader in a shape fit to be read. In a former Number (Journal, No. 1) we had occasion to remark briefly on some very singular errors in the American translation and the English reprint of Buttmann's School Grammar. Though the present translation does not appear entirely unexceptionable, we have not met with any mistakes calculated to give it the same distinction as the other translation just alluded to. Buttmann wrote three grammars: the School Grammar, the Larger Greek Grammar, and the Complete Greek Grammar (Ausführliche Griechische Sprachlehre).* The book which is the subject of the present short notice is the Intermediate or Larger Grammar, now translated for the first time, as we are informed by the editor and the translator, from the thirteenth German edition.

*We saw Professor Robinson's (of Andover, U. S.) translation of Buttmann too late to notice it in this Number.

The Complete Greek Grammar only contains the ety-mology of the Greek language. Buttmann did not live to finish it by the addition of the syntax. It is, as far as it goes, an admirable work for the more advanced Greek scholar, and should take precedence of all yet existing. A translation has been announced of this work also; but it is not a mere translation that is wanted in the present state of our knowledge; there are additions wanted, and errors to be corrected, which defects, had the learned author lived, he would have been the first to remedy.

The present work is dedicated by the editor to Dr. Keate, head-master of Eton school. Whether it is from the fulness of respect intimated in the dedication, or from a notion that the book is much wanted there, we cannot decide. We can only hope that the object of the dedication will be fully answered by the book being recommended by the masters to their more advanced pupils.

We have observed some errors in the translation of the examples in the syntax, and others have been pointed out to us by a friend. Several of them appear to arise from a slight misconception of English terms, and might readily have been corrected by the editor.

Ρ. 364.— Φιλοτιμότατος ἦν, ὥστε πάντα ὑπομεῖναι τοῦ ἐπαιVεTobaι Evena, he was uncommonly desirous of distinction, so as to put up with anything for the sake of being praised.' The expression put up with is not very appropriate. Would Cyrus have put up with a blow or a kick?

Ρ. 367. οὐ γὰρ ἐκπέμπονται ἐπὶ τῷ δοῦλοι, ἀλλ ̓ ἐπὶ τῷ ὅμοιοι τοῖς λειπομένοις εἶναι, (speaking of colonists, they are exported not to be slaves, but to be equal to those who are left behind.' This translation is altogether bad, and the use of the word exported quite out of place.

P. 374. Demost. Meid. 20. Εχρήν αὐτὸν, τὰ ὄντα ἀναλίσκοντα, ὥσπερ ἐγὼ, οὕτω μὲ ἀφαιρεῖσθαι τὴν νίκην, by expending his own (fortune) like me, he thus (i.e. by this expenditure) must snatch the victory from me.' This translation conveys a wrong impression, or rather no distinct impression at all. The proper meaning of exp in this passage is, no doubt, perfectly familiar to the editor, but the translation, as it now stands, will puzzle learners. The whole passage should have been quoted, which includes a previous infinitive (πooтñva), without which no complete translation can be made.

P. 404. We do not assent to Buttmann's remark that in the formulæ οὐχ ὅτι, οὐχ ὅπως, the verb λέγω, or some such verb must be supplied. The misconception of this usage of or and ows in such cases, has given rise to the theory of the

λέγω.

supplemental éyw. In the following instance from Dion Cassius, given by Buttmann:—δανειζόμενος οὐχ ὅτι παρὰ τῶν ἰδιωτῶν, ἀλλὰ καὶ παρὰ τῶν πόλεων,—the word ὅτι refers to Savellóμevos, and could equally well refer to a whole clause: "borrowing, not borrowing (in the place of the second borrowing stands r) from individuals, but also from cities.' The emphatic xa in the second member shows that the borrowing from individuals' is not here excluded from the affirmation, but that something is superadded to it. The version given by the translator is not only by private persons, but also by cities;' such a mistake as this should not have been made by the translator, or overlooked by the editor.

Ρ. 404.— Theophrastus. Ούχ ὅτι ἀνέφυ ἂν, ἀλλὰ καὶ ἐναυ ξεστέρας καὶ καλλίους ἐποίησε, it would not only have blown, but also,' &c. We do not see where the wind comes from: there is no blowing in the Greek. Εναυξεστέρας, qu. ἐπαυ SeoTépas. Blown, qu. grown, or what? ξεστέρας.

Ρ. 406. Thucyd. ii. 49. ἡ μὲν προτέρα ναῦς ἔφθασε τοσοῦτον, ὅσον Πάχητα ἀνεγνωκέναι τὸ ψήφισμα, the first vessel arrived only a very little earlier, as Paches had already proclaimed the decree of the people.' This is absolutely unintelligible, but bears the distinct impression of the confused idea which was the father of it. The exact measure (ooov.

a) of the arrival of the first before that of the second vessel cannot be deduced from the English version: the original is as distinct a thought as words can convey.

