most useful and lofty Themes. The Writer discovers in them a great Capacity, extenfive Erudition, and a lively as well as regular Imagination. I am under no Apprehenfion of this Character being difputed or difprov'd. The Father of this Author made the Name of Turrettin famous in the Church, and in the Commonwealth of Learning. This Son, worthy of his illuftrious Progenitor, inherited both his Abilities and Virtue, and has here, as well as in other Inftances, given the World fufficient Specimens of both. We Thall impatiently wait for further pofthumous Fruits of them, and hope we fhall e'er long fee that larger Compendium of Ecclefiaftical Hiftory which we were promised in his Life-time.

The third Volume of this Collection is of a diffe rent Nature from the two former. It is entitled Orationes Academice. Quibus multa, ad Scientiarum Incrementum, Chriftiane Veritatis Illuftrationem, Pietatis Commendationem, Pacémque Chriftianorum, pertinentia continentur: Or, Academical Orations, containing a Variety of Particulars, tending to the Advancement of Science, the Illuftration of Reveal'd Religion, the Commendation of Piety, and the Peace of Chriftians.

Thefe Difcourfes are twelve in Number, upon very entertaining Subjects, and of an elegant Compofition. The first treats of the fingular Excellence and manifold Ufes of facred Antiquity. It fhews what Service it is of to Religion, for proving the Truth of it, for explaining and clearing up the divine Records, for reflecting Light on the Controverfies of Chriftians, and for furnishing the most powerful Motives and Excitations to a virtuous Behaviour. It demonstrates the ftrict Connection there is between it and prophane Literature, in all its Branches. And laftly, it infifts upon the Dignity of this Subject.

The fecond Oration defcribes the Temper and Behaviour of a Clergy-man, ftudious of Peace and Truth. This and the foregoing Speech were both naugural. The firft was pronounced May 29. 1697. upon our Author's Promotion to the Profefforship of

Eccle

Ecclefiaftical Hiftory, then newly erected. The latter was deliver'd Dec. 1. 1705. upon his Advancement to the Divinity Chair. I fhall only mention the Titles of the other ten:

The third is a Panegyrick on William III. King of Great Britain; spoken to the University of Geneva at the publick Act celebrated presently after his Death. The fourth particularizes the Improvements of the laft Century in divers Articles of Learning, as on the other hand, the Danger there at prefent is of its Declenfion. The fifth directs to the propereft Methods of promoting it. The fixth points out both the Imperfections and Excellency of the Sciences. The leventh evinces the reciprocal Affiftances of Religion and Literature. The eighth expatiates on the Dif fenfions which unhappily fubfift among the reformed. The ninth defcribes the different States of the Chriftian Religion, from its first Promulgation to this Day: to this are prefix'd 1. A Letter of the Paftors, and Academical Profeffors of Geneva, to the King of Pruffia. 2. That Prince's Answer to it. 3. An Epiftle of the Count de Matternich, Minifter of State to his Pruffian Majefty, and his Envoy extraordinary and Plenipotentiary to the Swiss Cantons, to the aforefaid Profeffors and Paftors. The tenth confiders the Influence of the Affections in perverting us from the Perception and Profecution of Truth. The eleventh, which is a very short one, expreffes our Author's ardent Wishes and Prayers for the Peace of Europe. The twelfth fets before us the Causes from whence have arifen the Corruptions and Decays of the Faith and Discipline of the Catholick Church, and the most effectual Remedies for those Disorders: At the Close of this, which is the last, are added Encomiums on two illuftrious Persons then lately deceased; one of which was the noble Ezekiel Spanheim, of illuftrious Figure in the Scenes both of Politicks and Letters. This great Man, as Mr. Turrettin fays, was in the highest Estimation with the Princes of Brandenburgh and the Palatinate whom he ferv'd, and with

