The works of George Berkeley, D.D. late Bishop of Cloyne in Ireland. To which is added, an account of his life [by J. Stock] and several of his letters to Thomas Prior, Esq., Dean Gervais, and Mr. Pope, etc

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De Motu.

mathematicorum admittuntur. In philosophia prima, seu metaphysica, agitur de rebus incorporeis, de causis, veritate, & existentia rerum. Physicus series sive successiones rerum sensibilium contemplatur, quibus legibus connectuntur, & quo ordine, quid praecedit tanquam causa, quid

sequitur tanquam effectus animadvertens. Atque hac ratione dicimus corpus motum esse causam motus in altero, vel ei motum imprimere trahere etiam, aut impellere. Quo sensu causae secundae corporeae in telligi debent, nulla ratione habita verae sedis virium, vel potentiarum actricum, aut causae realis cui insunt. Porro dici possunt causae vel principia mechanica, ultra corpus, figuram, motum, etiam axiomata scientiae mechanicae primaria, tanquam causae consequentium spectata. 72. Causae vere activae meditatione tantum & ratiocinio e tenebris

erui quibus involvuntur possunt, & aliquatenus cognosci. Spectat autem ad philosophiam primam. seu metaphysicam, de iis agere. Quod si cuique scientiae provincia sua tribuatur, limites ass1enentur, principia &objecta accurate distinguantur, quae ad singulas pertinent, tractare licu erit majore, cum facilitate, tum perspicuitate.

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OR A

DISCO UR SE

AD DRES SED TO AN

Infidet MATHEMATICI AN

WHERE IN It is examined whether the object, Principies, and Inserences of the modern Analys1s are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Potnts of Faith.

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CONTENT S.

S E C T. I. Mathematicians presumta re be the great molers of Nasen. Hence an undue deferenoe to their decisons .here tho have no right to δε-cide. Nis one cause of infidelis II. Theis principies and me hori fο be examined Gith thesame fraeam, .hiebibo assume mith regata to the principies and inseries of religion. In inhat sense, and hom, far geometo is to be allowed an improvement of the

minae

III. Fluxions the great obea and emplument of the profund geometricians in the present age. What these suxions are. IV. Momenti or nascent incremenis ing quantities di cult to conceive. Fluxions os di erant ordeo. Second and third fluxions obscure mliseries. V. Disserentas, i. e. incrementi or decrementi in niteb suasi, UM θ fo- reio mathematicians instead of suxions or velocities of nascent and eva

nescent increments.

science.

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reta eae

XVII. Hard to disinguish bemeen emanescent increments and in ite aldisserenoes. Fluxions placed in various libis. The great auctor, is fems, not satisfed with his own notions.

XVIII. Quantities in Del ad suppostd and reje ita θ Leibnitet and his followers. No quantio, accorring to them, greater or smaller for the ad dition orsrbduction in iis in ite a XIX. Conclusons to be proved θ the principies, and not principies by the

conclusem.

XX. The geometricat Anahs consedered as a logician ; and bis discoveries, notis themselmes, but as derived rom such principies and θ such inferances.

XXI. A tangent dra n to the parabola accordiet to the calculus differentialis. Truth I eisn to be the result os error, and ho . XXII. O virtve of a t. OV misale Anahss arrive at truth, but not at science: ignorant ho tho come at their own conclusons. XXIII. The concluson never evident or accurate, in virtve os obscure or in- accurate premises. Finite quantities might be rejected as weli as in ite

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XXV. Sundo obserυations there m. XXVI. Ordinate fund from the area θ means of e nescent incrementi.

XXVII. In the fregoing case, the supposta evanescent increment is realb a nile quantitF, de Ied θ an equat quanti0 Nith an oppo te An. XXVIII. Ne foregoing case si generalist. Algebraices expresions comparia Gith geometrical quantities. XXIX. Correspondent quantities algebraical and geometricat equalia. The Analo De ed not to obtain in ins ite ais, bis it mus also oblata in ite quantities. XXX. The gestiet rid os quantistes Θ the received principies, hether of

suxions or of TFrances, netther good geometrF nor good logia. Fluxions orvelocities, πθ introducer XXXI. Velocities nos eo be abstracted iram time and space : nor theis propomtions to be investgased or consederia excis et time and space. XXXII. Di culi and obscure potata consitu e the principies of the modern Anal ses, and are the foundation on Ghich it is bulit. XXXIII. The rationaliacul es Ghether improved by such obscure Anal tici. XXXIV. O .hat inconcrimabis seps ite lines are found proportional tofluxions. Mathematical insitis in at a gnat an wallow a camel. XXXV. Fluxions os in ite ais not to be avoided on the received principies. Nice ab tractions and geometrical metaphscs. XXXVI. Velocities in nascent or evanescent quantities, πhether in realiu un-

