cube-root of any number less than fixteen thousand millions may be readily extracted. In short, M. Joncourt is the firft that has fhewn the practical use of these artificial numbers, and taken the pains to calculate tables for that purpose; and therefore his work cannot fail of being agreeable to those who are pleased with feeing fpeculations. reduced to practice. We mention the practical ufe, because the doctrine of figurate numbers, (fo called from their being capable of reprefenting certain geometrical figures, by a particular difpofition of their units) is a part of the ancient Pythagorean fpeculations on numbers and geometrical figures; from a comparison of which, they pretended to discover many myfteries and fecrets of nature. But fuch pretences have been long fince exploded, and the connections and properties of these numbers confidered as a subject purely arithmetical; tho' they ftill retain their ancient names. They are all no other than the fums of different feries of numbers in arithmetical progreffion; and are diftinguished by the common difference in the feries. Thus, if the common difference in the rank of progreffionals, whence they proceed, or whose fums they are, be an unit, as 1, 2, 3, 4, 5, &c. the fums 1, 3, 6, 10, 15, &c. are called triangles, or trigonal numbers. If the difference be 2, as 1, 3, 5, 7, 9, &c. the fums 1, 4, 9, 16, 25, &c. are called quadrangles, and particularly fquares. If the difference be 3, as I, 4, 7, 10, 13; &c. the fums, as 1, 5, 12, 22, 35, &c. are called pentagons, or pentagonal numbers; and so on. But it is not incumbent on us to purfue this fubject any farther; those who are defirous of feeing the doctrine fully explained, may confult Malcolm's New Syftem of Arithmetic, book V. page 396, where the connections and properties of thefe numbers are difplayed in a masterly manner. B. We are obliged to Mr. Joncourt for the compliment paid us, in dedicating his work to the Monthly Reviewers: but we wifh he had called in to his affiftance, fome friend better acquainted with the English language, which few foreigners write with any tolerable degree of elegance. De Dea Libertate ejufque cultu apud Romanos et de Libertinorum Pileo A Dissertation on the Goddefs Liberty, and the Worship paid her 3/ her among the Romans; as alfo on the Cap worn by the Freed-men of ancient Rome. TH HIS is a very learned and ingenious enquiry, worthy of the elegant pen of the Abbé Venuti, its Author. As the fubjects of it, however, may be thought rather curious than important, by the generality of our Readers, we beg leave to refer the Antiquarian to the treatise itself. K-n-k Memoire fur l'Ufage Economique du Digefteur de Papin, &c. A Clermont-Ferrand. Or, An Effay on the Economical Ufe of Papin's Digeftor. THI HIS is an account of an attempt to improve on this wellknown machine; and, by making it cheap and commodious, to apply it to culinary ufes. Mr. de Ballinvilliers, Intendant of Auvergne, hath occafioned many experiments of its utility to be made, in reducing the bones of animals into foup; which being rendered portable by evaporation, he thinks may be of public benefit to mankind, if diftributed, in times of fearcity, among the poor. Eclairciffement fur les Mours, par l'Auteur des Moeurs. 12mo. Amfterdam, 1762. Or, An Illuftration of the Work intitled Manners. By the Author. MR. Touffaint, the celebrated Author of Les Mœurs, apologizes, in the prefent performance, for fome exceptionable paffages in that work; declaring, in the moft pofitive terms, that whatever conftruction may have been put on fome unguard ed expreffions in his book, he looks upon the imputation of Deifm as the groffeft calumny; and that he then was, and now is, perfectly orthodox in his fentiments of Chriftianity. The publication of this apology, will probably be deemed much too late, to prevent the ill effects of the premature and inconfiderate fallies of his youthful genius. He endeavours to justify himself, however, in this delay; and, if his plea be not very folid, it is, at leaft, fpecious. K-n-k MONTHLY MONTHLY CATALOGUE, For MARCH, 1763. RELIGIOUS and CONTROVERSIAL. Art. 1. The Works of the Reverend Thomas Jones, M. A. late Chaplain of St. Saviour, Southwark. To