Wallis who mentions the controverted Question concerning the Angle of Contact made by a streight Line where it touches the Circle but in his Opinion thinks it nothing if not a right Angle in being perpendicular to the peripherial Point of the Circle because not otherwise numerically Computable He also Inserts his Disceptation as I remember by Letters that pass'd betwixt him and a certain Learned Person who undertook to defend against him the Determination of the famous Mathematician Clavius in whose Judgment the Angle of Contact was properly something tho' not Commensurable and therefore not otherwise definable than as being less than any acute Angle whatsoever which I take to be the more probable Opinion By reason that it could not be denominated Angular without it appertain'd to something tho' but of general or tacit Application And thus in the Judgment of Euclid the Angle of Contact has a singular Attribute where it touches the periphery of the Circle but not otherwise accountable or to be summ'd by Number The Reason is that in every Circle whether equal or unequal the Point in the Circumference touch'd by a right Line will be the same in all of them because no other Line can fall between the Point of Contact in any of their Peripheries And could it be Commensurable it would be of one Equality Whereas contrarily in every direct Figure or where two right Lines touch one another the Angle they make may be Geometrically lessen'd by any intervening Line or Lines that meet in the Angular Point But not so to be understood of the Angle of Contact which has no proportion in its self if compar'd with any other figurative Angle To which purpose the Learned Proclus signally Determines That the Point in the Circle where the Angle of Contact meets with a streight Line is mixtly Compos'd of a direct Line and the Curviture of the Circle and therefore not Commensurable by any distinct Line that can be numerically computed So that the Angle of Contact may be well Term'd singular by reason it has no proportional Similitude or Quantitative Propriety correspondent to any other Angular Delincament And the more Admirable because the wonderful Extent and Power of Geometry computatively Explains by the vastness of its Science all other Angles Mathematically qualified except that which is lineally annex'd to the touch of the Circle And what is yet more wonderful the tangent Line that Includes and makes the Angle of Contact is perfectly Commensurable tho' not the Angle where it touches the Circle a Geomemetrical Secret that has not a little perplex'd if not pos'd the Pens of famous Mathematicians Or this Proposition may be thus demonstrated the Angle at D made by the prickt Line D C in the Triangle A D C is a right Angle as is always the Angle in the Semicircle therefore the Angle A C D is less than a right Angle tho' it may be allow'd greater than any acute Angle and the Angle at C made by the tangent Line less than any acute Angle that can be given Otherwise the Point where the tangent Line touches the Circle could not be in that Point singular as before demonstrated So that in the Triangle A C D if D be a right Angle the Angle at C must be less than a right Angle because in every plain Triangle the three Angles are but equal unto two Right Which confirms the former Demonstration And from which may be concluded that of what demonstrative Quantity the Angle of Contact does actually consist is as yet conceal'd from Geometrical Inquisition Or not to be discover'd untill a certain Proportion can be found betwixt a streight and a curve Line which perhaps may never be Demonstrated If not as impossible as to prove a Curve commensurately distinguish'd from a Curve I confess I am not a little beholding to this Learned Monsieur for the occasion he has given me to discuss I conceive not unsatisfactorily to the Judicious the Question concerning the Angle of Contact so much controverted by Celebrated Geometricians And which by a certain fineness in Science is more pertinently apply'd to the purpose he would intend it than any Mathematical Proposition Theorem or Diagram of his that I have met with But I cannot thank him for the Conclusion he deduces from thence or because he takes it for granted That a streight Line by reason of the near approximation that it has to the Circle in the Point of Contact never less inflects from every of its Points than when it degenerates into a circular Figure By which Inference he does highly disparage the Contexture and Theory which he devises for the Motions of his Vortices and Globuli in order to their material compleating of the Universal World If their Motions in any kind tending to a direct Line be allow'd to degenerate when from that manner of Movement they convert to circular Revolution Which were all one as to charge the motional Exactness and Conduct of Nature providentially dispos'd with Mistake or Imperfection relating to her Operation and Works Because no figurative Motion can be imagin'd so