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we are fick and die, generally fpeaking, because we confent to Suffer thefe accidents. This confent (indeed!) in the present *ftate of mankind, is, in fome degree, unavoidable. We must "have stronger motives, and clearer views, before we can uni"formly refuse it. But though we cannot always, we may frequently refufe." P. 869. It is true, that the author, aware, notwithstanding his enthusiasm, that these doctrines may startle some minds, takes care to tell us, that all this is only conjecture; and that his grand argument "is altogether inde"pendent of its truth or falfehood." But indeed he is, as we have faid already, perfectly confiftent; and if we allow the omnipotence of truth, and the perfectibility of man, there is nothing in the wildest of these reveries that we can properly deny.

Now, reader, be pleased to recollect what was faid in the beginning of this article, on the empty vanity of the prefent times; and confider fairly what there is in all this, either in the conception of the author, or the authorities on which he refts, that can give a reasonable man any idea, that the work is the production of an enlightened age. Let us endeavour, if we can, to make it enlightened; but fince thofe of its writers, who have by fome been held the teachers of wisdom, have published doctrines that lead to fuch abfurdities as these, letus not, with idle flattery to ourselves, call it wife, for alas! it must appear, to fober reafon, a very foolish age! What is there in the entelechia, or occult qualities of Aristotle,] the Ideal fyftem of Plato, the fatalifm of the ftoics, the atomifm of Democritus and Epicurus, or even the wildest conjectures of the most barbarous fects, that is not quite as rational and as intelligible as thefe omnipotences, and perfectibilities, and neceffities? The true light, therefore, in which we ought to regard this book is, as a complete refutation of Helvetius, Rouffeau, the author of Syfteme de la Nature, and fome English writers of equal extravagance, by a fair reductio ad abfurdum; by showing demonftratively, to what nonfenfe and extravagance their doctrines, when pursued, must lead.

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As to the ftyle of the book, it is in general good; fome few words are used affectedly, but on the whole it is perfpicuous and clear; nor is there any thing that demands notice, in the way of cenfure, very particularly. The method of the author, as his object was, to conceal his real grounds as long as poffible, very different from that which is here stated; and from that which propriety demanded. He begins with the importance of political fcience; proceeds in Book ii. to the principles of fociety; in Book iii. to the principles of government. Book iv. contains mifcellaneous principles, many of which fhould have been prefixed. Book v. is on legiflative and executive power. Z Book ERIT. CRIT. VOL. I. JULY 1793.

Book vi. On opinion as a fubject of political inftitution. Book vii. On crimes and punishments. Book viii. On property. The marrow of the whole we have already given, in our own method; and if any one of those who shall perufe this account fhould feel any inclination to gain further acquaintance with the book itself, it is a feeling in which the writer of this article is not likely to participate. He takes leave of it finally, carelefs whether he shall ever view it again; certainly neither with ing or expecting to behold another like it.

ART. XIII.

ΑΡΧΙΜΗΔΟΥΣ ΤΑ ΣΩΖΟΜΕΝΑ ΜΕΤΑ ΤΩΝ ΕΥΤΟ

ΚΙΟΥ ΑΣΚΑΛΩΝΙΤΟΥ ΥΠΟΜΝΗΜΑΤΩΝ. Archimedis qua fuperfunt omnia cum Eutocii Afcalonita Commentariis. Ex reenfione Fofephi Torelli, Veronenfis, eum nova verfione Latina. Accedunt lectiones variantes ex Codd. Mediceo, et Parifienfibus. Folio. Chart. max. l. 155. Min. 11. 58. Oxonii, e Typographeo Clarendoniano, 1792.

ALTHOUGH the volume before us is dated 1792, we find, upon enquiry, that it was not published till the prefent year. It is, therefore, capable of coming under our notice, according to the limitations we had prefcribed to ourfelves, and stated to our correfpondents in our firft number: and, confidering the fame of Archimedes, the great reputation of Torelli, the editor, and of the learned univerfity, under whofe patronage, and at whose expence, the work has been published, we are induced to think our readers will be pleafed to fee it confidered rather fully in the prefent article.

