Σ' Αγαμέμνονος πέμψαντος, ω γύναι, μελα and this conclusion of the note is left out: Quis enim ovypai Topor in Euripide saltem damnet? In the note on V. 565. p. 25. the name of Captain Cook is changed into that of Wallis, Mr. Wakefield having mentioned the former by mistake. Page 37 has also been cancelled. In line 25 we find, quæ selegi, instead of quæ selexi, as it stands in our copy; and in the following page, 38, inter eruditos-non-obtrectatores, sed laborum socii participesque is rightly corrected into inter -; as in p. 39. 1. 21. we observe ad hoc autem inhumanitatis scopulum altered properly into ad Aunc socios scopulum. There may be other alterations, but these are all which we observed. In another Article we hope to conclude. Critical investigations, if intended to examine any questions thoroughly, do not readily admit curtailment. From the nature of Mr. Wakefield's pamphlet on the New Hecuba, it was impossible to satisfy our readers, or ourselves, with mere assertive contradictions. It was necessary to search deeply into every remark, in order to prove the solid and unshaken excellencies of Mr. Porson's edition of Euripides. [To be continued.] 2 D.C.B....Y. ART. XIII. An Introduction to Arithmetic and Algebra.. Vol. II. By Thomas Manning. Svo. pp. 218. 45. Boards. Riving( tons, &c. 1798. THE HE first part of this work was noticed in our Review for February 1797.-The contents of the present volume are, Proportion of variable Quantities, Rule of Three, Reduction, Arithmetical and Geometrical Series, Incommensurables, Application of Algebra to Rectilinear Geometry, Surds, Greatest Common Measure of Algebraic Expressions, Properties of Numbers, Logarithms. The chapter on Incommensurables is drawn up with much neatness and perspicuity; and, in a scholium, the author sums up forcibly, and with precision, the arguments diffused over the two lectures of Dr. Barrow, in which that great Geome trician defends Euclid's definition of Proportionality. We give a short extract: The 95th article, however, appears to us imperfeet in its enun ciation and proof; for g must be the same multiple of b that p is of a. • Various < Various objections have been urged by different writers against Euclid's definition of proportionality. Some have censured it as obscure and difficult to be understood; but that fault, if it exists at all, is in the subtil nature of incommensurable magnitudes, and not in Euclid's definition. Others have complained that they cannot, with out a demonstration, discern whether quantities, that agree with the definition, are proportional or not; as if proportionality was some thing independent of definition. Others again, defining numbers to be proportional, when the quotient of the first divided by the second is equal to the quotient of the third divided by the fourth, have endeavoured to obviate the necessity for Euclid's, by extending this their definition to all magnitudes whatsoever; thereby endeavouring to confound the distinct natures of commensurable and incommenA surable quantities; for what is the import of the expression, B when A and B are incommensurable with each other? A logical answer to this question would distinguish again what they thus endeavour to confound and blend together, and would satisfy the enquirer, that if he would have an accurate knowledge of the real nature of magnitudes, he must take the trouble of examining into the doctrine of Incommensurables, and at the same time shew him, that in point of conciseness nothing is gained by thus endeavouring to elude Euclid's distinctions, and in point of perspicuity much lost; the enquiry being of that nicety and subtilty, which cannot be easily d'spatched in few words.' The chapter on the Application of Algebra to Rectilinear Geometry is a valuable one: but we wish that the author had expressed differently the addition, subtraction, &c. of ratios. We are, indeed, previously informed what the symbols denote: but the ideas annexed to them, in their common signification, so frequently recur and intervene, that the mental progress is considerably impeded. The explanation of logarithms is intelligible and satisfactory. The logarithmic series is demonstrated by a process purely algebraical. If 1+ be the base of the system, then y is the logarithm of the number i+a. 2 If 1+a" be assumed = 1+by+ cy2+ dy3 &c. then b may easily be shewn equal to a a2 -+ a3 2 3 &c. and by a very ingenious method (for which the author acknowleges himself in some degree indebted to a work of M. de la Grange *, *Books from France, however unconnected with politics and religion, make their way into this country with so much difficulty, that it was not till very lately that we could procure this work, although printed in 1797. We hope, however, to notice it in our next APPENDIX: which will be published at the same time with our Review for May. Hh3 Théorie Théorie des Fonctions Analytiques) the law of the dependence of c, d, &c. on b is strictly determined; whereas Mr. Bonnycastle is obliged to prove by actual involution that 2 c, 2 × 3.d, 2X 3X 4. &c. are the square, cube, biquadrate, &c. of the The Appendix contains observations on Impossible Quantities, and on the use of the negative sign. Of the first volume, we have already expressed our favourable opinion; and the. second is not less entitled to commendation, The whole work is valuable for the evidence of its principles, the precision of its language, and the rigour of its proofs. Wood....e. ART. XIV. Flora Londinensis. By William Curtis. Folio. Vol II. A We gave a very ample account of the first volume of this splendid and valuable publication in our seventieth vol, p. 1.On a review of that article, there seems to be nothing which we could wish unsaid. The work has