Review of: Analysis Aequationum Universalis, &c An Universal Analysis of Equations; Or, A Short and General Method of resolving Algebraical Equations; deduced and demonstrated out of the New Doctrine of Infinite Series: By Joseph Raphson, Fellow of the Royal Society. London, Printed for Abel Swall, 1690. pages 50.

We are in a manner indebted to Chance for the composing of this little Treatise, since Mr Raphson, the ingenious Author thereof, accidently invented this Method, on the Occasion of a Problem that had been propounded to him by one of his Friends. For he declares, that he never saw any thing of the like Nature: And indeed, the Novelty of the Subject might be alone sufficient to recommend it to the World, and to induce the Author to appropriate to himself the sole Reputation of so considerable an Invention, were he not prevented by his innate Modesty, and the little regard that he hath for popular Applause. However, we shall leave it to those that are skilful in those Matters, to determine, whether any thing hath been hitherto Published, tending to the same effect; and in case there hath; nevertheless it cannot be imagined but that they will readily allow the just Commendation that is due to this worthy Member of the Royal Society; for it is not to be admitted, that Learned Men have often like Notions and Sentiments with respect to the same Subject.

Moreover, Mr Raphson explains his Method after the very same manner as he invented it, and to show the large Extent and Certainty thereof, he propounds a general Theorem, which he afterwards resolves more particularly in Two Propositions: Then he proceeds to illustrate his Method by Examples, in 32 Problems; wherein is exhibited the Resolution of Equations, of all manners of Dimensions, taken from the Resolution of a Simple Equations: Whereunto he adds Examples of Quadratic Equations, All his Operations are described at large; and to render the Practice more plain and obvious, the Author hath taken the Pains to compose certain Tables, which are inserted at the End; insomuch that if he continues to prosecute these Studies, as he hath begun, it is not to be doubted but that he will become one of the most skilful Mathematicians that are now living; since at the Age of 22 Years, he hath already attained to so great a Knowledge in those abstruse and difficult Sciences: Wherefore what improvement may we from not expect from the extraordinary Judgement of his riper Years?

Review of 2nd edition: Analysis Aequationum Universalis, &c Editio Secunda, etc. i.e. An Universal Analysis of Equations; Or, A General and Expeditious Method for resolving Algebraical Equations, Deduced and Demonstrated from the New Method of Infinite Series. Edition the Second: To which is annexed an Appendix, concerning the Infinite Progress of Infinite Series for extracting the Roots of Algebraical Equations; As also a Mathematical-Metaphysical Essay concerning Real Space, or Infinite Being. By Joseph Raphson, A.M.F.R.S. London, Printed for A and J Churchil, S Smith and B Walford; J Taylor, and T Vennet, 1702.

Mr Raphson's Universal Analysis of Equations is so well known to the Mathematicians, being of about Eight Years standing in the World, that we do not think our selves obliged to give any particular Account of it: Nor shall we insist upon the Appendix, which contains only some Additions made to the Analysis of Algebraical Equations. All that is proper, is to present you with a Summary View of his Essay concerning Real Space or Infinite Being; since this is wholly New, and abounds with many Curious and Uncommon Thoughts.

This essay is divided into six Chapters; In the First of which he recounts the Opinions of both the Ancient and Moderns concerning the Nature of the First Being. In the Second he Treats of the Certainty of Humane Knowledge. In the Third he considers the Nature of Infinity taken Abstractly. In the Fourth and Fifth he demonstrates that there is such a Thing as Infinite Space, which he farther Illustrates in the Sixth and last Chapter. This in general is the Scheme of our Author's Design, We shall now enter into the Detail of it.

In the First Chapter then, wherein we have an Account of the Opinions both of the Ancient and Modern Philosophers concerning the Nature of the Supreme and First Being, Mr Raphson tells us, that their Tenets may not improperly be reduced under these two General Heads: Some of them maintained that all things were in God or that there was not more than One Substance in the Universe; Others, on the Contrary, supposed more Substances, that differed very much from one another in their Nature and Whole Essence.