In a fhort addrefs to the reader, by the Delegates of the Clarendon Prefs, we are informed of the manner in which Torelli's papers came into their poffeffion. It appears, from a paffage towards the end of his preface, that he intended to pub lifh the edition in Italy; but prevented, perhaps, by bodily inArmity, and deterred by the profpect of a great expence, he deFayed to carry his defign into execution. In the mean time the late Lord Stanhope, whofe knowledge and encouragement of mathematical learning will long be remembered, brought about a treaty between Torelli and the delegates. Torelli, however, hefitated to intruft the publication to another, and, during his life, nothing was pofitively determined. His executor, Alberto Albertini, from a knowledge of his deceased friend's intentions, and a thorough perfuafion of their propriety, made a present of all the papers to the univerfity of Oxford, and tranfmitted the wooden blocks, upon which the diagrams had been cut, at the

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original expence. John Strange, Efq. at that time the British Refident at Venice, with a zeal which does him honour, was instrumental in bringing this affair to the above-mentioned conclufion. The whole materials were then put into the hands of Mr. Robertson, of Christ Church, Oxford, to whofe care the arranging of the papers, and the fuperintending of the edition was intrufted; and, according to the addrefs to the reader, now before us, and the preface of Torelli, the intentions of the learned editor have been fully completed. The hopes of the learned M. Montucla of a new edition of Archimedes, implied in in the following paffage of his Hiftoire Des Mathematiques, may now alfo be confidered as fulfilled: "L'Angleterre, qui s'inte"reffe encore à la gloire des géometres anciens, nous donnera "peut-être quelque jour une belle édition de celui-ci, qui puiffe "aller de pair avec celles d'Euclide & d'Apollonius que nous "lui devons."

Besides what we have already noticed, the following are the contents of this volume, 1. Clementis Sibiliati, de Vita ac Studiis Jofephi Torelli Veronenfis, Commentarium-2. Præfatio Jofephi Torelli. To these the following treatises of Archimedes immediately fucceed;-3. De Planorum Æquilibriis Liber Primus, cum Commentariis Eutocii Afcalonitæ ;4. Quadratura Paraboles ;-5. De Planorum Equilibriis Liber Secundus, cum Commentariis Eutocii Afcalonitæ ;-6. De Sphæra et Cylindro Libri Duo, cum Commentariis Eutocii Afcalonitæ ;-7. Circuli Dimenfio, cum Commentariis Eutocii;-8. De Helicibus ;9. De Conoidibus et Sphæroidibus, cum Torelli Commentario in Prop. 12;-10. Arenarius ;-11. De iis quæ in Humido vehuntur, Libri Duo;-12. Lemmata; -13. Opera Mechanica, ut cujufque mentio ab antiquis Scriptoribus facta eft. There is also an Appendix, in which are contained, 1. Commentarius in aliquas Archimedis Propofitiones de iis quæ in Humido vehuntur ;-2. Lectiones Variantes Codicis Florentini ;-3. Lectiones Variantes Codicum Parifienfium.

Of each of thefe we proceed to give an account, obferving. once for all, that we shall not confine ourselves to a literal tranflation of the terms which occur in the book, but shall use fuch as, in our opinion, brevity requires, and fuch as are most familiar to the generality of modern readers.

Jofeph Torelli, we learn from his biographer, was born at Verona, in November 1721. Luke, his father, was a merchant, and his mother, Alberta Albertina, was alfo of Verona. The entire parental care of Jofeph foon devolved upon the mother, as her husband did not long furvive the birth of their fon. The more early parts of his education having been carefully attended to, he was fent to Padua, where, to ufe the words of Sibiliati, who then studied at the fame feminary," Ita toto qua"driennil

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"driennii fpatio perdius ac pernox in ftudiis evigilavit, nulla ut "ei temporis particula vacaret ab auditione, lectione, fcrip"tione, commentatione; tantumque diligentiæ tribueret, ac si "non maxima ingenio, quod illi magnum inerat, gratia ha"benda videretur." His application and abilities gained him the esteem of the learned men of the place, and, after receiving a doctor's degree, he returned to Verona.

