1 [52] The Elements of Euclid, with Differtations, intended to affiff and encourage a critical Examination of thefe Elements, as the most effectual Means of establishing a juster i afte upon Mathematical Subjects than that which at prefent prevails. By James Williamjon, M. A. Fellow of Hertford College. Vol. I. 4to. 16s. in Boards. Elmfly. ΤΗ HE Elements of Euclid have received the united approbation of mathematicians for more than two thousand years; and, notwithstanding all the improvements of the moderns, in other branches of fcience, this excellent old Grecian still maintains his ground, and is yet without a rival In all human productions, however, there must be fome blemishes, and even Euclid himself is not without them. His theory of parallel lines, the doctrine of proportion, and many other things in the Elements, particularly in the twelfth book, are capable of confiderable amendments. Profeffor Simson, with the partiality of a profeffed admirer, places all the inaccuracy and false reasoning which he finds in this work to the account of unfkilful editors; but we are inclined to think, from many circumstances which might be adduced, that the proofs he brings in fupport of this opinion are frequently groundless., Euclid was not infallible; and therefore, whether the faults belong to him, or to his commentators, is but of little importance; they are ftill faults, and, for that reafon, ought to be removed from a work, which in other refpects, is the standard of perfection. Simfon, by his critical attention, and intimate knowlege of the subject, has, it is true, done more towards establishing the Elements upon a folid foundation, than all the rest of the commentators. But, in our opinion, there is ftill room for much ufeful emendation; and had the prefent editor purfued this plan, he would have rendered effential fervice to the fcience he profeffes to elucidate. This object, however, has engaged but little of Mr. Williamson's attention. His deference for Euclid is fo great, that he has even preserved all his buts and therefores with the moft fcrupulous exactnefs. The garb in which he has dreffed him is of the fifteenth century, and his commentaries are frequently as unprofitable, quaint, and endless as old John Dee's mathematical prefaces I could, fays he, have improved my ftile very much; but it feems to answer my purpose better in its prefent form; for I write not to make people read, but to make them think. What the advantages may be that arise from the thinking upen a fubject without reading, we will not pretend to determine; fope attention to language and perfpicuity is generally confidered as a very neceffary article in moft books of inftruction. This work appears to be a literal tranflation from the Greek of Grynæus's edition 1533; and Mr. Williamfon's determined refolution of expreffing every anna, aga, dn, de, &c. in the original, has led him into many needlefs repetitions, and a harth difagreeable prolixity. The continual occurrence of but, wherefore, therefore, certainly, &c. and the various figni fications which must be appropriated to them, together with the confufed order in which the feveral parts of the demonftrations are placed, to which may be added the carelessness of his punctuation, render many of the propofitions extremely confufed, and fcarcely intelligible. Concifenefs may admit of fome palliation for obfcurity, but prolixity of none. Brevis effe laboro, obfcurus fio,' fays the poet; but our editor may Fay, Longus effe laboro, valde obfcurus fio.' As a proof that this cenfure is not illiberal, or without foundation, we shall present our readers with the following Specimen, indifcriminately taken from the firft book. The figure may be feen in any edition of the Elements. Prop. XXIV. If two triangles have the two fides equal to the two fides, each to each, but have the angle greater than the angle, the angle contained by the equal ftraight lines: alfo they will have the hafe greater than the base. Let there be two triangles the triangles ABC, DEF having the two fides AB, AC equal to the two fides DE, DF, each to each; AB to DE, and AC to DF; but let an angle the angle contained by BAC be greater than the angle contained by EDF; I fay that the bafe BC is greater than the bafe EF. For becaufe the angle BAC is greater than the angle EDF; let there be made, with the ftraight line DE and at the point D in it, the angle EDG equal to the angle BAC; and let DG be made equal (by prop. 3.) to either of the lines AC, DF; and let GE, GF be joined. Since therefore AB is equal to DE and AB to DG; cer tainly the two BA, AC are equal to the two ED, DG, each to each; and the angle BAC is equal (by conft.) to EDG therefore the bafe BC is equal to the bafe EG, Again because DG is equal to DF, the angle DFG is equal (by prop. 5.) to the angle DGF; therefore the angle DFG is greater than the angle EGF; therefore the angle EFG is greater by much than the angle EGF; and because there is a triangle, the triangle FG, having the angle EFG greater than the angle EGF; but (by prop. 19.) the greater fide is extended under the greater angle: therefore the fide EG is greater than EF: and EG is equal to BC (by part. 1. of this prop.); wherefore alfo BC is greater than EF. E 3 Where Wherefore if two triangles have the two fides equal to the two fides, each to each, and have the angle greater than the angle, the angle contained by the equal ftraight lines; they will also have the base greater than the bafe. Which was to be demonftrated.' A About a hundred and twenty pages of this performance are filled with directions to the ftudent, and obfervations upon various parts of his author, which are frequently fo little to the purpose, that a particular account of them would be unneceffary; especially as Mr. Williamson himself affirms that an author who writes upon fubjects of fcience may find it often by no means convenient to deliver himself in fuch a manner as to be always intelligible even to those whom he would wish to have for readers.' The Progress of Romance, through Times, Countries, and Manners. Two Volumes. 