Of the former sort, some there were who asserted a certain Universal Substance, as well Material as Intelligent, which formed all things whatever out of its own Essence, and hence they were called Pantheists; whilst others of them, acknowledging nothing in the Universe more Excellent than Matter, have endeavoured to explain all things from this single principle, and these are commonly styled Atheists, and may (he says) not improperly be styled Panhylists. The Philosophers of the second sort, who maintain that there are many Substances in the Universe, do chiefly reckon up these Three; a Spiritual Nature, or a Thinking and unextended Substance, a Corporeal Nature or Matter, and a real Incorporeal Space. But these same Deny a Real Space: Others admitting of it, reject the Hypothesis of unextended Beings, supposing it to be contradictory. According to this Order of the Different Opinions of Philosophers does our Author proceed in accounting for them. He begins with the Atheists or Panhylists who Assert that there is nothing besides Matter with its Properties and Affections in the whole World; And of this Number he reckons the Disciples of the Ionick School, Anaximander the Scholar of Thales, who was followed by Anaximenes, Hippo, Diogenes Apollionates, Diagoras Melius, and Theodorus Cyreniaciu; among those of the Italian School, Leucippus (whose Opinion as delivered by Laertius, Raphson gives us) Democritus, Protagoras, Epicurus and Lucretius; and among the Moderns, Julius Caesar Vaninus, condemned to be Burnt by the Parliament of Toulouse, and our Hobbes. Next he passes to Pantheism, maintained by the Ancient Egyptians, as appears in the Testimonies of Sanchuniathon, Manetho, Iamblichus, Apuleius and Ficinus. The same Doctrine our Author says was held by the Persians, Syrians and Assyrians, and was afterwards introduced into Greece by Orpheus, and maintained by the modern Cabbalists among the Jews; as also by Spinoza and the Modern Brahmins among the Indians, who represent God, or the first Cause of things by a Vast Spider, Weaving all things out of its own Bowels, which at some time or other it will draw back to, and swallow up into itself. Of the same Stamp Raphson esteems some Fanatics and Enthusiasts among Europeans to be. He concludes this Chapter with laying down the Opinion of those Philosophers who are for several Substances in the Universe, differing from each other in their Nature and Essence; and under this Head he discourses particularly of the Doctrine of Non-Extension, and of Incorporeal Space, which last is asserted by Gassendus, Mr Newton, Dr Locke and the Famous Metaphysician Dr More.

The second Chapter treats of the Certainty of Human Knowledge, wherein our Author among other things premises, That whatsoever can be proposed to be contemplated by our Understanding, either has its Essence without us in the very Nature of Things, and upon that account is called Ens Reale, or a Real Being, comprehending Substance and the Modes of it; or else has its Entity in our Understanding only, or within ourselves, from whence it is styled Ens Rationis, and by some, Modus Cogitandi, the Mode of Thinking. From this Genuine Distribution of a Being, he says, the ultimate Limits and Bounds of Human Comprehension may by a plain and Natural Method be discovered, provided every Man attends to his own Thoughts freely and carefully. But that we may fall into no Mistake in our Apprehending or Judging of the Nature of Beings, whether Real, or of our Reason, he lays down these two Rules, which he explains more at large. First, that we admit of nothing as a first Principle, but what appears to be certain and most evidently true even to the meanest Capacity; such a Principle he reckons a Simple Idea to be, an Attribute Essential to the thing to which it belongs: That it may be certain tis requisite it should the first and undoubted Truth; and that it be evidently True, a clear and distinct Perception is Necessary. Secondly, that all our Deductions drawn fro first and self-evident Principles ought to be connected with one another by an Immediate Connexion, and eternal Necessity, and whatsoever does not flow from those Principles after such a manner, or from Propositions before demonstrated in the whole Course of the Ratiocination, ought not to be allowed of.

Mr Raphson in the next Chapter considers the Nature of Infinity taken in an Abstracted Sense. And here he first of all takes notice that the Word Infinite is an Ambiguous Term, and therefore before it be defined, he saith tis necessary to distinguish betwixt a Potential and Actual Infinity. He begins with the former, and illustrates its Nature, first by considering it Abstractly, and then by applying it to some of the most noted Examples. As to Actual Infinity, he tells us that there are two sorts of it, The one, called by him, Infinitum ad intra, or which may be conceived to be in exhaustible even by perpetual Division; and this Kind of Infinity he evinces by two Arguments taken from Geometry: The other he styles Infinitum ad extra, having some relation to extension.

