as those on indeterminate problems and transpositions. Five. copies of the text have been examined and compared by the translator: they agree more exactly than is usual in distinct editions of a manuscript: but the preference has been given to a copy written in Guzerat during the year 1673, on account of its containing several kshepaka, or interpolated rules, not recorded in the others. Something of expansion has been indulged in the translation, in order to render intelligible the rules that are delivered very elliptically: but all inserted words are noted in italics. Dr. T. observes that the Arabians call the decimal scale of arithmetic, Hindasi, or Indian arithmetic, which indicates their opinion of the source of this numeral notation. Several hundred years have elapsed since this manner of reckoning was adopted by the Arabians, and introduced among the nations of Europe: but neither in Europe nor in Arabia has it yet altogether superseded the use of alphabetical characters to express numbers. Both Europeans and Arabians still occasionally employ letters for this purpose; and among the latter people it is considered as elegant, in noticing an event, to employ a word of which the literal powers shall point out the date of its occurrence: 6 but,' continues Dr. Taylor, 'I never met with any Hindoo, who was aware of this use of letters, except through Mahomedan intercourse: nor did I ever observe any thing like it in Sanscrit works, or in any books written in the colloquial dialects of Hindostan.' His inference is that the Hindoos invented the decimal notation of numbers, and have thus been the parents of all arithmetical science to the modern world; and certainly an inspection of the work itself strongly corroborates the opinion that it was written in the infancy of arithmetical practice, and preserves many round-about processes which subsequent experience has abbreviated among the nations of the West. Thus, addition is directed to be performed by beginning at the left-hand column, and, the sum being put down, the figure is changed according to the excess of the next column; and thus two or three figures must often be noted, obliterated, and replaced in the same situation: but, by the newer method of beginning with the right-hand column, the sum is ascertained at the first intention. In subtraction, the less number is ordered to be placed above the greater; when a greater figure is to be taken from a less, ten must be borrowed on the next minuend figure; and, the subtrahend figure being then subtracted from the ten, the remainder is added to the figure in the minuend. Thus, to subtract nine from seventeen, their process is this: take nine from ten, one remains, which, 13 added added to seven, makes eight. Of multiplication, five methods are given; and these throw great light on the manner in which processes were gradually contrived that are now simplified, neat, and familiar. No multiplication-table occurs: but some ingenious rules, which display curious properties of number, are given such as the following method of proving or verifying a multiplication. Multiply one of the factors by ten, and also by the number by which ten differs from the other factor; and subtract the one product from the other. -Division is very complex, and exhibits all the parallel lines of a Chinese abacus. Rules also occur for extracting square and cube roots. What we call the rule of three is named by them the rule of proportion. They have also a rule of errors, which may be termed the algebra of arithmetic, and which teaches to find an unknown quantity by assuming first an excessive and then a deficient answer, and returning to that approximation which gave the least absurd result. Algebra is Arabic for inversion; and the Hindoos call by the name of inversion the algebraic process. There is a sexagesimal numeration, in which letters of the alphabet serve for figures, which the Hindoos and Arabians employ in such astronomical calculations as require immense numbers. The signs called plus, minus, into, by, equal, are not in use, but the corresponding prepositions are employed as words. In the list of numerals, the earth, or moon, signifies one; the eyes, two; the yug, or creation, three; and the Vedas, or gospels, four so that the Hindoos seem to have had their religion before they had their arithmetic. Kshetra, which signifies a holy precinct, is the word for any geometrical figure. The mathematical sciences are declining in estimation among the Hindoos, according to Dr. Taylor. In Poona, which is a distinguished seat and asylum of Braminism, not more than ten or twelve persons understand the Lilawati, or the Bija-Gannita: but this arises, we presume, from their preference of the European methods of reckoning, which, for practical purposes, may best be acquired in the counting-room. Prayers and invocations, and pious texts of the Hindoo scriptures, introduce the several chapters. Many of the questions illustrate local practices, and some are ludicrously imagined: e. g. A girl sixteen years old is purchased for thirtytwo nishas: what will a girl of twenty years old cost? -A pond is filled by one stream in one day, by a second in half a day, by a third in one third of a day, and by a fourth in a quarter of a day in what time will it be filled by the four at once? In Montucla's History of the Mathematics, this very question is ascribed to Diophantus, and thus given, as versified by Bachet: "Totum implere lacum, tubulis e quatuor, uno Est potis iste die, binis hic, at tribus ille, Quatuor at quartus: dic, quo spatio simul omnes." Questions in dialling abound, and an appendix describes the method of teaching arithmetic in Hindoo schools: it is the Madras system of Dr. Bell. The general result of an attentive perusal of this volume has been to persuade us, that the sciences are less antiently domesticated in Hindostan than Sir William Jones was disposed to assert. After all, were not figures invented at Alexandria, and are not the nine digits obvious imitations of the letters in the Greek alphabet? ART. IV. Memoirs of the Embassy of the Marshal de Bassompierre to the Court of England, in 1626. Translated; with Notes." 8vo. pp. 150. 98. 6d. Boards. Murray. 