Scuoter da Febo il verdeggiante alloro) Tra facondi fcrittor miniftro eletto Spingo con quell'ardor ch'entro m'avvampa, Ora Sorga mirando, or Dirce e Tebe." He then particularly addreffes Mr. Rofcoe on his Life of Lorenzo, and introduces the spirit of that great man lamenting the prefent flate of Italy, and giving appropriate praises to his biographer. After his fpeech, which occupies the greater part of the Ode, the conclufion is as follows: Qui tacque l'Ombra, e al fuo fparir scoperse Di pennello legiadro; Di marmo e di diamante alto Colonna Sorgeva altera e macstofa Donna Ch'ora il fuolo guardava, ed ora il mare ș Vi fi leggeva in note ardente e chiare, CANZON, fe mai quell' onorata riva E fe negletta giaci e ignota all' Arno, It is not often that any man acquires the power of writing with fuch fpirit in the language of a foreign country; and perhaps, fince Milton, no Englishman has been able fo to found the Tufcan lyre. If there are any faults in the language, they must be for Italian not for English critics to discover. Let us give also a fpecimen of the Italian profe of this editor, fpirited and elegant almoft as his verfe, and then conclude. We choose the part in the Addrefs to the Reader, prefixed to Tirabofchi, where he affigns the reasons for his Italian publica tions. "Non "Non v'e lingua certamente ch'io ftimi, coltivi, e veneri, più della mia propria; ma questo appunto mi rende piu ftudiofo ed ammiratore della Italiana, sembrandoni trovare tra le due lingua una fomma analogia per la facilità e corrispondenza della frafi, e fpezialmente un aria di franchezza e libertà nella fublime poefia che eccita in me piacere infieme e meraviglia. "Indi mi volgo all'Arno, E, corfa già l'immenfa ftrada Argiva, Nuovi fregi agguingendo aurei, immortali; Tofche gemme fcoprendo o ignote o rare "Ma fe alcuno mi domandasse, da quai motivi incitato, con tanto ardente e fervorofo zelo verfo le amene e fiorite lettere, m'inchino fi affettuofamente all'Italia; rifponderei altamente: E a chi dunque dovrei inchinarmi fe non all'augufto e dominante feggio di Febo, all madre e nudrice delle scienze e dell'arti, alla rifvegliatrice del buon gusto, alla fonte di vaghiffime fantafie, e all'inefaufta miniera de'tefori dell'antichilá e delle dotte memorie d'ingegni Greci e Latini? "A voi dunque, eruditi e ftudiofi miei compatriote, raccommando di nuovo la Patria, le Mufe, l'Italia, e tutti i fuoi piu degni eccelfi leggiadri ed eloquenti scrittori, storici, critici, e poeti, di cui fi fente la fama in un movimento continuo co i fecoli. T. J. MATHIAS." Though this editor has doubtlefs exerted the care in correcting the prefs, which fo beautiful a publication deserved, yet we have obferved a few errors, which have escaped his eye. For instance, in the Life of Crefcimbeni, p. 36, 1.13, Arcardi for Arcadi. In that of Tirabofchi, p. 10, l. 4, rittatto for ritratto, and one or two fmaller lapfes before. In the text of Tirabofchi, p. 11, l. 3, decimo fecolo for duodecimo; p. 22, 1. 14, la o miglianza for fomiglianza. Very great is the difficulty of printing much with correctnefs, in a language which the compofitors and correctors do not understand; but though we have obferved these little blemishes, we have alfo remarked that the text in general, fo far as we have examined it, is printed with no less accuracy than beauty. To this therefore, as to the other Italian volumes of Mr. M. we fincerely with the favourable reception of the public. A&T. ART. XIII. A Geometrical Treatife of Conic Sections. In Four Books. To which is added, a Treatife on the Primary Properties of Conchoids, the Cifford, the Quadratrix, Cycloids, the Logarithmic Curve, and the Logarithmic Archimedean and Hyperbolic Spirals. By the Rev. Abram Robertfon, A. M. F. R. S. Savilian Profeffor of Geometry in the Univerfity of Oxford. 8vo. 268 pp. 11S. Ox. ford printed; Payne and Mackinlay, London. 1802. O branch of mathematics has been ftudied with more affiduity than that of conic fections, nor has any one a higher claim to the attention of the geometrician and natural philofo. pher. The former, by their means, is enabled to proceed to the folution of fome of the moft curious and ufeful problems in abftract fcience; and an intimate knowledge of their properties was one of the principal means employed by Sir Ifaac Newton in producing a work, which the intelligent and liberal will ever confider as one of the greatest efforts of the human mind. We have been led into thefe reflections by the tendency and extent of the work before us, of which the author gives the following account. ers. "The defign has been to furnish the young mathematician with fuch a feries of propofitions as might prepare him for confidering some of the most important truths in fcience, and enable him to enter on the ftudy of natural philofophy with the profpect of obtaining a thorough knowledge of the fubject. According to thefe views, the felection of properties and the extent of the work have been regulated; and, at the fame time, the arrangement and division of the whole have been made with a defign of accommodating two defcriptions of readThofe who are considered as conftituting the firft clafs, are fuppofed to be defirous of a general but refpe&table portion of knowledge of the fubject. For the ute of fuch, a perufal of the first three Books will be found fufficient, as they contain the properties of the fections moft frequendly referred to in pure and mixed mathematics. For thofe who rank under the fecond, or higher defcription, a knowledge of all the four Bocks will be requifite, as they complete the original defign of rendering the whole a preparative for the Newtonian philofophy. The author flatters himself, indeed, that he fhall be found to have carried his elucidations of the Principia in the prefent work confiderably beyond what have been attempted in other treatises of conic fections." To guard his reader against disappointment, he ftates, in the Advertisement prefixed