From what he argues concerning the first kind of Actual Infinity he draws these Corollaries: (1) That an extended Being (as such) may be conceived as Divisible in Infinitum; though (as in other Potential Infinities) the Actual Process of Division will always be Finite. (2) That Magnitude and Parvity are nothing else but certain Relative Terms, or, in other Words, there is nothing absolutely Great or Small in the Nature of Things but are only Comparatively such. (3) That there is a possible Unity, or an uniform Homogeneousness, of an Extensum taken abstractly, free from all Alterity and true Composition. (4) That Beings, infinite in Number, extended, cannot coexist, unless their Infinity were adequate to the First Cause, which is impossible. (5) That this Infinity belongs to the most infinite Parts of a Finite Being, so far as they are United, and not existing separately. (6) That an Infinity of this Nature may be conceived to be greater and less, than another Infinity of the same Kind.

As to the other sort of actual Infinity, called by him Infinitum ad extra, our Author informs us of the following particulars. (1) He says, tis plain, That a Line, whether Absolutely or ex parte Infinite, cannot by any means be conceived to be Moved, but is rather really Immoveable: Since every Removal necessarily implies the Finitude of the Thing removed. (2) Every finite line, to be repeated Infinitely cannot Measure it. For to repeat Indefinitely, is an Infinite of the Potential Kind; therefore it can never be actually Infinity. (3) That the Space intercepted between Infinite Parallels of an Infinite Longitude is infinitely greater than any of the greatest finite Space. (4) The Case, he says, is the same with Solids, considered Abstractly, and actually Infinite. (5) That there are Infinites infinitely greater or less than Infinities, till at last they be wholly swallowed up of the One Absolutely Infinite Being.

After these things premised, he come to the main Point, viz. To prove that there is in Nature a Real Space distinct from Matter. This he undertakes to Evince by two Sorts of arguments, the One drawn from the nature of Motion in the Material System; the other from the very Nature of the Thing, and the Necessary Concatenation of Ideas flowing from it.

The First sort of Arguments he lays down in the Fourth Chapter, wherein he pursues this Method; First he evinces that there must of necessity be such a Space, vulgarly called a Vacuum: and then he subjoins some few things out of Gassendus, concerning the Extramundane Termination of it.

That there is such a space he proves first, from the noted Arguments of Democritus, Leucippus, Epicurus, and other Atomists, viz. the Impossibility of Motion in an Absolute Plenum. To this purpose he quotes those Remarkable Words out of Lucretius,

Quod si non esset nulla ratione moveri
Res possent, etc.

which Words Raphson looks upon to contain in them the Force of Demonstration: But for the farther Conviction of the Plenitudinarians (as he calls them) he demonstrates it after the following Manner. (1) Every Body moved describes in its Motion either a Straight or Curve Line. (2) Every Curve Line returns back to it self, or it does not. (3) Motion describing a Finite Curve (if there be any Motion at all in a Plenum) must needs by some way or other return back to it self: For else a Rectilinear Motion must be supposed, or else, what is in Question, a Vacuum. (4) Motion returning back to it self; or describing a Curve recurring to it self, if it be Circular; either turns round a certain indivisible Centre; or else moves like a Ring, whilst all things else between the Centre and the Periphery are at rest: But if it be not Circular, then it may be of Infinite Kinds, since there are Infinite Curves returning back to another. (5) It is contrary to the Nature of an Actual Infinite to be able actually to propagate Motion to is self. (6) In an Absolute Plenum, all things which be so compressed and solid, that it would be impossible to squeeze them closer together. For if they could be brought into a lesser Bulk (how little soever) there would not be an Absolute Plenum, which is contrary to the Hypothesis. (7) The Moving Force ought always to be greater than the Resistance, from whence it follows that No Moving Force, (though Infinite) can be able to surmount Infinite Resistance, or Cause Motion. (8) There are no such things as Particles of Matter infinitely small, or wholly unextended, existing separately from each other. After these things our Author for the strengthening of his Argument lays down several Propositions, which he demonstrates, and draws Corollaries and Scholia from them.