which is prefixed, a hort Account of his Life, in a recommendatory Preface. By the Rev. William Romaine, M. A. Lecturer of St. Dunstan's in the Weft. 8vo. 4s. fewed. Dilly. Republication of Mr. Jones's fingle Sermons, first published in A his life time. fs to the subjects of them, they are thus fet forth by the Editor."Some of the leading points, fays he, are thesethe univerfal corruption of mankind by the Fall, their guilt, mifery, and helplefinefs;-the gracious method contrived by the Eternal Three of bringing many fons unto glory by Jefus Christ;-the office of the Holy Spirit in the covenant of grace," &c. &c. The character of Mr. Jones and his writings being fufficiently known, efpecially among the Hutchinfonians, Methodists, and other enthufiaftic fectaries, it were needless to enlarge on them here. Mr. Romaine, however, for the edification of the Brethren and Sifters about Moorfields and Tottenham-Court, has copiously dwelt on the pious excellencies, and rare gifts of his departed friend: for they were congenial fouls, and a long and intimate acquaintance had fubfifted between them. As to what related to God's dealings with Mr. Jones's foul,—our Editor had given an account in his Funeral Sermon; and as to other particu lars of his life, it is of no confequence, fays he, to lay the.n before the public: and truly we are quite of Mr. Romaine's opinion. Neverthelefs, we must acknowlege, that, according to the best accounts we have heard concerning the late Chaplain of St Saviour's, he was one of the least exceptionable, the leaft fanatical, of all our modern Pretenders to apostleship. He was probably fincere in his way. Tho' deluded himfelf, he was, perhaps, not confcious of the delusion; and might have no intention to mislead others. His piety we fuppofe unquestionable; and from Mr. Romaine's account we learn, that Mr. Jones died in perfect peace of mind, and in a manner becoming the Christian character. In a word, Charity bids us hope, that all our Mob-leaders are not Impoftors; tho' there is great reafon to conclude, that few of them a diftinguished by that fimplicity of manners, and integrity of mind, which characterised the Author of thefe Discourses. Art. 2. Evangelical Principles and Practice: Being Fourteen Ser- Jonal fonal Holiness-the Means of Holiness-the Bleffedness of Righ teoufnefs. By the Rev. Thomas Haweis, of St. Mary Magdalen-Hall, Oxford; and Chaplain to the Right Hon. the Earl of Peterborow. 8vo. 5s. Keith, &c. Thefe Difcourfes are fent into the world, we are told in the preface, to obviate the manifold mifconceptions and mifreprefentations which the Author of them has lain under. He profeffes himself to be confcientioufly attached to the Articles and Homilies of the Church of England, which he calls her only authentic Standard of Doctrine; and as by the royal Declaration prefixed to the Articles he is forbidden, fo he prefumes not, [good man!] to take them in any fenfe but that which a literal and grammatical construction of them imports; and knows no authority by which any Minifter of the Church of England can indulge himself in a greater latitude of interpretation.-Subfcriptions, he thinks, bring the foul under the deepest obligations to fincerity before the great Searcher of hearts, who requireth truth in the inward ports, and he looks upon those, who in any degree allow themselves to trifle or prevaricate with them, to be men devoid of confcience towards God, and of honefty towards man. -That the Reader may have fome general notion beforehand of what he is to expect from thefe Difcourfes, the Author, in his preface, gives the following abftract of them. "The Divinity of the Son and Spirit, fays he, co-eternal and coequal with the Father, not the idol-monster of inferior divinity, is here maintained, in full oppofition to the Arian and Semi-Arian: whofe blafphemy, though more fpecious, is not lefs real than the more avowed and open blafphemy of the Socinian. The Maintainers of the doctrine of the rectitude of human nature, and the freedom of man's choice to good as to evil, will find thefe proud imaginations attacked, he hopes laid low to the ground, even in the dust, by the word of the Spirit, which is the word of