evident properties suggest themselves. They are, for example, equidistant; their directions are the same, that is, they always mark the same point of the compass, and so on. Now, conceive a fixed line, and a point exterior to it. From the exterior point draw a perpendicular to the fixed line, and about the exterior point let a right line revolve. It is as evident to the senses as that two straight lines cannot inclose a space,' that the revolving line will first, if long enough, cut the fixed line on one side of the perpendicular, and afterwards on the other, and that, in passing from one of these positions to the other, there is one position, and one position only, in which the moving line will never meet the fixed line, though both be ever so much lengthened. All this is not only selfevident, but demonstrated, with the exception of the assertion in italics, that there is only one such position. For this Euclid appeals to the senses, though in an indirect way, not well calculated to make the simplicity of the assumption perfectly manifest.

A

B

D

6

Having demonstrated that the line AC passing through A is parallel to BD, if the angles CAB and A B D are together equal to two right angles, instead of saying that A C is the only parallel to BD which can be drawn through A, he says that every other line passing through A is not parallel to BD, which is pretty much the same thing. This is the famous twelfth axiom, which Mr. Darley says has been justly denominated the disgrace of Euclid.' This is what is to keep geometry from ever becoming a popular study. We confess to having simplified the form of the axiom, but the actual point assumed, is that of Euclid; the monstrous and unwarrantable supposition,' (p. 123.) not self-evident,' p. 38. But we have Mr. Darley's authority for stating that his system of parallels is simpler, shorter, and more strictly demonstrative than that given in the common Euclid.' (p. 38.) To it then we turn with great expectations, for though we think the method of Euclid extremely simple, and fond as we are of what is simple, we are still fonder of what is simpler.

"Two right lines are said to be equally distant from one another, when any two points whatsoever in the one not the greater, and any two equally remote points in the other being taken, the right lines which join each opposite pair of points towards the same hand are equal to each other.'

'Parallel right lines are those which are equally distant from each other. This is the simple, clear, and familiar notion of parallels, &c.'

Now suppose a pupil were to put this question-You tell me that, in order to ascertain whether or no lines are to be called parallel, I must measure equal distances on both, and join the extremities, and see whether or no the lines which I get are equal; if I have done this with twenty sets of distances, and found the new lines equal, may I conclude that the lines are those which you mean to call parallel, or must I measure a twenty-first pair of distances, and so on ad infinitum? The author must reply, No; for one trial is sufficient: if the new distances are equal in one case, they will be so in every other; but this I cannot prove, it is a theorem which you must take for granted. In fact, we conceive the principle must be self-evident to any one who has a clear notion of right lines' (p. 39). To this we conceive the pupil would demur; in fact this theorem is assumed in the definition, in spite of the author's frequently expressed disapprobation of such a proceeding. Thus it is by no means certain to the beginner, that there are such things as parallels at all, according to this definition; but this, the author says, ' depends on a self-evident truth in the mind of the reader, which, because it is so obvious, writers on geometry do not think it necessary to mention.' What is it so clear as to require no mention, that there are lines from which if millions of pairs of equal distances were cut, the two lines joining the extremities of each pair would be equal, and this when it is declared that Euclid, in assuming the axiom above mentioned, has assumed that which is not self-evident? Euclid, having shown that there is such a thing as one parallel to a given line passing through a given point, assumes on the clearest grounds, as far as the senses are concerned, that there cannot be two: Mr. Darley sets out with a definition which leaves the student without any certainty that there are such things as parallels, and which definition involves a theorem of as much complexity, as any which is proved in the first book of Euclid. And yet in the same work we find Euclid's definition of perpendicular lines objected to, because it assumes that an angle can be divided into two equal parts. (p. 37.)

This monstrous and unwarrantable' doctrine of parallels is of itself a serious objection to the work in question. We recommend it, nevertheless, to parents and teachers, urging them however to replace the system of Euclid upon this point. If, however, in a subsequent edition the author strikes out most of his notes, placing in the text as much of them as is

absolutely necessary, and does not quarrel with the simple and natural doctrine of parallels, until he can supply another in its place which requires less assumption, we shall rank his work among the most successful efforts to simplify the abstruse science of geometry, which have ever been made in this country.

SCHOOL EDITIONS OF TERENCE.

In a former number of this Journal it was recommended, that the first book to be put into the hands of one commencing the Latin language should be the Gallic war of Cæsar, and, among other reasons for selecting this work, we pointed out the fact, that in the first book of the Commentaries no verb ever appears in the second person, and one only in the first. This circumstance enables the teacher to consult the convenience of his pupil by abridging the accidence of the grammar, and by placing before him the conjugation of the verb in one third of the usual space.

We shall not at present state any other reasons for selecting Cæsar, though other reasons may readily be given; but it may be asserted with some confidence, that a pupil will learn from this book a very considerable portion of the Latin language; and under a judicious teacher he will soon be able to translate into the original any passages of his author given him in English.