His Second Argument for the Proof of Real Space it taken from what Dr More has advanced in his Enchiridion Metaphysicum, who treating of the Motion of Bodies, demonstrates that the Removal of every Body moved must necessarily be performed through an unmoved Space. The Doctor's Argument with all that belongs to it Mr Raphson quotes and sets down at large; and then adds what Gassendus has urged concerning the Termination or Extramundane Bounds of such an Extended space; from when he deduces the following Corollaries. (1) That the Universal Mass of Moveable Beings (or the World) is necessarily Finite, Because every System of them may from a supposed Vacuum and Moveableness, suffer being compressed within a Narrower Compass, which would necessarily follow, though the Mind of Man could never have apprehended such an Extramundane Termination. (2) That all Finite Beings actually existing separately may be numbered; Not perhaps by a Finite Mind, but by the Infinite Author of them. (3) That from hence the Notion of Spinoza is convicted of Falsehood, who maintains, the Matter does express the Essence of the Infinite Being, and is One of its Infinite Attributes.

The other sort of Arguments for the Proof of real Space distinct from Matter, Mr Raphson in a Geometrical Way deduces from the Necessary and Natural Concatenation and Consequences of simple Ideas. These he lays down in the Thirteen Propositions of the Fifth Chapter, demonstrating each Proposition Mathematically as he goes along.

In the sixth and last Chapter our Author treats of Infinite Extension, so far as it relates to the Supreme and First Being: But we shall not trace him any farther, referring the Consideration of these abstruse Points to those who are more intimately conversant in Metaphysical and Mathematical Studies.

Review of: Demonstratio de Deo, etc. Or, A Demonstration of the Being of a God; being a New, Short and a Demonstrative Method of coming by the Natural Knowledge of God. To which are added some Miscellaneous Epistles, relating to the Nature and Imortality of the Soul, the Truth of the Christian Religion, the Universe, etc. London; Sold by Will. Taylor, at the Ship in Pater-noster-Row. 1710.

That something has existed from all Eternity, Mr Raphson, the Author of the Piece, observes, is a Truth which all Atheists must of necessity admit: The Question is, Whether That Something is Matter or not? And this Question our Author had had a Design of examining into the Merits of, for some time, designing at the same time, in his Enquiries upon this Great Subject, not to proceed upon Rhetorical Flourishes and plausible Conjectures, but upon the strongest and most irrefragable Arguments the Nature of the thing would admit of: And in the Disquisitions upon the Subject, which he now presents the Learned World with, he looks upon it that he leads his Reader by a most easy and convincing Method, not only to the Knowledge of the Existence, but in part of the Nature of the Infinite Transcendental Being, whom we call God: Whence he looks upon it, that we are furnished with a Method à priori of determining how many sorts of finite Substances are capable of existing, and of making it evident that no Substance can possibly exist unless it is extended. Mr Raphson has proceeded in this Work in the Synthetic Method of Geometricians; not that he looks upon this Method of Demonstrating, to add anything to the Force of a Demonstration; but because in forming Demonstrations of this kind we see the best whether we make any false Steps, and so must every one who is previously acquainted with this Way of Reasoning.

Mr Raphson's Demonstratio de Deo, etc. is divided into two Parts; In the First of which he demonstrates in order these Propositions: First, That there is a Self-existent Being. Secondly, That whatever a Self-existent Being is, it is so from it self, or in its own Nature. Thirdly, That a Self-existent Being is absolutely and in its own Nature eternal, or its Existence flows from the Necessity of its Nature. Fourthly, That a Self-existent Being, whatever it may be else in its own Nature, is necessarily infinite. Fifthly, That a Self-existent Being is indivisibly One of its self; by a natural Necessity there is but One Self-existent Being. Sixthly, That a Self-existent Being is in its own Nature a most simple Being. Seventhly, That it is Immutable, and, Eighthly, That it is infinitely Perfect.