1819. F ROM very unpromising materials, the Editor of this hasty diary has elaborated a curious and amusing work. He modestly disclaims all the honours of authorship, and satisfies himself with the humble pretensions of a mere editor, but he is intitled to much higher praise: for, in point of fact, he has thrown so rich and abundant an embroidery over the original fabric, as almost to conceal the meagreness of its texture, and to bestow on it a value of which it is intrinsically destitute. Francis de Bestein, or Bassompierre, was born of a noble family in Alsace, in 1579: he was sent into Germany and Italy, and, to complete his travels, arrived at Paris. He was one of fortune's favourites in person, in accomplishments, and in prosperity; unless a dozen years of imprisonment in the Bastille should be deemed by some very fastidious and sensitive personages a draw-back on the latter. To the qualifications of a diplomatist, sagacity in penetrating the secrets of others, and caution in disclosing his own, he united all the gallantry of a perfect courtier; and the gay Grammont himself could scarcely enjoy more numerous or more brilliant successes among the Nymphs and Graces of "fair Venus' train," than the Marshal de Bassompierre. "Ruris huic erant puellæ, Et puellæ fontium, Quæque sylvas, quæque lucos, On the day before he went to the Bastille, he burned more than six thousand love-letters, with which different ladies had been, from from time to time, so good as to honour him. A few days after his arrival in France, a ballet was performed before Henry IV. in gratulation of his convalescence. When the ballet was over, young Bassompierre was introduced to the King, and by him to the Belle Gabrielle," Duchess of Beaufort, the hem of whose garment he at first kissed; but the gallant Henry walked aside, to afford the young cavalier an opportunity, as he tells us, of kissing her in earnest.' Henry and Bassompierre were captivated with each other, and the latter passed . his life in the service of France; in which he obtained, besides the King's orders of knighthood, public embassies, and other minor favours, the great military offices of Colonel-general of the Swiss, and Marshal of France. By Louis XIII. he was respected, employed, and advanced; by Mary of Medicis he was honoured with a confidence and esteem that were softened, perhaps, says the Editor, by the difference of sexes; and Richelieu paid him the still higher compliment of fearing and persecuting him. It was on the recovery of Richelieu's influence that Bassompierre was immured in the Bastille, from the fifty-second to the sixty-fourth year of his age; and he was at last released only by the death of his persecutor. We have heard the story of a prisoner, who, after a long confinement in that prison, one day took the liberty of asking his gaoler why he was kept there; on which the latter turned round with admirable sang froid, and exclaimed, "Upon my word, Sir, you have a great deal of curiosity." Bassompierre says that he passed twelve years in a dungeon, because he had not kept an engagement to dinner with the Cardinal. The story is rather too long to be told: but the Marshal's attachment to the Queen-mother, Mary of Medicis, and his suspected intrigues against the haughty priest, would account for his imprisonment, even if he had not broken his engagement. Yet it might appear that the parties had lived on very friendly terms: for, as the Marshal did not possess the attribute of ubiquity, and could not possibly reside in his villa at Chaillot (a beautiful spot, on which, it seems, he had employed all his taste and magnificence,) while he was shut up in the Bastille, the Cardinal would, every now and then, ask permission of his victim to enjoy the use of Chaillot, its luxurious couches, and costly furniture. On his release after Richelieu's death, Bassompierre was offered and refused the honourable, but perhaps perilous, trust of being governor to the young king, Louis XIV.* He died of an apoplexy at the house of * If Bassompierre shed tears of joy at the death of Richelieu, tears of sorrow likewise flowed on that occasion: as we learn from of his friend, the Duke of Vitry, in Champaigne, April 12. 1646. He wrote his memoirs to beguile the weary hours of imprisonment: but hope and fear, says his editor, forbad him to give them frankly; and the wittiest man of his time has left behind him half-a-dozen of the dullest, or at least the driest, of all volumes. They are the work of a gazetteer, rather than of a man of the world; facts and dates are preserved, but motives and characters are lost. So much for the Ambassador. As to the mission itself, the object was a remonstrance from the court of France to that of England for the fulfilment of a treaty, the details of which most historians consider as never intended to be carried into execution. James I. entertained an opinion that any alliance below that of a great monarch would be unworthy of a Prince of Wales, and accordingly he would not allow any princess but a daughter of France or Spain to be mentioned for his son Charles; both which courts took advantage of his imprudence or his pride. Charles was first betrothed to the Infanta, James acceding to such concessions in favour of the Catholics as gave the greatest alarm and offence to his Protestant subjects. This negotiation fruitlessly lingered through seven long years; when, by the influence of Buckingham, it was broken off, and was succeeded by an overture to Louis XIII. for a marriage between his sister, Henrietta Maria, and the Prince of Wales. The conferences began a few days after the King of England, in consequence of the termination of the Spanish match, and in conformity with his promises to Parliament, had put into execution with renewed severity the laws against Popish recusants, and had actually imprisoned several priests and friars. The Catholics complained of their sufferings; the treaty went on, the concessions in their favour which had been granted to Spain serving for its foundation; and the marriage was ultimately celebrated, although not till after the decease of James. In looking to the terms of this treaty, we cannot but be perfectly astonished that any monarch, Protestant or Catholic, should have submitted to the humiliation of allowing a foreign potentate such a direct interference with the laws of his realm; and, if he could so debase himself, that an epitaph on him by Isaac de Benserade, to whom he had allowed. a pension of 600 livres during his life. "Cy git, oui, cy git, morbleu, Le Cardinal de Richelieu; Et, ce qui cause mon ennui, Benserade's sorrow was very sincere, no doubt. the |