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each set may be returned to the Publishers, free of expence, and that Gentlemen who have been supplied with the work from their own Booksellers, will apply for the Index through the same medium.

During the course of the summer will be published a complete refutation of Mr. D'Oyley's Remarks on Sir W. Drummond's Edipus Judaicus, by Vindex.

Speedily with be published, in one volume octavo, Select Remains of the late Rev. James Bowden, of Tooting, Surrey: comprising an Annual Review of his Life and Ministry, Family Legacy, Sermons, and Letters. Edited by the Rev. R. Bowden, of Holloway. To whom Subscribers are requested to send their names, or to Mr. Conder, Bucklersbury.

On the 1st of September, will be published, part the 1st, of a new History of England; to be completed in three parts, forming a handsome quarto volume, illustrated by forty copper-plates of Fengraved Symbols, designed as an Assistant to the young Student in History.

By Mary Ann Rundali, of Percy House, Bath, Author of the Grammar of Sacred History.

Dr. Watts no Socinian: a refutation of Dr. Lardner's Testimony concerning his supposed Manuscripts, as produced in Mr. Belsham's Memoirs of Mr. Lindsey, that Dr. Watts' last Sentiments were completely Unitarian. By Samuel Palmer.

The Rev. Dr. M'Leod, of New York, is preparing for publication in one large elegant octavo volume, price two dollars and fifty cents, in boards, Lectures upon the principle Prophecy of the Revelation. In this work connection of the prophecies of Daniel with the book of Revelation the author proposes to give an outline of the History of the moral world in the order and within the period contemplated in those inspired writings. He will endeavour faithfully to apply the fact to the prediction and make true religion the meridian line to which the several parts of the crowded map are referred.



The History and Antiquities of Hinckley, in the county of Leicester; including the Hamlets of Dadlington, Stoke, Wykin, and the Hyde. The second edition, embellished with twenty-two folio plates. To which is added, the History of Witherley, in the same County, and a large extract of the Manduessedum Romanorum; being the History and Antiquities of Manceter, [including the Hamlets of Hartshill, Oldbury, and Atherstone;] and also of the adjacent Parish of Ansley, in the county of Warwick; by the late Benjamin Bartlett, Esq. F. S. A. with additions. IIlustrated by seventeen folio plates. By John Nichols, F. S. A. London, Edinburgh, and Perth. Of this Edition no more than fifty copies are printed, folio. Price 21. 2s.

The History and Antiquities of Hawsted, and Hardwick, in the County of Suffolk. By the Rev. Sir John Cullum, Bart. F. R. S. and F. S. A. The secoud edition, with Corrections by the author, and Notes by his brother, Sir Thomas

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LL. D. F. R. S. F. S. A. &c. late President of the Royal Academy. By James Northcose, Esq. R. A. Comprising Original Anecdotes of Dr. Johnson, Goldsmith, Burke, Garrick, and many other distinguished Characters. 4to. price 21. 12s. 6d. bds.


E. Gregorii Nazianzeni Carminibus et Orationibus Excerpta quædam curâ H. S. Boyd, sm. 8vo.

Prælectiones Academicæ Oxonii Habitæ ab Edvardo Coppleston, 8vo. price 15s.


The Nature and Objects of Educatiou explained, with Mr. B. H. Smart's Prospectus and Terms, price 1s.

A Hebrew Grammar, in the English Language, together with the whole Book of Psalms. By Joseph Samuel C. F. Frey, Editor of Vander Hoogh's Hebrew Bible. Price 10s. 6d. cxtra bds.


The third Part, containing two views in the Island of Madeira, and one in the Island of St. Helena, with descriptive Accounts, in English and in French, of a Series of Views of Picturesque and Romantic Scenery. By William Westall, price 10s. 6d. Proofs 15s.


A Sketch of the History of the EastIndia Company, from its first Forma. tion to the Passing of the Regulating Act of 1773; with a Summary View of the Changes which have taken Place since that Period in the Internal Administration of British India. By Robert Grant, Esq. Royal 8vo. price 15s. boards.


A Practical Treatise of the Law of Marriage, and other family Settlements. By Edward Gibson Atherley, Esq. royal 8vo. 11. 4s. bds.

A Treatise on the Law of Slander, Libel, Scandalum Magnatum, and False Rumours. By Thomas Starkie, Esq. Barrister at Law, 8vo. price 18s. bds.