To transcribe into this Place the Demonstrations which Mr Raphson gives us of these Propositions, and the Corollaries and Conclusions which he draws from them, would be to take down the whole first Part of the Work. I shall present the Reader with the Demonstrations which he gives of one of these Propositions, as a Specimen of the Whole: And I shall choose the Fifth above the rest, because the Unity of the Godhead has been thought by a great many to be by no Means demonstrably deducible from the bare Principles of Natural Reason.

Prop. 5 A Self-existent Being is indivisibly One of its self; by a natural Necessity there is but One Self-existent Being. Dem. If you deny it, it must follow from thence, either, first, That a Self-existent Being is divisible; or, secondly, that there are more than One. A Self-existent Being can't be divisible, because, if it be conceived divided into Parts, these Parts will be either self-existent, or they will not; if they are not Self-existent, then the Self-existent Being is destroyed, which is inconsistent with its Nature as Self-existent: If the Parts resulting from this Division are Self-existent, then (by the fourth Proposition) they are all infinite; and consequently, there might be two or more Infinities of the same kind; contrary to the Corollary from the second Definition. Hence it is clear, that a Self-existent Being is indivisible: When it follows, that there is but One Indivisible Self-existent Being. Q.E.D.

Another Demonstration of the Proposition, which Mr Raphson gives us, is as follows. The Nature of a Self-existent Being is infinite, by the fourth Proposition: If we conceive it therefore divided into Parts, the Beings resulting from that Division must be either Finite, or only partially Infinite; both of which are inconsistent with the Proposition before cited; whence it follows, That a Self-existent Being is indivisible: And in as much as more Infinities than One can't exist in the same kind, it must be simply and necessarily One. Q.E.D.

In a Scholium upon this Proposition, our Author observes farther, That the very Nature of necessary Existence as necessary, implies and supposes Unity, as well as it implies it as infinite; for all Number or Plurality implies Finiteness, and more Beings than one of the same kind must have an exclusive Respect one to another, be circumscribed by Bounds, which is the formal Nature and Essence of Finiteness.

I cannot transcribe the Demonstrations which Mr Raphson brings for his fourth Proposition into this Place, which he refers to in his Demonstrations of the Proposition before us: His second Definition is, That that is infinite in its Kind, or simply infinite, which in that Kind is actually without Bounds; or which in that Kind, as to that Nature, or in that Respect, cannot be limited; as Infinite Extension, Action, Thought, etc. The Corollary from which is, That there can't be two Infinities of the Same Kind.

In the Conclusion of the first Part Mr Raphson observes, That as the Self-existent Being necessarily exists, so such Beings as are not self-existent owe their Being to something extraneous to themselves: That as the former is what it is of it self, so the later receive all that they are and have, from something else: That as the former is in its own Nature eternal, so the later are in the same manner temporal: As the one is infinite, the other are finite: As the one is necessarily and of it self one, the other owe their Unity not to themselves, but to what made them such: As the one is a most absolutely simple Being, so the other are either compounded, and so resolvable into the Principles of which they consist; or if they are in their Nature simple, as they were made, so they may be unmade; or, as far as they were produced, so far also are they capable of being destroyed by the Being that produced them: As the one is immutable, the other are mutable: And as the one is all that is or can be, in an absolute and infinitely perfect Sense, the other are of restrained and limited Essences, which is the Reason that there are many of them, for Finiteness is the natural Root of Plurality.

The second Part of this Work Mr Raphson divides into three Sections; In the first of which he treats the Self-existent Being as infinitely extended, or as the infinite Cause of all finite extended Beings: Proving, first, that the Self-existent Being is the Cause of all other Things: And, secondly, that the Self-existent Being, or Cause of all things, is necessarily and infinitely extended. Under the later of these Propositions Mr Raphson endeavours to prove the absolute Necessity of Infinite Expansion; and draws from it these three Corollaries: First, That the Self-existent Being, or First Cause of all things, as infinitely extended, is necessarily intimately present with all things, or omnipresent: Secondly, That the Self-existent Being, as infinitely extended, is as it were the Basis and Foundation of all things extended, without whom they had never been, and without whom they would immediately vanish into nothing, the same Power being required to keep them in being, as was requisite in their first Creation, as they have intrinsically and in themselves no Power or Sufficiency at all: And, thirdly, that the Self-existent Being, as infinitely extended, by the Immensity of its Extension, is a sufficient Foundation for innumerable Worlds to exist in: For, says he, in as much as created extended Substances are not yet infinite, nor indeed ever can be actually infinite (as he has shown in the 6th Chapter of his Treatise De Spatio Reali) hence it necessarily follows, that they are capable of being increased to all Eternity.

