contrivance, the steps of the reasoning which were before fo far feparated, are brought near to one another, and the force of the whole is fo clearly and directly perceived, that I am perfuaded no more diffi culty will be found in understanding the propofitions of the fifth book, than of any other of the Elements.

"A few changes have also been made in the enunciations of this book, chiefly in those of the fubfidiary propofitions which Euclid introduced for the fake of the reft; they are expreffed here in the man ner that feemed best adapted to the new notation."

Several of the obfervations, in this quotation, are, in our opinion, perfectly juft; but we are far from being per fuaded, that an algebraical method of demonstrating the ele mentary propofitions relating to proportion, is the most perfpicuous. On the contrary, we think that employed by Simfon the moft clear, and, at the fame time, the most likely to make a lafting impreffion upon the mind of the ftudent.

The alterations and additions, relating to plane figures, made in the prefent edition, are judicious and ufeful; and fuch we also esteem Mr. P.'s method of demonstration, when he treats of folids. Of this he gives the following account :

"With refpect to the geometry of folids, I have departed from Euclid altogether, with a view of rendering it both fhorter and more comprehenfive. This, however, is not attempted by introducing a mode of reafoning loofer or lefs vigorous than that of the Greek geometer; for this would be to pay too dear even for the time that might thereby be faved; but it is done chiefly by laying afide a certain rule, which, though it be not effential to the accuracy of demonftration, Euclid has thought it proper, as much as poffible, to observe. "The rule referred to, is one which regulates the arrangement of Euclid's propofitions through the whole of the elements, viz. That in the demonstration of a theorem, he never fuppofes any thing to be done, as any line to be drawn, or any figure to be constructed, the manner of doing which, he has not previously explained. Now the only ufe of this rule, is to prevent the admiffion of impoffible or contradictory fuppofitions, which no doubt might lead into error; and it is a rule well calculated to answer that end; as it does not allow the exiftence of any thing to be fuppofed, unless the thing itself be actually exhibited. But it is not always neceffary to make use of this defence, for the existence of many things is obviously, offible, and far enough from implying a contradiction, where the method of actually exhibiting them may be altogether unknown. Thus, it is plain, that on any given figure as a bafe, a folid may be conftituted, or conceived to exift, equal to a given folid (because a folid, whatever be its bafe, as its height may be indefinitely varied, is capable of all degrees of magnitude, from nothing, upwards) and yet it may, in many cafes, be a problem of extreme difficulty, to affign the heigh of fuch a folid, and actually to exhibit it. Now this very fuppofition is one of thofe, by the introduction of which the geometry of folids is much fhortened, while all the real accuracy of the demonstrations is preferved;

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preferved; and therefore to follow, as Euclid has done, the rule that excludes this, and fuch like hypothefes, is to create artificial difficulties, and to embarrafs geometrical inveftigation with more obftacles than the nature of things has thrown in its way. It is a rule too, which cannot always be followed, and from which, even Euclid himself has been forced to depart, in more than one inftance.

"In the two books, therefore, on the properties of folids, that I now offer to the public, though I have followed Euclid, very closely, in the fimpler parts, I have no where fought to subject the demonstrations to fuch a law as the foregoing, and have never hesitated to admit the existence of fuch folids, or fuch lines as are evidently poffible, though the manner of actually defcribing them, may not have been explained. In this way alfo, I have been enabled to offer that very refined artifice in geometrical reafoning, to which we give the name of the Method of Exhauftions, under a much fimpler form than it appears in the 12th of Euclid; and the fpirit of it may, I think, be bett learned when it is difengaged from every thing not effential to it. That this method may be the better underflood, and because the demonstrations that require it are, no doubt, the most difficult in the Elements, they are all conducted, as nearly as poffible, in the fame way through the different folids, from the pyramid to the fphere. The comparison of this laft folid with the cylinder, concludes the eighth book, and is a propofition that may not improperly be confidered as terminating the elementary part of Geometry.

From thefe extracts, our readers may eafily form an idea of Mr. P.'s chief defign in the prefent publication. For particular information, concerning minute alterations and additions, recourse must be had to the volume itfelf. The notes, at the end, afford indifputable proofs of abilities and learning, and are correctly and clearly expreffed*.

ART. V. The Enquirer; or Reflections on Education, Manners, and Literature; in a Series of Effays. By William Godwin. Svo. 7s. 6d. Robinfons. 1797.

RECOLLECTING the "Political Juftice" of this danger

ous and extravagant authort, we opened this volume with the expectation of much difguft; which expectation, an attentive perufal neither wholly difappointed nor fulfilled. The author informs us, in the preface, that, with as ardent a paffion for innovation as ever, he feels himself more patient and tranquil than when he wrote his enquiry concerning Political Juftice. We are inclined to give full credit to this information; for, though the work before us is certainly not free from paradoxes,

* We are forry that this book has been fo long overlooked: but we think it better to infert a notice late, than to omit it altogether. See Brit. Crit, vol. ii, p. 307.

it contains many hints both original and ufeful, with which we were fo well pleased, that it grieved us to find them interfperfed with others deferving of the fevereft reprehenfion. It confifts of a series of ellays, which the author has divided into two parts; of which the former relates chiefly to the education of youth, and the latter to the duties, employments, and pleasures of manhood. In his preface, he acknowledges that he has not been feverely anxious relative to the inconfiftencies that may be discovered between the fpeculations of one effay, and thofe of another;" and the reader will proceed through the volume in a very carelefs manner, if he perceive not the truth of this acknowledgment.

