'the Imperial library at Paris, having been deposited there after the wars in Italy, whence they were brought by the victorious army; viz. one from Florence, which appears to have been written in the 12th century; two from St. Mark at Venice; a third and fourth from the Vatican; and a fifth, of the 6th century, which seems to have belonged originally to the French; - besides others of minor importance. It is impossible, in reading these open declarations of usurpation and pillage, not to feel some regret that these venerable buildings have been thus despoiled of such precious relics of their antient learning and magnificence: yet, when we contemplate the use that has been made of them by the French philosophers, and contrast it with the probable obscurity in which they would now have been placed in those abodes of superstitious bigotry, where the Inquisition is again established in all its disgusting forms, our first impressions are converted into a sort of acquiescence if not of approbation, and the crime appears to be expiated by the result which it has produced. The first eight chapters of the first book contain a sort of introduction, or popular view of the Ptolemaic system; in which it is curious to observe the arguments employed by such a rigid geometer, in support of an erroneous hypothesis. Thus, in endeavouring to prove that the earth remains immoveable in the centre of space, he says, But, if the earth had a motion of translation common to other heavy bodies, it would soon, in consequence of its superior mass, precede them in space, and pass beyond even the bounds of the heavens; leaving all the animals and other bodies without any support but air; which are consequences to the last degree ridiculous even in imagination.' In the same place, he adds, Some persons pretend that there is nothing to prevent us from supposing that the heavens remain immovable, while the earth turns on its own axis from west to east ; making this revolution in a day nearly; or that, if the heavens and the earth both turn, it is in a ratio coinciding with the relations which we observe between them. It is true that, as to the stars themselves, and considering only the phanomena of them, there is nothing to prevent us, for the sake of simplicity, from making such a supposition: but these people are not aware how ridiculous their opinion is, when considered with reference to events which take place about us: for, if we concede to them that the lightest bodies, composed of parts the most subtle, are not possessed of levity, which is contrary to nature, or that they move not differently from bodies of a contrary kind, although we daily witness the reverse; or if we concede to them that the most compact and the heaviest bodies possess a rapid and constant motion of their own, while it is well known that they yield only with difficulty to the im`pulses which we give to them; still they would be obliged to acknowlege Ggz knowlege that the earth, by its revolution, would have a motion more rapid than any of those bodies which encompass it, in consequence of the great circuit through which it must pass in so short a period: wherefore such bodies as are not supported on it would always appear to possess a motion contrary to itself; and neither clouds nor any projected bodies, nor birds in flight, could ever appear to move towards the east; since the earth, always preceding them in this direction, would anticipate them in their motion, and every thing, except the earth itself, would constantly appear to be retiring towards the west,' &c. &c. The remaining part of this book is much more interesting, being a specimen of the antient trigonometry, and the method of computing the chords of arcs; which in fact involves our fundamental theorems of trigonometry, though expressed in a manner totally different. Ptolemy first shews how to find the side of a pentagon, decagon, hexagon, square, and equilateral triangle, inscribed in a circle, which he exhibits in parts of which the diameter is divided into 120. He next demonstrates a theorem equivalent to our expression, sin. (a—b) — sin. a. cos. b. sin. b. cos. a., by means of which he finds the chords of the differences of any two arcs of which the chords are known. He next finds the chord of a, that of a being given; he then demonstrates what is equivalent to our formula ́sin. (a + b) sin. a. cos. b. + sin. b. cos. a., and by means of these computes the chords to every half degree of the semicircle-which, according to the report of M. DELAMBRE, who has aken the pains of verifying them, are remarkably correct. In the table of climates, which forms a part of the second book, and which is nearly equivalent to our nonagesimal tables, we are surprized to find no particular table for the climate of Alexandria, such as we have for all the principal observatories in Europe; because, without such an auxiliary, Ptolemy must have contented himself with interpolations, which were not only difficult to make, but attended at the same time with great inaccuracy: a circumstance from which it has been concluded that Ptolemy himself made few calculations, or that he was not very particular about the accuracy of those which he did make. Book III. treats of the length of the year, the motion of the sun, the mean and apparent anomaly, &c. &c. The length of the year, according to the sexagesimal notation, is 365 d. 14′ 48′′, which answers to 365 d. 5 h. 55 m. 12"; the diurnal motion of the sun is stated at o° 59′, 8′′ 17′′" 13" 12′ 31", and the horary motion at 2' 27" 50" 43" 31". This part contains contains two tables, one of the mean motion of the sun, and the other of the solar anomaly. The fourth book is employed in treating of the motion of the moon, being prefaced by a few remarks, respecting the observations of which it is best to make use for this purpose, and recommending the most antient and those which depend on eclipses. In the third chapter, Ptolemy gives a sort of abstract of all the lunar motions, and afterward a table of them; or rather three distinct tables of 45 lines each, disposed in five columns. In the first table, the motion is exhibited for periods. of 18 years; in the second, for years, and then for hours; and in the third for Egyptian months and days. The four other columns present the number of degrees which belong to each of the times indicated in the first column; viz. the second column, the longitude; the third, the anomaly; the fourth, the latitude; and the fifth, the elongation. Book V. treats of various subjects connected with the lunar motion; viz. its general anomaly; its excentricity; the parallax of the moon; the