In the second Section Mr Raphson undertakes to demonstrate, first, That the Self-existent Being, or First Cause of things, is eternally and infinitely active: Secondly, That as infinitely active in a Way, which implies, or is necessarily related to infinite Expansion, it is an adequate Cause of the Essences and Existences of things: Thirdly, That the Essence of the Self-existent Being as infinite, can't be adequately comprehended by a Finite Understanding: Fourthly, That the Essence of the Self-existent Being, as infinite, is the adequate Object of an Infinite Understanding, or proves the Possibility of an Infinite Understanding: Fifthly, That an Infinite Essence, as the Object of an Infinite Understanding, does necessarily exist, or an Infinite Understanding necessarily follows from the Existence of an Infinite Essence, or is a necessary Attribute of an Infinite Being: Sixthly, That all possible things, as possible, flow by a natural Necessity, and consequently an eternal One, from the infinite Essence of God; or, God's Essence is the natural and infinite Root and Foundation of all things possible: Seventhly, That God, considered as an infinite Mind or Understanding, comprehends all things possible in his infinite Essence in one infinite and absolutely perfect View, and that from all Eternity: Whence it follows, That all things which ever were, are, or can be, together with their Relations, habitudes, respects, and Consequences, etc. are present to Him; that is, his Knowledge is infinite, or infinitely perfect: Eighthly, That God is infinitely Good, True and Just, &c or the Moral Perfections of God are Infinite; or an infinitely perfect Rectitude is an Attribute of the Divine Nature: And, lastly, That all God's Actions, or the Decrees of his Will, depend upon the absolutely infinite perfections of his Nature; by which He is necessarily, that is, most freely, (for in God Freedom and Necessity are the same) determined to act; or, God is necessarily and solely determined by himself.

The Demonstrations of all or any of these momentous Propositions can't be brought into this Place; Mr Raphson draws some Corollaries from the Last, which are as follows; Viz. First, That from this and the fifth Proposition, in Combination it follows, that God can't exist without his Decrees, and consequently that the Decrees of God are eternal: Secondly, That there is in God no Will of Indifference, because that would argue Him of Imperfection, who is absolutely perfect: And, thirdly, That God is not to be determined, properly speaking, by any thing extraneous to himself, because He can't possibly receive any extraneous Impression but at the Expense of his own Infinity.

In a Scholium subsequent to these Corollaries, Mr Raphson observes, That Perfection, Intellect, Will, Decrees, and all the other Distinctions which we ascribe to the Essence of God, are in Him the same; but, by reason of our Weakness, as we can no better speak of Him as an Infinite Understanding, than by Analogy to what Perfections we find in ourselves, and general Terms raise our Ideas the highest towards Infinite, and absolute ones fill our Minds more than negative; therefore it is that Mr Raphson says, That God is determined by the Perfection of his own Nature to do what he does; because, Perfection in the most absolute sense is best adapted of any Word to express any things of Infinity by, or rather absolute Perfection and Infinity in themselves are really reciprocal, etc. God therefore, he says, is determined by the Perfection of his nature to all his Actions, and that necessarily, and from all eternity, according to his Decrees, viz. by decreeing, That those things shall come to pass in time, which in their own Natures could not have been from eternity, which is the Nature of all created Substance, and whatever flows from their Existence, Operations, etc.

Mr Raphson observes farther, That from what determines the Will of God, and the Necessity of its being directed by the absolute Rectitude of his Nature, we may deduce what was that true and genuine Liberty, and whence it was derived, which God at first implanted in his Images the reasonable Part of the Creation: Though it must be acknowledged in his opinion, that there are very few Footsteps of this genuine Liberty left among Mankind at this Day.

And whereas God is often said to act according to his Will, our Author observes, That if by the Will of God is understood his Perfection, or something immediately and necessarily flowing from it, this is most true. But whereas some of the Use of this Expression seem to mean, That God can arbitrarily act either consistently with, or contrary to his Absolute Perfection and the Rectitude of his Nature; This Mr Raphson rightly concludes is, in effect, to destroy the very Being of a God.