all the Sovereigns of Europe with whom he negotiated; particularly with our late Queen Anne, who teftified the utmoft Refpect to him, living and dead; and with the Princefs Sophia Electrice of Hanover, a Lady of the moft confummate Knowledge and Erudition, who maintained an epiftolary Intercourse with him. Through a Series of arduous Employments in Embaffies, &c. he maintained a delightful Commerce with the Mufes, and cultivated an Intimacy with all kinds of Antiquity; of which the World has reap'd the ineftimable Products. In him there center'd a Variety of Accomplishments, rarely united: he was at once a most compleat and finished Politician, and a Man of unblemished Integrity and Devotion; candid, generous, charitable to the poor, and beneficent to all whom he could affift, declining no kind Office, nor refufing any Request which he could gratify; foftening and adorning the feverer Character of an exquifite Philofopher and Scholar with fuch Humanity of Temper, fuch Affability of Behaviour, and Sweetnefs of Converfation, as attracted the Affections of all who had the Felicity of approaching him. Grac'd with all the Virtues and laudabie Qualities of the learned, he was free from the Vices and Blemishes fo incident to that Species, viz. Pride, Envy, Obftinacy, with the Love of Oppofition and Difpute. Instead of which, hard to provoke, he was mild and gentle in Controverfy, filent under the injurious Treatment of his Oppofers, though vaftly inferior to him in Knowledge, or anfwering their Cavils calmly, and without the leaft Shew of Refentment. Laftly, tho' he was perfectly vers'd in all the Greek and Latin Writers, whether ancient or modern, in every kind, whereof he had the quickest Relish and the politeft Tafte, yet the facred Scriptures were his daily Companions, and the Study of them his fupreme Delight.

ARTICLE

ARTICLE IV.

A new Treatife of Fluxions: Wherein the direct and inverfe Method are demonftrated after a new, clear, and concife Manner, with their Application to Phyfics and Aftronomy: Alfo the Doctrine of Infinite Series and Reverting Series univerfally, are amply explained, Fluxionary and Exponential Equations folved: together with a Variety of new and curious Problems. By Thomas Simpson, Teacher of the Mathematicks. London: Printed by Tho. Gardner in Bartholomew-Clofe; For, and are to be bad of the Author in Crown-Court LongAlley, near Upper-Moorfields; G. Powell in Shrewsbury-Court, Whitecross-street,; R. Shirtliffe at a School-Houfe in Wimple-street, near Oxford Chappel; D. England at the Alienation-Office, in the Temple, and Jacob Robinfon next the One Tun Tavern, near Hungerford in the Strand. 1737. 4to. Pag. 163.

TH

HE Author of this Work, bred to a mechanick Employment, has raised himself to a confiderable Skill in the Mathematicks, almoft wholly by the Force of his own Genius, and intense Application: he was by Trade a Weaver, but he now profeffes himself a Teacher of the Sciences; of which this of Fluxions that he here infifts on is one of the nobleft and most useful.

In this Treatife Mr. Simpson lays down and demonftrates the Principles of them in a Method exactly true and genuine, and, as he conceives, not effentially different from that of their great Inventor, being altogether expounded by finite Quantities: and in the Application thereof, he has every where been as plain

and

and perfpicuous as he poffibly could, or as the Want of Room, or the Abftrufeness of the Subject would admit; efpecially in the firft and fecond Parts, where he has, for the Sake of those who have made but fmall Progrefs in thefe Studies, given a great many new, and fome very uncommon Examples in the Solutions of Problems, and has endeavoured to render them fo plain as to be understood by Perfons of the meanest Capacity.

The fecond Part treats of the Doctrine of infinite Series, wherein there is not any thing proposed, but what he has endeavoured to demonftrate; and, befides feveral valuable Things on that Topick, and a Variety of cafy Examples, there are fome Improvements, and a Set of new Rules to find the Forms of Series, without taking in any of the fuperfluous Terms, which in fome particular Cafes has rendered the Methods hitherto delivered impracticable.

The Reader will in the third Part meet with a familiar Method of finding and comparing Fluents, illuftrated by fome useful and easy Applications.

In the fourth Part, the Author has fhewn the use of Fluxions in fome of the fublimeft Branches of Phyfics and Aftronomy, in as clear and concise a manner as he poffibly could; where, befides feveral curious Things done in a Method quite different from what is to be met with in other Writers, there are some very useful Speculations relating to the Doctrine of Pendulums and Centripetal Forces, which have not, as he knows of, been taken notice of before. I fhall name a few of the Propofitions that are here investigated. As,

1. To determine the Times of Defcent of heavy Bodies in Curves, whofe Axes are perpendicular to the Horizon. 2. The Length of a Pendulum being given, and the verfed Sine of the Arch defcribed; to find the Time of one Vibration. 3. To find the Time loft in any given Time, by a Pendulum measuring equal Time in an infinitely fmall Arch, when

made