As soon as he is thoroughly acquainted with the whole Gallic war, he will be well prepared to encounter the new difficulties presented in dialogue; and he will not easily find a book better adapted to his purpose than the plays of Terence. It is therefore important to examine the different editions of this author that are used in English schools. This task we propose to undertake; but we shall first mention those conditions, which, in our opinion, must all be fulfilled before we can give unqualified praise to any edition. We look, then, first for a correct text, founded on manuscript authority, allowing some latitude, however, for correction of the text, even in opposition to MSS., where that correction is founded upon undoubted principles of criticism. Important variations of the text may always be given at the foot of the page without any material sacrifice of space. In addition to a good text, we may fairly expect some short account of the author, of course in English; and in a chronological table of a single page, it would be easy to give a few dates connected with the writer, or the political events

of his time. Any disquisition upon his style and writings is, perhaps, better omitted. Such essays are seldom of much value; and in boys they only encourage an affectation of knowledge. A collection of good notes is almost essential for the use of the master, who has but rarely time enough to draw up any for his own use, even supposing him to possess the ability. But these notes, we cannot too often repeat it, must be in the English language; and, farther, it seems expedient that they should be separated from the text; for when, as is usually the case, they are given at the foot of the page, the pupil will, for the most part, neglect them while preparing his lesson, seeing that he can answer any question from his master by referring to them at the time, and, of course, if no question be asked, no note is ever looked at. As to the matter of the notes, the most valuable are those which explain any peculiarity of construction, by reference to other similar instances in the same author. Indeed, in such a writer as Terence, where scarcely any historical or geographical information is called for, such notes as we have described are nearly all that is requisite. We must make, however, one addition. It is true that, in almost every school, Terence is treated as a prose author; but it is equally true that his lines are strictly subject to the laws of rhythm; and considering that his metres bear a much closer affinity to those prevailing in our own language, than the hexameters of Virgil, or the lyrical compositions of Horace, there does not seem any good ground for this neglect. We must therefore look upon any edition of Terence as imperfect, which does not afford a pupil the means of comprehending his metres, and classifying those prosodial difficulties which school-grammars omit to notice. Lastly, a good verbal index will be of great service both to master and pupil, where the mode of explanation consists mainly in comparing one passage with another similar to it. The six plays of Terence occupy but little space, so that all we have proposed may certainly be afforded to the schoolboy without any extravagant increase of bulk or expense.

The Delphin edition, with which we commence, possesses none of these requisites, with the single exception of an excellent index; and this indeed is too often the only merit of the Delphin editions of other authors, and has alone saved them from the neglect which they merit.

The Westminster edition contains, we know not why, only four plays, the Heautontimorumenos and the Hecyra being

JULY-OCT. 1821,

2 A

omitted, though the former of these two plays is referred to in one of the notes. It is difficult to decide what text has been adopted by the anonymous editor, as he gives no information upon the subject; but, from a collation we have made of the Adelphi, we may venture to state that the readings are almost always supported by MS. authority. An unnecessary attempt is, however, occasionally made to reduce the orthography of Terence to the standard of our English schools, by rejecting such forms as neclegentia, Prol. 14; servolus, 1, 1, 2; parvolus, 1, 1, 23; tristitiem, 2, 4, 3; totiens, 1, 2, 48; and the accusatives nobilis, Prol. 15; aedis, 1, 2, 8; 2, 1, 16; testis, 2, 1, 49, &c. Yet even in these changes there is a want of consistency, for we find in different passages, clivos, aequom, volt, salvos, and even the very words servolum, 4, 2, 27; parvolam, 2, 4, 10.

In 3, 1, 1 we observe a passage that requires notice. It must be granted that the editor has a numerical superiority of MSS. in his favour for the reading. S. Obsecro, mea nutrix, quid nunc fiet?-C. Quid fiet rogas? Three of the best, however, have quid fiat rogas? And even if all had agreed in the reading fiet, still the idiom of the language must have decided against it. Thus 3, 3, 19.S. Quid agitur?-D. Quid agatur ?-and again, 1, 2, 4.— M. Quid fecit?-D. Quid ille fecerit? Nothing is more common than, when a question has been asked by one party, for the other to repeat it with an expression of surprise; and invariably is the indicative changed to the subjunctive.

Again, in 2, 1, 24. The Westminster text has-Non sivit egestas facere nos. Tu nunc tibi, &c.-with every MS., except the Codex Bembinus; but this being by far the best among them, and as the metre supports it, we certainly prefer siit.

We confess these criticisms are minute, but it is through these slight corruptions that the text of Terence has been converted from verse to prose; and though Bentley may have been too bold in his notions of restoring the original, there can be little doubt that his alterations are for the most part judicious. Certainly no critic had ever a better conception of his author than Bentley had of Terence. If he has materially erred, it has been in giving more than the proper weight to his ideas upon accent, and altering the text so as to meet these ideas in defiance of all authority; for instance, in 1, 2, 50,—