Hence Mr Raphson takes Occasion to determine what Liberty is in a Reasonable creature, or a Finite Image of God, viz. A Power of Determining and Directing all its Actions according to the Laws of Reason: For if a Reasonable Creature is determined in its Actions by Reason, tis determined by it self, and to be determined to act by one's self is Liberty in the strictest Sense: Whoever therefore in his Actions is determined by Reason, determines himself to act, or acts freely; and whoever is determined by any thing extraneous to right Reason, acts so far necessarily, or rather strictly and properly is acted. A power therefore of acting from one's self, or according to the Dictates of Reason is Liberty, and when we exert that Power we act freely.

Indeed Mr Raphson rightly observes, Tis common for Persons who are otherwise determined by their Reason, when they are ignorant of the Motives they act upon, to think they act freely; in as much as they look upon themselves to act then most freely, when neither Reason from within, nor any external Motives contribute to determine them to act: Whereas, indeed, none who is absolutely indifferent acts at all as long as he remains indifferent; and as soon as a Man is determined to act (without which Determination he acts not at all) the Freedom of his Action is discovered by its Conformity to, or Inconsistence with Reason, etc. The Motives which determine us to act are three, viz. First, Our own Reason: Secondly, What external Principles work upon us in ways consonant to Reason: And, thirdly, such as are repugnant to it. When we are determined by this last, we may more properly be said to suffer than to act; to yield to the Assaults of our Enemies, which when we have once yielded to, their Conquest becomes easier by degrees, till our Slavery becomes habitual, and in Process of Time and Negligence it is next to impossible for us to rouse our selves up out of our Spiritual Lethargy, and re-assume a genuine Power of acting freely: For when our Old Companions are become dear to us, and have got such an Ascendant as to make themselves thought necessary, tis natural for us to hug our Chains, and to take Delight in those Witcheries and Enchantments which we can't without infinite Uneasiness break through.

In this State we lay the Foundation of a Kind of Spiritual Mechanics, of which this is the Fundamental Principle, that "Human Inclinations (viz. such as are destitute of the Power and Use of Reason) are as the Forces of the External Motives which act upon them." Whence it comes to pass, that an Animal once capable of directing its actions according to the Laws of Reason, and which therein its Author at first created free, degenerates by degrees into a mere Mechanical Automaton, leaves its Power of Acting from within behind it, and throws it self into everlasting Chains and Slavery; those of Sin and Slavery which the Scriptures of the New Testament so often speak of, and warn us to avoid, as we love our own Liberty, and would be free indeed.

In the third Section of this second Part Mr Raphson demonstrates this single Proposition; That God, or the Cause of Things is infinite, as well in Intenseness as Extension; or, that the Essence of God is active to an infinite Degree of Intenseness. What he means by Intenseness our Author tells us at large in a Definition precedent to this Proposition: And from the Proposition it self he draws several Corollaries and Scholia, none of which I have room to transcribe into this place. From the Whole he gives us a short Description of God as a General Corollary, which is as follows.

"God is, first, a Being absolutely Self-existent, Infinite in all manner of Perfection, i.e. Containing in himself primarily, and in infinitely the most real Way, the essential Perfections of all things to infinite Degrees; infinitely active, or an infinite Mind: Secondly, The truly efficient Cause of all Things that exist; which, though in Essence not absolutely unlike their Creator, yet really totally and essentially distinct from him He not only produced, but perpetually preserves: Who, thirdly, both in the Acts of Creation and Conservation demonstrated and still continues to demonstrate the infinite Intenseness of his Attributes."

As to the Letters which Mr Raphson has added to this Works about the Nature of the Soul, the Truth of the Christian Religion, the Universe, &c he says of them himself, That the Reader must not expect to find such an Air of Demonstration in them as is to be expected in the former Part of his Book, most of the Subjects he writes about being not strictly able to bear it: He proposes upon all Occasions what seems most probable to him; and whatever he advances he submits to the candid Censures of the Judicious, and especially to that of the Church of England.