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The Laws relating to the Clergy, includng the latest statutes and judicial de

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The Pamphleteer, No. II. price 6s. 6d.

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Tales of Real Life.-By Mrs. Opie. In 3 vols. 12mo. 18s bds.

Correspondence of the late Gilbert Wakefield, B. A. with the late Right Hon. Charles James Fox, in the Years. 1796-1801, chiefly on Subjects of Classical Literature, 8vo. price 9s. bds.

Margate; or, Sketches amply descriptive of that celebrated Place of Resort, with its environs, and calculated to inculcate in the Mind of Youth a Fondness for the Productions of Nature and Art. By Mrs. Pilkington, 12mo. price 5s. bd.

With Engravings. A description of an Improved Method of Delineating Estates, in which the Advantages of Mathematical Accuracy are combined with the Beauties of Landscape Painting representing not only the Estate itself, but also the adjacent Country, in Panoramic Perspective. To which are added, Opinions on Landscape Gardening and Rural Ornament, By T. Hornor, 8vo. price 7s. 6d. bds.

Critical Observations on Books An. cient and Modern, this Work is published occasionally, and will be complet ed in about four more Numbers, No. XVI. price 2s. 6d. sewed.

Reflections on Suicide. By Mad. de Stael, Baroness of Holstein. Translated from the French, 12mo. price 5s.

A Letter to the Hon, the East-India Company, in Reply to the Statements of Charles Buller, Esq. M. P. concerning the Idol Jaggernaut. By the Rev. Claud Buchanan, Extracted from the printed Minutes of the House of Commons, 8vo. price 1s.


The Russian Chiefs, an Ode. 4to. price 5s.

A New Translation (in Rhyme) of Ovid's Metamorphoses, with the Latin Text. By Thomas Orger. 1st vol. price 10s.

The Wanderings of Woe. With an appendix interesting to the Clergy. By the Rev. J. Cox, 8vo. price 5s.

The Year, a Poem. By the Rev. J. B.dlake, 8vo. price 10s. 6d.


A Theological Disquisition on the characteristic Excellencies of Christianity; or, an Inquiry into the Superior Assistance it affords, and Motives it contains for the practice of virtue, cultivation of the best affections of the Heart, and preparing the moral Offsping of God for permanent felicity. By T. Cogan, M. D. 8vo. 12s 6d. bds.

The Genuine Influence of Scripture Principles in Life and Death. A Sermon, preached at Silver-street Chapel, Whitby, on Sunday, March 21, 1813, occasioned by the lamented death of the Rev. Edward Williams, D.D. By John Arundell, 8vo. 1s. 6d.

Lent Sermons, or an Inquiry into the nature and design of Christ's Temptation in the Wilderness. 8vo. 5s, bds.

An Essay on the Equity Divine Government and the Sovereignty of Divine Grace. By Edward Williams, D.D. 8vo. 12s. bds.

A Sermon preached by order of the Hon. Court of Directors of the affairs of the East India Company of England, September 6th, 1807, on the opening of a Monument set up in St. Mary's Church, Fort St. George, to commemorate the the virtues and services of the late Rev. C. F. Swartz. By R. H. Kerr, D.D. Senior Chaplain of Fort St. George. Price 2s. 6d.


sleep of the Soul, and the resurrection of the Body; bieng an attempt to prove that the resurrection commences death. 8vo. 1s. 6d By John Platts. Sermons on the Duties of Children, as set forth in the Catechism of the Church of England. By a Lady. 12mo. 2s. 6d, bds.

The Doctrine of New Jerusalem, respecting the Lord. Translated from the Latin Amsterdam, 1763. Royal, price 12s. Demy 6s.


A New Edition, with several Additions and a map, of a Tour in Teesdale, including Rokeby and its Environs. 18mo, Ss. bds.

A Chronological History of the Voyages and Discoveries in the SouthSea, or Pacific Ocean. The present volume comprises the pericd from 1620 to 1688. By James Burney, C.R. N. Part 3, 4to. 21. 2s. bls.

A Journey through Albania, and other Provinces of Turkey in Europe and Asia, to Constantinople. By J. C. Hobhouse. Illustrated by Views of Athens, Constantinople, and various other Plates, Maps, &c. 4to. 11. 5s. boards.