8vo. 55. Sewed. Robinfon. THIS fubject has been frequently examined, when it has oc curred in larger works; but, as a part only of a whole, it has not probably been confidered with the attention which it deferves. The romances of the fixteenth and seventeenth cẹnturies have been fo often the objects of ridicule, that authors have commonly decided without reading, and rejected without examination; and almost every work, under the fame title, has funk into equal contempt. It was in vain to lead the reader to thefe forgotten fables, by telling them that they were once the fources of entertainment to the gay, the witty, and even to the learned; that from this fire Milton frequently kindled his torch, and scattered light and flame into metaphyfical difquifitions, or auftere complaints; that from this fource he frequently threw an additional luftre on even his own fplendid imagery. Thefe and all other argumentswill fail, for the torrent which has changed its fource will pur fue it in fpite of human efforts. The author of the two little volumes before us feems to be bet ter acquainted with thefe antiquated hiftories, than her predeceffors in the fame department. Her views are more general and extenfive: fhe purfues the whole train of ideal adventurers, collects them into groupes, and examines their pretenfions. In this tract the fometimes feems to trefpafs on what the claffical enthufiaft will call holy ground; for fhe dares, fhe boldly dares, to infinuate, that the Iliad and the Odyffey are only romances. Let us examine this fubject. Dr. Johnson calls a romance a military fable of the middle ages; a tale of wild adventures of war and love.' · This is cer certainly the idea which we commonly affix to romance; but it will be obvious that, if in the earlier periods, we find tales equally wild, containing fimilar adventures, we must not exclude them from this clafs. This will bring us more nearly to the definition of our author, viz. a fabulous story of such actions as are commonly afcribed to heroes, or men of extraordinary courage and abilities. Though there be nothing to object to the description, it is obviously too extenfive; for it includes the epic poems, which, though they are arranged under a feemingly unexceptionable definition, are certainly not included in the original idea. The error is in the attempt to define what will not bear to be limited. From the Æneid, the moft judicious and refpectable form of the epos, to the moft incredible romance, there are so many fhades, differing in a manner scarcely perceptible, that we can fix at no one point. It is the fame in the varying forms and functions, between a man and an oyster, yet they ought not to be arranged together; from the vegetable, upward to the animal, and downward to the mineral kingdom. In fact, when knowlege is extended, definitions are no more. It may be asked, as we have not objected to the definition which our author has a dopted, why we will not include the epic poem in a class so refpectable as this will be in fuch circumstances? For this reafon, that when we make our limits fo extenfive, we deftroy their ufe; we blend the most diffimilar objects, not only diffimilar in form and appearance, but in their conftituent parts and effects. Romances, even in a more limited view, are certainly not peculiar to the middle ages; we have formerly hinted, that the Life of Thefeus by Plutarch is strikingly of this kind; in poetry, the Argonautics of Apollonius is a performance not very different; furely thefe ought not to be confounded with the Iliad and the Æneid. Of dogs, the valued file 、, མན Diftinguishes the fwift; the flow, and fubtle, That writes them all alike' If we were obliged to point out any difcrimination between fome of these hiftories more nearly refembling epics, and the epics themselves, it would be the conduct of the story. The fubject is a fingle one, and the conduct of it relates to that only. The ftory is taken up at the middle, at the part which is connected with the defign; and, when it is accomplished, faddenly breaks off. A modern performance, in its progrefs refembling the epic, and in some of its events, the romance is De Solis' Conqueft of Mexico. Perhaps we have already ftaid too long on the threshold; but our author's opinion came in a delufive questionable shape. It was worth examining; and, if not true, worth refuting. In pursuing the fubject, this fancied analogy feems to have misled the enquirer. We allow that there is often a striking resemblance between works of high and low estimation; but the resemblance is in fome trifling points: thofe who have read the Odyffey, and the Adventures of Sinbad the Sailor, cannot certainly perceive it in any great degree. Both authors undoubtedly poffefs, bold imaginations, the adventures of each are marvellous, and the characters various; but the fame refemblance will occur between the Arabian Nights Entertainments, and the plays of Shakspeare: fhould thefe very different kinds of compofition be on this account confounded? The author begins with the early romances, which are principally thofe of the modern Greeks, and continues her history through the middle ages, to the close of the year 1770. In many refpects, this hiftory is little more than a catalogue: the decifions are fometimes juft and candid; but we cannot observe in them any deep difcernment, or very accurate dif crimination. The catalogue is moft perfect in the earlier periods. The author is often deficient in determining even the moral tendency of different works; the frequently feems to decide from common report. We shall infert a fhort defence of Cervantes, which we fear is just. The paffion for thefe books, (viz. romances,) was in fome degree checked; but it was not eradicated.-There is good reason to believe, that even Cervantes himself, was not cured of it. Hort. Nay, if you animadvert upon Cervantes, I know not what to say-but I fhall expect proofs of this affertion. Euph. I fhall produce them prefently.-Befides his Galatea (of which he fpeaks with pleasure, and refcues it from the condemned books in Don Quixote's library, and after he had written his novels upon a new plan,) he compofed a serious romance, called Perfiles and Sigifmonda, which remains extant, as a proof against him. It is faid that he preferred this to all his other works:he compares it with the Ethiopics of Heli odorus, being written in the fame ftyle and manner. What fhall we fay of the man, who had produced Don Quixote, and could afterwards write a book of the fame kind as thofe he fa tyrized? May we not conclude that he ftill loved them in his heart? Horts |