be divided into any other number of equal parts, except those above specified; nor can any regular figure, or polygon, be inscribed in a circle, by any known method purely geometrical, excepting a triangle, square, pentagon, and those figures which arise from thence by continual bisections, or taking their differences.' Has Mr. Keith never heard of the celebrated problem of M. Gauss? who has shewn how a polygon, consisting of any prime number of sides of the form 2m+1, may be geometrically inscribed in a circle; such as 3, 5, 17, 257, &c. We do not find fault with the author for not entering on that subject, in his elementary treatise, but for not apprizing his readers that such a problem existed, and referring them to those works in which its investigation was to be seen; viz. Gaúss, "Disquisitiones Arithmetica ;" Le Gendre," Essai sur la Théorie des Nombres," 2d edition; or Barlow's "Theory of Numbers." We had some farther remarks to make on the author's notes relative to the 5th book on ratios, in which we find much objectionable matter, particularly his note on def. 3. and the illustration which he has attempted of incommensurable quantities: but we cannot admit additional extracts; and we shall therefore conclude this article by observing that the present treatise will be found to contain a great number of notes on the first six books of Euclid's Elements, more conveniently arranged than in the generality of former editions; some of which are ingenious and instructive, but others very defective and erroneous. We are also bound in justice to add that, while we easily trace many of the former to preceding writers, as Playfair, Ingram, Bonnycastle, &c., the latter, at least as far as we can judge, are almost exclusively due to the author of this extended edition of Euclid's Elements." MONTHLY CATALOGUE, FOR JANUARY, 1815. POETRY. Art. 15. A Sketch from Nature. A Rural Poem. Crown 8vo. 3s. 6d. Boards. Gale and Co. 1814. Early risers are most struck with the scenery of nature; and they contemplate it under such peculiar advantages that, if they have any mind, they must feel all its inspiration. Milton has acquainted us with his practice of seeking the fields "ere the high lawns appeared under the opening eyelids of the morn," and with the effect of this habit on his muse. The present writer is also alive to the pleasures of the morning, and advises those who wish to enjoy the beauties of the rural landscape to survey them at sun-rise. His sketches plainly prove that he has availed himself of the practice which he recommends, and that he has regarded nature with a poet's eye. Nominal allusions, he tells us, are omitted: but his descriptions evidently are local; and, from the mention of the Severn and a great commercial city, we conclude that these poetic drawings were taken in the vicinity of Bristol. We have no doubt of the fidelity of the delineations; which, though not remarkably striking, are in general pleasing. One or two natural touches, and the pious complexion of the whole, remind us of Cowper. The most novel sketch is the description of the influx of the tide into the Severn, which we select as a sample of the poetry : Now wakes the vernal gale; and, as it sounds In various cadence through yon stately grove, That turns the course of Severn's rapid stream, 'Tis heard ;-then dies away:-but, as it gains Till, bursting into view, the thund'ring Tide, At the end, some additional notes are given: but, as they consist merely of texts of Scripture, they might have been omitted, and references made to chapters and verses at the bottom of the page. * The peculiarities in this description of the Tide apply almost, exclusively to its progress up the river Severn.' REV. JAN. 1815. H Art. Art. 16. The Battle of Vittoria. By an Officer. Crown 8vo. 1S. Hatchard. A soldier, who unites to the heroism of his profession the enthusiasm of poetry, could not use his sword in the splendid action at Vittoria without afterward employing his pen towards the celebration of the memorable victory gained on that day, On such an occasion, a little vanity is excusable, and we must allow this officer the following poetical egotism: O Wellington! this arm hath sway'd In the former part of this little poem, each peasant is represented as leaving his plough, each shepherd his flock, and each lover his maid, to unite in repelling the cruel invader: but, had this been the case, such vast sacrifices of blood and treasure on the part of Great Britain would not have been necessary to drive the French out of Spain. At Vittoria, as in all the previous conflicts, the day was won by British skill and valour; and our military history receives everlasting renown from the late Peninsular war.-We cannot place this officer in the first rank of poets: but he sketches his battle-piece with some spirit, and presents (we should suppose) a faithful picture of the bloody Scene: • Zadora's stream roll'd clear and bright Standards and arms reflected gave ; But not more quick the mists which rose Than that proud host was swept away. Now And, dreaded more than loss of crown "Stand, Frenchmen, stand; let yonder sun Or gild, as he goes down to rest, Their blood the plunging points shall steep, And Gallic wives the contest weep,' Poor King Joseph makes a miserable figure on the canvas, for on this day he lost his crown, his treasure, and his credit, and narrowly escaped with his life. Art. 17. Poems by Frederick Thornhill, Esq. Crown 8vo. 5s. Young poets are always in love, and one smile from the fair compensates for a thousand frowns from critics: but then it is only while the lady is smiling that they are thus contented. At other times, vanity comes in full play, and they sigh for a little of what is called Fame. This consideration accounts for the publication of their amatory effusions, and for their collecting into printed volumes the scraps and morsels of their Muse. Mr. Thornhill begins with thus addressing Rosa, Oh! what's the critic's wrath to me?' but, if the critics were to inform Rosa that his lines were too bad for her to tolerate, he would find their decision operate to his disadvantage. We would only hint to him that the critic's wrath is not so much to be despised as he supposes, and that his mistress will judge of his abilities, as a poet we mean, by the public verdict. Luckily for him, we are not disposed to make mischief between him and his Rosas, Stellas, and Julias; since, though his amatory effusions may be too glowing for our vale of years, his lively fancy, his easy versification, and his activity in turning every incident which occurs to what may be styled a poetical account, plead so much in his favour that we will not put on our magnifying spectacles to look for little defects. We shall only H 2 observe observe that his love-effusions are rather too monotonous; and that, if Rosa, Stella, and Julia, are never tired of hearing how ardently he adores them, the reader is not much gratified nor delighted by the frequent repetition of the same thought. We copy one or two samples. DIAN'S SEAL. • Oh Stella! lovely in thy tears, Oh Stella! Stella! come, my dear, • JULIA. Oh! what's the nectar Bacchus sips And, oh! for me she slacks her zone, |