Travels through Norway and Lapland, in the years 1806-7. By Leopold Van Buch, Member of the Royal Academy of Sciences at Berlin. Translated from the German by John Black, with Notes, and a life of the Author, by Professor Jameson. 4to. bds. Illustrated by

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Articles on Montgomery's World before the Flood, Saumarez's Oration, Steinkopff's Tour, and Berzelius on Animal Chemistry, are unavoidably postponed to our next Number.




Art. I. An Elementary Treatise on the Geometrical and Algebraical Investigation of Maxima and Minima, being the Substance of a Course of Lectures delivered conformably to the Will of Lady Sadler To which is added a Selection of Propositions deducible from Euclid's Elements. By D. Creswell, A. M. Fellow of Trinity College, Cambridge. 8vo. pp. iv. 339. Price 10s. Deighton, Cambridge. Longman and Co. 1813.


MR. Creswell is a writer of whom we have already had occasion to speak so favourably, that we are happy to meet him once more on mathematical ground. Our approbation of his present performance, however, is by no means unqualified. It would have pleased us better if at least one-third had been omitted and we think that much more satisfactory reasons ought to have been assigned for publishing it at all, than any that Mr. Creswell has formally adduced. It is,' he informs us ' a part of the plan of his work, to invite a comparison between Geometry and Algebra,' especially by tracing their respective tendency to produce those collateral effects which have been ascribed to the mathematics considered as a discipline of the mind.' He gives the preference very decidedly to the geometrical method, and among his reasons for this preference are the following:

1. There exists, in the first place, this manifest distinction between a synthetic and an analytic process, that, in order to compre hend the former, the whole chain of reasoning must be kept in view, as it is continued from the beginning of the proposition to the end: whilst, in pursuing the latter method, the attention is fixed only upon each single step, as each of them successively offers itself; and the conclusion is to be admitted independently of all but the last of them, whenever it is to be arrived at.'

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2. Even when the same method is used in both, geometry afford a better exercise for the mental powers than algebra. Pure geo. VOL. X.


metry, is a'ways precise and logical; it carries on its demonstrations by the exact comparison of ideas, adhering to the constant use of terms, the meanings of which are always verified by a reference to precise definitions. Its reasonings proceed by means of syllogisms, in which, for the sake of brevity, the minor proposition is suppressed. But even in the demonstration of those theorems in algebra, in which little depends upon the employment of its peculiar symbols, the reasoning is seldom close and exact.'

3. The absurdities which have been published with a view of explaining the rule for algebraic multiplication; the common method of shewing that the numerator and denominator of a fraction in its lowest terins are measures of the numerator and denominator respectively of every other equal fraction, &c.;-the defects in the demonstration of the binomial theorem; and many more examples might be adduced in support of the assertion made above. Nay, it is well known that some propositions of the greatest importance i Algebra have never yet received a satisfactory proof: and although mere metaphysical objections ought not to stop the progress of any science, it is time that these faults were remedied.'

4 When a question is proposed in order to be answered algebraically, the greatest exertion of intellect which is called for, is usually the mere translation of the conditions into a language, the peculiarity of which is, that it is so concise as to exhibit several propos.tions in a small compass this having once been effected, and it is seldom dif ficult to perform, the attention is then withdrawn from the things signified and confined to the signs?


5. Algebra is doubtless the more powerful and convenient instrument for use. "Idem omnino mihi (says Euler) cum Newtoni Principia et Hermanni Phoronomia perlustare cœpissem, usu venit, ut quamvis plurium problematum solutiones satis percepisse mihi viderer, tamen parum tantum discrepantia problemata resolvere non potuerim." But the same causes which give analytics their superiority in that respect, prevent them from being so valuable considered as a mental discipline. The great praise, it may be further remarked, which has been bestowed upon mathematics as conducing to strengthen the mind, has proceeded from men, who lived when geometry constituted the principal part of them: and those who have lately denied them this merit, seem to have been biassed in their estimate by a partiality for extended analytics.'

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6. If the view which has here been taken of this subject be just, it should seem to be no disservice to our established system of education to afford scope for the efforts of our junior students in an easy extension of what they learn from Euclid. It is impossible for them to enter upon a more fertile field than that of geometry, which really seems to admit of the exercise of as much genius and invention as poetry itself: and after having thus strengthened their faculties, they will proceed with better success, to the remaining part of their academical course.'

Now, in our judgement, the view of the matter taken by Mr. Creswell in these passages, is extremely partial and defective.

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