XXXVII. Signs or exponenis obvisus; but fluxions the elves not fio. XXXVIII. Fluxions, hether the velocities coith πhich in ite at diFrenoesare generatia PXXXIX. Fluxions offluxions re second suxions, ether o be conceived asvelocities of velocities, or ratiar as Selocities of the second nascent incrementi rXL. Fluxions cons reri somelimes in one sense, sometimes in another; one iis in the elves, another in their exponents : hence confuson and obscurib.

X et XLI.

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XLI. Isechronat increments, whether Mite or nascent, proportional to theis respective velocities. XLII. Time supposta to be dividia into momenti: incrementi generatia in

those momenti : and velocities proportional to those increments.

XLIII. Fluxions, second, this fourth, &c. Ghat tho are, λω obtainia, and hois represented. What idea os velocis3 in a moment of time and potat offace. XLIV. Fluxions os ali orders inconta able. XLV. Signs or exponenis con fundia πith the fluxions. XLVI. Series of expressons or notes easb contrivia. Gether a series of mere velocities, or os mere nascent incrementi corresponding thereunto, beas ea T conceived rXLVI I. Celerities di issed, and inseta thereos ordinates and areas introduceae Analogies and expressions useful in the modern quadratures, mo)et be ineles for enabling us to conoe e suxions. No right to applν thera is .ithout inomis e of the principies.

XLVIII. Metaphses of modern Analbs mos incomprehen D. XLIX. Anal emplodita about notionat Rado entities. Theis logies asexceptionabis as theis metaphss. L. Occason of this ad es. Concluson. Queries.

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a stranger to the reputation you have acquired in that branch of learning which hath been your peculiar study; nor to the authority that youthere re assume in things soreign to your profession ; nor to the abusethat you, and too many more of the like character, are linown tomahe of such undue authority, to the misseading of un ary persons in matters of the highest concern ment, and whereos your mathematicalhnowledge can by no means quali0 you to be a competent judge. Equity indeed and good sense would incline one to distegard the juddiment of men, in potnts whicli they have not considered or examined. But severat who mahe the loudest claim to those qualities do neverti, Iesi the very thing they would stem to despise, clothing thenaseives in the livery of other men's opinions, and putting on a generat deserencesor the judgment of you, gentiemen, who are presumed to be of ali menthe greatest masters of reason, to be mosi conversant about distinct ideas, and never to take things upon trusi, but alWays clearly to see your way, as men whose constant employment is the deducing truth by the jus est inserence stom the most evident principies, With this blas on theirminds, they submit to your decisions where you have no right to decide.

II. Whereas

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II. Whereas then it is supposed, that you apprehend more distinctly, c sider more closely, inser more justly, conclude more accurately thanother men, and that you are there re lese religious hecause more judicious, I shali claim the privilege of a Free-Thinher; and taliethe liberty to inquire in to the objeci, principies, and method os demonstration admitted by the mathematicians of the present age, withthe same Deedom that you presume to treat the principies and mystcries of religion ; to the end, that ali men may see what right youhave to lead, or What encouragement others have to sollow you. Ithath been an old remari , that geometry is an excellent logic. Andit must be oKned, that when the definitions are clear ; When the postulata cannot be rem sed, nor the axioms dented ; when Dom thedistinct contemplation and comparison os figures, their properties arederived, by a perpetuat well-connected chain os consequences, the o jects being stili hept in view, and the attention e ver fixed upon them; there is acquired an habit of rea ning, close and exact and methodicat : whicli habit strengiliens and marpens the mind, and bein νtransferred to other subjecis, is of generat use in the inquiry after truth. But how far this is the case of our geometrical Analysts, it may be worth while to consider. III. The method of Fluxions is the generat hey, by help whereos the modern mathematicians unloch the secrets of geometry, and consequently of nature. And as it is that which hath enabled them soremariably to oulgo the ancients in discovering theorems and sol ving problems, the exercise and application thereos is become the main, is not sole, employment of ali those who in this age past for pro undgeometers. But whether this method be clear or obscure, consistent orrepugnant, demonstrative or precarious, as I shali inquire with the ulmost impartiality, so I submit my inquiry to your own judgment, and that os every candid reader. Lines are supposed to be gene-