The first effay, which treats of awakening the youthful mind; fets out with affirming, that the true object of education is the generation of happiness; that man is a SOCIAL being; and that men fhould be taught to affift each other." The fame fentiments are repeated in other effays, particularly in the feventh, where it is faid, that" fociety is the true awakener of man;" and yet, in direct contradiction to all this, the author labours, through the whole of the tenth effay, to prove that "cohabitation is fundamentally an erroneous fyftem!" We shall not attempt to reconcile fentiments, which doubtlefs he himfelf knows to be irreconcileable; but taking it for granted, as it is to be hoped we may, that man is a focial being, it may be worth while to make fome remarks on the author's affertion, that the object of true education is the generation of happinefs." If it be his meaning, that the youthful mind fhould be trained to the purfuits of happiness through the whole of its exiftence, comprehending a future life as well as the prefent, we fully agree with him; but if the happinefs to which it is to be trained, extends not beyond its prefent ftate of existence, we cannot help ifpecting that Mr. Godwin's pupil, pursuing the object of fuch an education, would frequently be induced to violate political juftice. To this indeed, the author would probably have no objection; for, he fays, the method of inveftigation by which he established his doctrines concerning political juftice, is incommenfurate to the powers of men:" perhaps he means that the powers of men are inconmenfurate to that method, and that the whole of his fyftem is confequently precarious. He affures us, however, in the ellay before us, where truth is investigated by a more cautious method, that "virtue is effential to individual happiness;" and, in this fentiment, we here again agree with him: but truth forbids that we should agree with him, when he defines virtue to be "a compromife between oppofite motives and inducements;" or when he affirms, that none but "a man of vigorous comprehenfion, and long view, can be a man of genuine virtue." Surely

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Surely virtue genuine virtue-makes no comparifon with motives and inducements to vice; and though Cæfar was certainly a man of vigorous comprehenfion, and long view, we can hardly fuppofe that this author confiders him as having acted a virtuous part when he enslaved his country! On the other hand, we are convinced that the man who thinks marriage an odious monopoly, and a republican form of government the very best form poffible for every nation, is, with respect to thofe fubjects at least, a man of short views; but we should have been much to blame if, when we found Mr. Godwin maintaining fuch paradoxical pofitions, we had, without further enquiry, concluded him to be a man of vicious habits. Notwithstanding these extravagant paradoxes, this effay contains fome good fenfe, on the neceflity of commencing the course of education at a very early period; for, as it is well obferved,

"Improper treatment, the rendering the child, in any confiderable degree, either the tyrant or the flave of thofe around him, may, in the first twelve months, implant feeds of an ill-temper, which, in fome inftances, may accompany him through life."

It feems to be the object of the fecond effay, to prove that talents are more valuable than virtue.

"Talents, in general," fays the author, "hold a higher eftimation among mankind than virtues; and the decifion of common fame, in favour of talents in preference to virtues, is not so abfurd as has fometimes been imagined."

We do not know that the decifion of this question by common fame; as far as common fame decides it, has ever been imagined abfurd. Eminent talents are, perhaps, rarer endowments than eminent virtues, and, like every other thing of value, are prized in proportion to their rarity. A man of virtue, with eminent talents, is likewife a more valuable member of fociety, than a man of equal virtue with inferior talents; and, of courfe," the trump of fame is more completely filled" by the former than by the latter; but is there a man alive who prizes the talents of Cromwell more than the benevolence of the Man of Rofs; or the oratorical powers of Bolingbroke more than the bashful virtues of Addison? When Mr. Godwin affirms, that a weak man can be good only as a dog is good, and that he can poffefs the name of virtue only by way of courtely," he at once betrays strange ignorance of the mental conftitution of man, and lofes fight of his own darling democracy. To democracy indeed, he has, without intending it, given, in this effay, a mortal wound; for he affirms, that the offices of men, in fociety, are not of fo fimple a texture.

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that they require only common talents to guide them; and that the weak man neither knows whom he ought to approve, nor whom he ought to difapprove." To thefe affertions we give our hearty affent; but, becaufe a weak man is unfit to guide the helm of ftate, or to judge of the excellence or defects of particular forms of government, it furely does not follow that he must be destitute of virtue."

It was the opinion of Johnfon, that "the true genius is a mind of large general powers accidentally determined to fome particular direction." This opinion feems to have been adopted by Mr. Godwin, who, in his third effay, fays, that "genius appears to fignify little more, in the first instance, than a spirit of prying obfervation and inceffant curiofity." On the fervices of genius, the author has thrown out, in this and the fol lowing ellay, many juft obfervations; but he very needlessly deviates from his fubject, first to fhow that he has embraced the doctrine of philofophical necessity, and then to excite discontents among the vulgar.

"The cares of the world," he says, "fall upon the peasants! They are inlifted in the crimping-house of oppreffion. They are brutified by immoderate and uninterrupted labor. Their breafts are hardened, and their fpirits broken, by all that they fee, all that they feel, and all that they look forward to."

Whatever may be the cafe in other countries, furely the fpirits of the English peasants are not so much broken, as to male them liften with patience to an author like this, who compares them to brutes, and denies that they poffefs the fympathies of humanity.

In the fifth, fixth, and seventh effays, which treat of an early tafte for reading of the ftudy of the Claffics; and of public and private education; there are many hints worthy of the attention of those, who are intrufted with the important charge of educating youth; but there is nothing in them very remarkable, except that the author lavishes exclufively, on the Latin claffics, praises which are more justly due to the clallics of ancient Greece.

In the eighth effay, he attempts to prove, that youth is the fcene of wretchedness, and that the restraints of a school are intolerable. To thofe who have had the happiness of a libera! education, it can hardly be neceffary for us to obferve, that this attempt is fruitless; nor to the attentive reader can it be neceffary to point out the fallacy of the author's reasoning, which proceeds entirely on the fuppofition, that the fentiments of youth and of manhood are the fame.