absolutely compleat excellent and of certain continuance as is circular Movement By reason that no Part of a Circle can be Term'd its Beginning or End Whereas contrarily no Motion can be made in a streight Line but must have separate intervall'd and terminated Parts Which enough disproves the Allegation of this Author as sure as that by Geometrical Dignity and Proof the Circle has a superlative perfection above all other Figures And were it not to be so acknowledg'd there is little reason why the Wisdom of Providence should annex the admirable Computation of Days and Years to circular Revolution But so much has been said by way of Confutation in my former Remarks on this Subject that I need not renew them here Nor is it requisite that I should farther reflect on his elaborate Expressions Draughts Schemes and Delineations by which he undertakes to confirm the Motion of Things in order to the Constructure of the Universe together with the Being of the Earth since I doubt not I have refell'd his total Hypothesis on which his Principles are grounded Wherefore I shall pass from all of them to the Entertaining of my Reader with some especial Thoughts relating to the Original of the World and Earth we inhabit as are Ancient or Modern of most erudite Reputation I. Concerning the Magnitude of the Universal World the Questions are Whether it be Infinite or Finite materially replenish'd or not II. As to its Duration or Continuance Whether it had any temporary Beginning or eternally Constituted III. As to Number Whether it be one or numerously Existing Tho' as to Number there can be no Controversie if the World be granted Infinite because there can be but one Infinite IV. Another grand Querie is From what Cause or Matter was the World Originally Compos'd V. And next From whence or in what manner that Cause and Matter did proceed
by Nature Which is very different from the Epithet he gives to Motion and Rest in his 38th Paragraph where he determines That by the Ordainment of God Matter together with Motion and Rest were as to their ordinary Course originally Constituted From whence he concludes That all Parts of Material Things were primarily so dispos'd by the Will of the Almighty as by their divers Conservations the World 's total Matter might be continually preserv'd by the same determin'd Method that every of its Particulars receiv'd when first Created From which Immutable Decree of the Omnipotent he derives several Laws or Rules of Nature The First of which he considers as her constant Industry and Prerogative whereby she would as far as her Regalia's extend unalterably continue every particular Thing in its Manner of Being And thus whatsoever Mov'd should by her Intention be always Mov'd So that if any Part of Matter represented its Motion in a Square or other suitable Figure it would so perpetually continue did not some other Thing interrupt its Movement All which might be conceded were not Nature oblig'd to dispense with for Universal Convenience such Alterations in her Methods of Rule that she accommodates to the frail Disposition of her Elementary Subjects whose Distempers unless so prevented would be more disorderly or confus'd For which Reason she necessarily waves her Original Intention as to the permanent continuance of her Subordinate Individuals by Exercising in a manner against her Will a Tyrannick Power by which she kills some Beings to give Life and Repose to others Which could not otherwise have room to Exist were the Compass of the World far greater than its conceiv'd Dimension And thus we ought to apprehend the various Effects of Motion as also such Alterations as relate to Generation and Corruption by which Things cease to be and others have Being Tho' neither Motion or any of its Concomitants or Tendencies here mention'd can be reasonably suppos'd according to the Opinion of this Author to endeavour incessant Movement did not some other intervening Thing put an end to their Motion by obstructing its farther progress Which were to Affirm That Motion were void of Design if any Thing Mov'd regardless of its proper Residence If granted That the Motion of one Thing may cause the Motion of another to cease 't is not to be understood as any hindrance that its natural Capacity can receive or the Intendment it has to Arrive where it ought to remain It being absurd to suppose That Motion as it is appropriated to Material Composition of which only we can be sensible should be actually or potentially Imbu'd with a perpetual motional Faculty which were to allow it Indeterminate and therefore Infinite contrary to the undoubted Philosophiaal Maxim non datur Infinitum actu in rerum Natura And as experimentally certain as that a Man cannot always Run or Walk The Second Law which he Attributes to Nature he thus delivers Every Motion of it self is in a streight Line and therefore whatsoever circularly Moves always endeavours to depart from the Center of the Circle it describes Before I enter my Replication to this Head