construction of instruments for observing the parallax; the distance of the moon from the earth, which is stated at 38 43' terrestrial radii, when in the quadratures; the apparent diameters of the sun and moon; the distance of the sun from the earth, which is stated at 1210 radii; and, lastly, the relative magnitudes of the sun, moon, and earth, the diameters of which he finds to be in the ratio of 18, 1, and 33, and their masses as 6644, 1 and 391. The remainder of this book is allotted to a table of parallaxes, and the method of determining them both for the sun and the moon. In the sixth book, the author is wholly occupied with the doctrine of eclipses of the sun and the moon; the determination of their limits and duration; tables of conjunctions; and methods of computation and construction. The only observation, which we shall at present make as to the translation, is that it is perhaps too literal, thus becoming uneven, and in some places rather obscure. It is, however, performed with fidelity; and we sincerely hope that M. HALMA will meet with that encouragement which he so well merits, for the great accuracy with which he has completed such a laborious undertaking. ART. II. De l'Esprit de Conquête, &c. ; i. e. On the Spirit of Conquest and Usurpation, viewed in Connection with the present State of Civilization in Europe. By BENJAMIN DE CONSTANT REBECQUE, formerly Member of the Tribunate, but removed from his Seat (eliminé) in 1802; and Correspondent of the Royal Society of Sciences at Gottingen. 8vo. pp. 208. Murray, London. 1814. IT r appears, from a notice in the preface, that this treatise is only a part of an extensive work on politics which was prepared several years ago, but withholden from the public in consequence of the fettered condition of the Continental press. The recent revolution in politics has fortunately removed this formidable obstacle, and put it in the power of every writer to contribute to general utility in the full proportion of his zeal and information. In the opinion, however, of this author, the time is not yet come for the examination of abstract questions on the principles of politics; a consideration which has induced him to narrow the scope of his reasoning, and to confine his present investigations to topics of immediate interest. M. DE CONSTANT is one of the few who aim at great precision in the division and subdivision of their materials, since he has arranged a tract which scarcely exceeds the pamphletsize into thirty-five chapters: of which the first fifteen treat of the Spirit of Conquest, and the latter twenty of its twin-sister, Usurpation. The author takes pains to describe the qualifications under which he comes forwards as the adversary of the war-system, and premises that, so far from considering war as wholly and absolutely pernicious, he admits it to be favourable for the display of our greatest and noblest qualities. In the present state of society, however, war can deserve this eulogium only when founded on justice, and on the cordial co-operation of the people at whose charge it is carried on. Now in these important points modern Europe differs, he says, (p. 6. and 7.) most essentially from the condition of antient Greece and Italy. Instead of petty states living in perpetual jealousy, and almost always at open variance with each other, we have now nations of vast population, united under one sovereign, secured by their numbers against the dread of foreign invasion, and cultivating those habits which cause war to be felt as a severe burden. Productive industry is now the channel for arriving at those possessions which, in the days of antiquity, were accounted the meed of warlike exertion; or, in other words, we endeavour to obtain by an appeal to the interest of our fellowcreatures that which our forefathers demanded by a less gentle course. War,' says the author, is the impression of a savage mind; commerce is the result of civilized calculation.' Among Among the antients, successful hostility produced large addi tions to individual property, in the shape of slaves, tribute, and territory; among the moderns, the spoils of war are almost invariably inferior in value to the results of peaceful industry. The Roman government, in giving a military turn to the spirit of the people, proceeded in concurrence with the leading circumstances of its situation; while a modern government, desiring to imitate the policy of the Roman, would have to encounter the most serious opposition from the condition of its subjects. M. DE C. proceeds to examine, in the same philosophical style, the various relations of his subject, under the heads of Character of a Military Race acting merely from interested Motives; - Influence of such a Military Spirit on the Interior of a State; Tyrannical Measures required to circulate false Impressions; - Various Disadvantages of the Military System as to the Progress of Knowlege;'—and he concludes with what most of our readers will regard as an argument more to the purpose, viz. ' a demonstration that the successes of a conquering people must necessarily be of short duration in the present state of Europe, because they are at variance equally with the happiness of the nation in question and with that of all her neighbours.' Such is, in substance, the first part of the work; and the second discusses, in the same methodical manner, the incompatibility of Usurpation with the present state of society. Here are passed under review the repulsive effects of arbitrary power on our various habits and feelings, our intellectual progress, our social sympathies, and our religious impressions. The inefficacy of despotic measures to support an unjust authority for any length of time is next considered; and the general result is that, whether we look to the usurpation of power at home or to the forcible acquisition of territory abroad, the efforts of the most daring or most able rulers can be successful only for a season. Our readers will easily perceive that this is nothing else than an attempt to reduce to general reasoning the wonderful occurrences of the present day; and to prove that the signal overthrow, which followed the destruction of the usurper's force in Russia, would have sooner or later been effected by the natural operation of less extraordinary causes. The author discovers considerable ingenuity and knowlege of history, together with the talent of conveying his thoughts in that animated strain which is so natural to Frenchmen: but his style is by no means free from those metaphysical effusions which so easily find admittance into the abstract reasonings of our Gallic neigh Gg 4 bours; |