to the work, what acquifitions are neceffary for entering upon its perufal. "It is expected that the young ftudent fhould understand tho roughly the first fix Books of Euclid, the first twenty-one Propofitions of of the eleventh Book, the two firft of the twelfth, and the first principles of algebra and plane trigonometry." This conduct of the author towards his reader is fair and open, and is fuch as ought to be obferved by every writer on fubjects of fcience. The young ftudent enters upon a work with confidence when he is informed of the full extent of knowledge previoully necellary, and is confcious that he has attained it; and he proceeds with alacrity when affured that he is advancing towards the object of his wishes. It may feem unaccountable to fome readers, that a difference of opinion fhould exift in any department of mathematical science, which boasts of indifputable principles, and a certainty in its conclufions, deduced by correct reafoning from obvious axioms but the astonishment will immediately vanish, when the various abilities of the human mind enter into the confideration, and the confequent variety of views in which even the fame fubject must be contemplated at different times by Individuals.. "It is well known," fays the author before us, "that, about the middle of the feventeenth century, a difference of opinion took place among mathematicians, concerning the proper fource from which the properties of the conic fections fhould be deduced. But notwithtanding the objections which then began to be made to their deduction from the cone, and which have fince been continued, it appears to the author of this work, that the difficulties attributed to the deductions from it were not to be imputed to the folid itself, but that they were occafioned folely by the manner in which the deductions had been made. The early writers did not happen to perceive that the general and extensive property, expreffed in the thirteenth Propofition of the first Book of this Treatife, could eafily be obtained from the cone; and, not adverting to this, their deductions from the cone were fometimes tedious and intricate. "The above-mentioned property, as far as fecants are concerned, occurs (I believe for the first time) in a folio volume, of which a treatife of conic fections makes a part, entitled, Euclides Adauctus et Methodicus, &c. published by Guaremes in 1674. The property, to the fame extent, is to be found in Jones's Synopfis Palmariorum Mathefeos, published in 1706; but neither of thefe two authors confidered the property as a fundamental one, nor do they feem to have been aware of the advantages it was capable of producing. Its extenfive utility was first evinced in Hamilton's Conic Sections, publifhed in Latin in 1758; and, on the appearance of this work, objections to the cone ought to have ceased. This was my perfuafion when I published my former Treatifet; and every deliberation on the subject fince, has tended to Foundations for fyftems, independent of the cone, are stated in the work before us. + Of this we gave an account in our number for August, 1793; vol. i. p. 371. ftrengthen frengthen my conviction of its juftice, for the following reafons. First, the whole trouble with the cone is reduced to a very few demonftrations, for which no farther knowledge of Euclid is neceflary than what is requifite for fpherical trigonometry. Secondly, by this method the general properties are obtained with most eafe and elegance. Lastly, by deducing the properties from the cone, the treatife is rendered more extenfively ufeful. No work on conic fections, confined to their defcription on a plane, can be applied to elucidations in perfpective, projections of the fphere, the doctrine of eclipfes, and in fome other particulars of the highest importance in fcience." We do not perceive any objection of weight, which can be urged in oppofition to the opinions above ftated. For the demonftration of the general property, above alluded to, no particular exertion is neceffary. The man who alledges diffi culties in its attainment confeffes, by implication, his inability to understand solid geometry; and, with reference to autho rity, we do not recollect any author on conic fections who founded his fyftem on their defcription in plano, and wrote to a refpectable extent on the fubject, except the Marquis de l'Hofpital, and Dr. Simfon of Glasgow, whofe publications confiderably preceded Dr. Hamilton's. Having prefented our readers with thefe general remarks on the work before us, we proceed to a fhort analysis of its contents. In the first Book, the general properties of the Sections are deduced from the Cone, and their general properties conftitute a foundation for the fucceeding Books. The demonstrations reft chiefly on the firft Propofitions of the eleventh Book of Euclid, the thirty-fifth and thirty-fixth of the third, and the common properties of fimilar Triangles. This Book confifts of feventeen Propofitions. The fecond Book is on the Ellipfe and Hyperbola. This connection we confider as very judicious, as most of the properties of these sections may be enunciated in the fame terms. In the demonftrations alfo the fame words, almoft always, apply to both fections; and where this is not the cafe, the effential difference between the two is preffed upon the reader's attention. This Book contains twenty four Propofitions. The third Book treats of the Parabola, the Directrices of the Scations, the Afymptotes of the Hyperbola, Conjugate Hyperbolas, and of hyperbolic Sectors and Trapezia. The method of arrangement, enunciating, &c. obferved in this Book muft prove highly advantageous to the young ftudent. It opens with the most general properties of the parabola; but the author takes every occafion to connect this with the other two fections; and as often as it can be done, he enunciates in terms extended to the three curves. By this mode of proceeding it frequently happens, that the properties proved |