to boast of unrivalled excellence, undiminished splendor, unabated accuracy, and is stil! patronised by the learned and the munificent. There is scarcely a name of any consequence in the botanical world, which is not recorded as a contributor, or a friend, to the richness of the observations contained in it. The specimens, from which the figures are drawn, are uniformly well chosen, and remarkable for their characteristic significance; the colours are vivid and expressive; and the dissections of the flowers are uncommonly well executed, and will prove more didactiq than the very lectures of any but superior teachers, To carry science to perfection, the life of man should be doubly lengthened. The ordinary allotment of time enables an individual to form a general outline of much, but to work * See his method for determining Logarithmic Series, in Addenda to Hutton's Dictionary, or in Monthly Review for April 17984 page 379: out out the detail (so that others may profit from it) of a very little. Then again the different wants, not to say the different em ployments and pursuits, of a man, are perpetually clashing, and thwarting each other; so that the very little which he could do is oftentimes made less, and not unfrequently rendered wholly abortive. This, however, is an evil inseparable from the nature and condition of Man; and we are not to repine at our lot. Doubtless, Providence ordered it thus for general wise and beneficial purposes. No labour of man, howsoever conducted, is incapable of making those who come afterward either wiser or better. Adverting to the clashing of different pursuits, many have regretted that Mr. Curtis should have undertaken two such works as the Flora Londinensis and the Botanical Magazine; arguing that, had he confined himself to the Fl. Lond., we should have had a more ample storehouse of botanical treasure. Undoubtedly we might: but, at the same time, there is much impropriety in this remark. The public had no right to call on him thus to confine himself; and, if it be duly investigated, self-interest will be found to have suggested the idea of this complaint for it must have been raised by hopes of self-advantage from his confined labours, and self-improvement. It must be obvious to every person of common understanding, that the Flora was conducted on too expensive a plan to have been very lucrative to the author: but it is "Diva pecunia" which must of necessity regulate many of the actions of man kind. The much-esteemed Botanical Magazine is simple in its plan, easy of execution, accommodated to the MANY, and making its way by its neatness and its cheapness, where more costly works would never have been known. Perhaps the cause of Botany, therefore, through the execution of this work, and the example which it gave to its spirited, rapid, and charming follower, ENGLISH BOTANY, has been more effectually promoted, than by any other publication during this century. The very support of the Fl. Lond. was centered to a certain degree in the success of the Magazine, so that the public was a gainer, not a loser, on the whole; and, all the while, the slow pro gress of the Flora enabled the author to give to it that consummate perfection, which nothing but very deliberate progress could accomplish. The flow of emolument from the Botanical Magazine enabled the author to be so deliberate, so accurate, and in consequence so peculiarly instructive, in his Flora Londinensis. In appreciating the merit of the Flora, we should not overlook the general foundation which it has laid for the extenHb 4 sion sion of botanical knowlege and botanical improvement, to the end of time. Let systems vary as they may, the descriptions of the Fl. Lond. must be of prime utility to every one of them. All the parts of the plant are so well described, the characteristic difference of every species is so expressed in every figure, and the minuter parts are so displayed in numerous and magnified dissections, that no system can be invented which will not be aided by them; and no lapse of time can occur, when such truth of nature will not be equally valuable. We lament that Mr. Curtis was led, by bad counsel, to dis◄ continue figuring the Mosses and Lichens, on the idea that Dillenius had anticipated all labours in that department.—Experience teaches us otherwise, and that his figures are too small to supersede the necessity of farther illustration. Close affinities are not easily distinguishable by the Dillenian method of figuring them. In Mr.C.'s work, there is such a bold representation, that the minutest part appears tractable and tangible: no publication, except the costly work but impracticable system of Hedwig, can be said to exceed this, in conveying just notions of the construction of this wonderful tribe of vege tables. The Flora Londinensis will ever remain a monument of the author's taste and singular abilities. Compared with the works of the veteran, Jacquin, we may say, "Vitulâ tu dignus & kic"-Compared with the Flora Danica, we may ask, not without due regret, "Why was not the FLORA LONDINENSIS also honoured with Royal Patronage ?" Good..... ART. XV. A Treatise on Mortal Diseases; containing a particular View of the different Ways in which they lead to Death, and the best Means of preventing them, by Medical Treatment, from proving fatal. Translated from the Latin, by the Author,. Conrad George Ontyd, M. D. 8vo. PP. 643. 98. Boards. Johnson. 1798. TH "HIS volume exhibits the principal facts relating to the causes of death, compiled from various sources, and arranged under different heads. The author forms them into the seven following classes; 1. Death from old age. passions of the mind. either from the abundance or want of caloric. from the electric shock. |