P. 418. Buttmann illustrates the usage of pwv commonly, but very incorrectly, called redundant, by this passage—' eis τοῦτο φέρων περιέστησε τὰ πράγματα, he has (irresistibly) brought affairs to that point.' We do not think irresistibly a good translation of pépav; much less do we assent to the propriety of the Latin quotation of the editor as illustrating this usage of φέρων:

So Virg. Æn. 8, 609,

At Venus æthereos inter dea candida nimbos,

Dona FERENS ADERAT.'

P. 341.—' où яavròs eivas, not to be every man's business (i.e., not to be so easily done). The explanation mends the matter a little, but the translation is positively wrong. The original means that it is not in every man's power.'

Ρ. 327. οὐδὲ τὰ ἀναγκαῖα δυνανται πορίζειν, they cannot even procure the needful (the necessary things).' We do not know where this passage is taken from, no reference being given; but it is pretty certain that the translator does not see the distinction between πορίζειν and πορίζεσθαι. The emphatic

word even is wrong placed, as usual in our ordinary translations of similar passages.

--

Ρ. 336. Plato. Gorg. init.—Ἀλλ ̓ ἦ, τὸ λεγόμενον, κατόπιν kopts noμer; do we come, as the saying is, after the feast? ' This translation of ouε seems ambiguous: possibly the right meaning-have we arrived, or are we come, too late?' may be intended, but it is ill expressed.

P. 340. Buttmann is assigning the usages of the genitive. 4. To the question when? but only of an indefinite time of some duration—πολλῶν ἡμερῶν οὐ μεμελέτηκα, I have not practised for several days ; ἐκεῖσε οὐκ ἀφικνεῖται ἐτῶν μυρίων. But this usage of the genitive is not limited to an indefinite time. Xen. Anab. I. 7, 18. Βασιλεὺς οὐ μαχεῖται δέκα ἡμερῶν. Other examples may be found.

Ρ. 359. Ἐὰν τίς τινα τῶν ὑπαρχόντων νόμων μὴ καλῶς ἔχειν ἡγῆται, γραφέσθω, if any one should think any of the existing laws improper, he may propose a new law.' Not having the original German before us, we do not know whether the mistranslation of papio0w is due to the author or translator. It does not mean he may propose a new law'-but, let him proceed (i.e., in the usual form) against the old law,' for its repeal.

Such mistakes as we have pointed out, from a cursory examination of the translation, will show that it is not as accurate as it should be in the version of the syntactical examples. This is not a small defect, as the right translation of such examples is a great help to all students, and more especially to those who are obliged to trust mainly to their own exertions in learning the Greek language. We hope the translator, or rather the editor (for this is his business), may soon have the opportunity of correcting these, and whatever other mistakes there may be, in a second edition.

PRINCIPLES OF GEOMETRY.

Principles of Geometry familiarly illustrated, and applied to a variety of useful purposes. By the Rev. W. Ritchie, LL.D. F.R.S., &c. London: John Taylor, 1833.

We have elsewhere so fully exposed our views on the method in which geometry should be taught, that, whether we are right or wrong, our readers will better judge of the actual contents of a book, by our comparison of it with the articles to which we allude, than by anything else that could be contained in the space which we are able to devote to the subject. Our

opinion remains unaltered; namely, that the truths of geometry should be first taught, as matters of ocular demonstration; that the first principles of reasoning should then be attended to; and lastly, the connexion of the facts in the first part by the methods taught in the second. Our creed, however, has no anathemas for any difference of opinion except one: we cannot tolerate the admission of any bad reasoning, for the sake of avoiding the occasional prolixity of that which is good; or the dressing up of anything in the shape of demonstration, which is not at least as strict as Euclid. With this proviso we can imagine many very useful modifications of our plan.

The work before us is intended principally for the use of teachers, or of pupils under vivá voce instruction. We infer this from the occasional brevity of the illustrations, and the use of terms and modes of speech, which would be difficult, and of what we will venture to call tuitional remarks which would be useless, to the unassisted learner. We shall, therefore, judge the work by its actual contents, and not by the manner in which they are expressed.

At first sight this book made an impression upon us of the most favourable character, which, though seriously modified by further examination, is by no means destroyed, and in one of its grand features, at least, remains totally unaltered. So far as it is an exposition of geometrical facts, accompanied by practical illustrations and useful developments, we approve highly of all that is done, and consider the present production as an acquisition to the geometrical teacher, furnishing him with a well-selected supply of interesting matter, bearing immediately on the use, and even meaning, of the truths before him. But in all matters relating to definition and reasoning, our author has written in a manner which has filled us with astonishment, and has left us perfectly at a loss to understand whether he really means what he says, or whether some strange hallucination, either in ourselves or him, has interfered with the signification of the most common terms. We shall put the grounds of all we have said before our reader, and leave him to decide.

The fundamental propositions, as well of plane as of solid geometry, the latter however very partially, are placed before the teacher correctly and perspicuously. To these are added practical illustrations, such as are contained in the principle of the theodolite, and the various instruments of surveying, the vernier, &c.; and, which we are highly pleased to see, the method of geometrical analysis is brought forward, and insisted upon. We have not the slightest doubt that any reader who