Being in eafy circumstances, he did not enter into any profeffion, but employed his time in the acquifition of knowledge, and in writing on several fubjects. He gave up much time and attention to the Hebrew, Greek, Latin, and Italian languages: to the first two, that he might obtain a competent knowledge of them, to the others that he might be able to write in them as occafion required. To thefe he added French, Spanish, and English; and this latter, it is pleafing to be told, he learned more thoroughly than the other two, from the refpect and love he had for our nation, and writers. To his knowledge of languages he added a profound skill in mufic, architecture, geometry, medals, and antiquities of every kind. His mind, equally remarkable for its verfatility and strength, was at one time engaged in the moft rigorous mathematical investigations, and at another employed in the amufing departments of literature.

With these abilities, in Torelli, an excellent heart was happily affociated. Piety and virtue were confpicuous in his character, and procured him the friendship of the great and good.

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Defatigarer equidem," fays Sibiliati," numerando, fi exteros quoque percenfere fatagam, genere aut ingenio aut utroque "nobilitatos, quibus aliqua cum eo conjunctionis neceffitudo "interceffit. Sed tacitus præterire nullo modo poffum Philip"pum Stanhopium Toy xxxpirn proxime fublatum ex oculis, "non animo, bonorum omnium atque fapientum; Davidem "Stormontium (now Earl Mansfield) fummatem virum, quem "nominare laudare eft; Archiepifcopum Cantuarienfem inge"nio ac virtute dignitati quam fuftinet prorfus parem, qui "unam atque eandem effe putantes literariam rempublicam in "omnia pertinentem loca, iifque tantum quibus terrarum orbis

finibus contentam, Italo homini atque operi adeo impensè "patrocinati funt, ut conterraneo fuo non potuiffent impen"ius." Thefe few particulars relating to this extraordinary and amiable man, we thought proper to select and lay before our readers; for a fuller account, we refer to the work itself, where a lift of his publications and writings is alfo given.

In Torelli's Preface, of 19 pages, which next claims our attention, we have a short account of Archimedes, reafons for a new edition of his works, a statement of obligations to former editors, and a good deal of claffical and mathematical criticism. Archimedes,

Archimedes, according to the account of Torelli, was born at Syracufe, in the year 287, before Chrift. By his father's fide he was related to king Hiero, and he was alfo an intimate friend of that prince. After travelling into Egypt, and some other countries, he returned to his native place, where, it is highly probable, he composed the Treatifes which we now poffefs. Plutarch, in his life of Marcellus, mentions feveral particulars relating to him, from which it appears, that he pursued his ftudies with extreme intensity and perfeverance. Exercifes for his bodily health were interrupted by his defcription of geometrical figures; and, during the investigation of truths which he had in view, fometimes food and fleep were forgotten.

As fo many ages of ignorance and barbarifi elapfed between the time of Archimedes and the revival of literature, a distinct historical account of his MSS. is not to be expected. Some appear to have been lost at a very early period; the fubject mat ter of a few has come down to us only in tranflation; and those which are found in the libraries of Europe have fuffered all the evils ufually confequent upon frequent transcription, performed by men more folicitous of gain than attentive to accuracy. Eutocius, who flourished in the fixth century, ufed a MS. belonging to his preceptor, Ifidorus, one of the architects of the church of Saint Sophia. Torelli fuppofes that this must have been a very good MS. but of its fate we have no information. The beft, perhaps, which has reached modern times, is that from which the Bafil edition was printed, in 1544; which is not only the first printed copy of Archimedes, but the only one, as far as we know, which, till now, deserved to be called an edition. Other publications, which pass under the name of Archimedes, are either tranflations, or are confined to one, or at most only a few particular treatises.

In preparing his edition for the prefs, Torelli ufed that of Bafil; and the firft alteration he propofed was a different arrangement of the treatifes. We highly approve of the reafons given for the alteration. The words of Archimedes, indeed, in fome inftances, amount to a direction on this head, and, in others, the connexion of the fubject matter pointed out the propriety of the difpofition in the prefent volume. The fecond particular, in which Torelli proposed to exert himself, was the correction of the text; and the third was the production of a new tranflation of the whole. Thefe intentions were fulfilled with much care, ingenuity, and learning; and in printing the work, a defign, not expreffed but implied by Torelli, has been carried into execution, by making the edition fimilar to those of Euclid and Apollonius, publifhed alfo at Oxford. The Greek, and the Latin translation of it, are printed in columns in

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