God. The strong evidences of a fallen and corrupted nature, with its dire effects, are produced and confirmed; and the inability of man in his fallen ftate to any thing but evil, clearly, he trufts, made manifeft, "The extent, parity, and fpirituality of God's law are laid open, that the confcience may discover and feel its tranfgreffions against it. The eternal obligation of this law is fhewn; its awful fanctions declared; the impoffibility of obeying it as a covenant of life evinced; and confequently the conviction of our state, as a state of helpless guilt, evidenced. "The one great glorious and all-fufficient oblation of the Son of God for the fins of the world, as a true and real facrifice, atonement and propitiation, is pleaded for; its neceffity and influence proved; and the various bleflings for finners thereby fet forth. Faith, as the only means of juftification and acceptance with God, is urged, from confiderations demonftrating the impoffibility of righteoufnefs before God any other way. And as works of any fort are not admitted as the condition of our pardon and acceptance with God, the pofition that we are juftified by Faith only, is maintained and vindicated. "The works of piety and virtue which become men profeffing godliness, are at large opened, and the neceflity of them enforced, from the only true true principle of Faith which worketh by Love. The Antinomian blafphemy is rebuked and cenfured. "Finally, the means of Grace are ftrongly urged, and the diligent ufe of them fhewn to be the only method of obtaining advancement in the divine life. "The bleffednefs of the religion of Jefus concludes the whole, as the natural refult of the principles and practices above recommended." This abftract, which the Author himself has given of his Difcourfes, faves us the difagreeable talk of characterising them. R Art. 3. A Letter to the Right Reverend the Lord Bishop of Glocefter. Occafioned by his Tract* on the Office and Operation of the Holy Spirit. By John Wefley, M. A. late Fellow of Lincoln College, Oxford. 12mo. Is. Flexney. Mr. Wefley has answered the Bishop's book with all that art, address, and fpecious appearance of primitive integrity, decency, and dove-like innocence, which must be naturally expected by fuch as are acquainted with the character of a man who is fo much matter of his own, as well as of other men's, paffions. His tract is, indeed, a notable one; he ftands his ground manfully, repels the learned Bishop's attacks with fuch we had almost faid-Jefuitical evafions, and fhelters himself fo fnugly under the authority of the Scriptures, and of the Church of England, (which he well knows how to twilt and turn to his purpose) that we doubt not this performance will fully answer the great end of preventing his dignified Antagonist from enticing the sheep out of his fold. *See Review for November and December 1. ft. Art. 4. An Effay on the Revelation of the Apostle John. In which a new Explication is given of fame Paffages in that Book, and applied to the Circumftances of the prefent Times. By Lauchlan Taylor, A. M. Minifter of Larbert. 8vo. 2s. 6d. Millar. This learned Gentleman has, after infinite labour and study, difcovered, that the book of Revelations afcribed to St. John, " contains in it all the grand revolutions of the Chriftian church, from the Apoftle's time to the prefent, and from this time to the end of the world ;" alfo, among other new and amazing explications, that many things predicted in the faid book, have been fulfilled in the perfon, and by the great actions, of the King of prefent Pruffia: to whom the Author has dedicated this most important Effay; and whom he ftyles, "a great Deliverer of God's church, refembling Moses, as a Larugiver, a Philofopher, a Prince, and a General.". -You fmile, Reader; but perufe our Author's book throughout, and you will find in it fuch things as eye hath not seen, nor ear heard, nor have entered the heart of any man, except the heart of Mr. Lauchlan Taylor, Minifter of Larbert, or of that other wonderful Decypherer, who difcovered the Cherokee Indians in the prophecies of Ezekiel*; with a few other Gentlemen of uncommon pe * See Review for laft Month, page 164. art. 2!. netration, |