which in some respects is very questionable I think fit to Inform the Reader how he does here Dissent from what he deliver'd in his 32d Particular where he grants That Motion may be not seldom exceedingly Contorted Twisted or Wrested which he must intend by such a lineal Movement as might be neither Direct or Circular And therefore it must have such a kind of oblique Curvitude as cannot be comprehended by the Definition of regular Curv's or such as may be term'd Geometrically Commensurable which by Learned Mathematicians is solely Attributed to the Circle Parabola Hyperbola and Ellipsis The Reason they give is by demonstrating That no other Curvitudes can in every of their Points have a due Relation to streight Lines as it may be equally prov'd On which Mathematical Certainty is grounded their rejecting of all other Curv's as Mechanical because in particular they cannot be Geometrical by right Lines applied to such Figures and therefore not to motional Things and Parts by Indistinct Commensurations and such as may express their common equality Whosoever desires to be assur'd by Geometrical Delineament and Proof to this purpose he may Inspect the Commentary of Van-Schooten a Dutch Mathematician on the Geometry of this Author In the mean time this Observation is sufficient to explain the egregious Mistake of this Writer as to the Place before-mention'd Where contrary to the actual Performance and Method of Nature that allows to every Thing Mov'd Commensurable Space and Parts he Allys the possibility of Motion to such a perverse and irregular Figure as would render it absolutely confus'd instead of being orderly consistent with the Certainty of Measure But now in the above-mention'd Second Law of Nature as he defines it he thinks 't is very manifest That Motion by its simplicity of Operation should be conits simplicity of Operation should be continu'd in a streight Line but never in a crooked Which is true if meant of such Things that by their Inherent Proprieties of Length or Weight Ascend or Descend which are always continu'd in a streight Line But are not so in every Thing that Moves as may be evidently perceiv'd in that admirable Providence by whose Conduct the Celestial Motions of the Sun and Planets have a constant Circular Revolution Which sublime Manner and excellency of Motion is no otherwise naturally theirs than suitable Gravity or Lightness is the Cause that Things so compos'd Move upwards or downwards These Examples are sufficient to refell his general Hypothesis by which he would limit the genuine Action of whatsoever does Move to a direct Line without excepting the Orbs above That he well understood did Move otherwise To which purpose he delineates a Diagram the same in Effect with this that follows Let a Stone be suppos'd to Move by any Force according to his Example in a Sling as E A Circularly Mov'd in the same instant in which it is in the Point A determin'd to Move any whether in a Right Line towards C so as the Right Line may be the Tangent of the Circle It cannot be imagin'd to terminate Motionally Contorted tho' it first comes from L to A by a crooked Line because nothing of that Curvitude can be understood to remain in it whilst it is in the Point A. But should it then be out of the Sling it would not Move forward towards B but towards C. From whence he concludes That whatsoever does Circularly Move would always endeavour to depart from its Center Here he undertakes to give Nature a Law against her natural Legalities if not such a fictious Swing as would whisk her ordinary Operations out of their usual Course into the Region of Fables It being very Demonstrable that both Parts of the Proposition to which this Diagram Relates are erroneously Applied As to the First by which he would prove
height or utmost Distance from the Center of her Orb and at another a Perigaeon-nearness unto it Which were much the same as to think it feasible for clusters of Flies no bigger than Gnats when they numerously seem to Circulate in Sun-shine to remove the weighty firmness of the terrene World or perform instead of the Sun the Ecliptical Revolution of the Day or Year Yet on this preposterous and feeble Conduct is erected the main Hypothesis of this French Writer both as to the Composition Being and Motion of the Earth with all her Circumjacent Particulars Which shews that he takes to himself an unpresidented Dictatorship in Science whereby he would celebrate the Fictions of his Brain without any requisite or probable assurance that they ought to be Conceded To which purpose he Inserts the various Actings of his several Elements tho' by no Body but himself so nam'd and by these so Invented by him together with Vortices and Globuli form'd from them he judges That the Earth with whatsoever it Comprehends might be totally Constituted as he their prime Artificer has contriv'dly set them at work The first Action tending to the compleating of the most refin'd Substance or Parts of the Earth he considers as produc'd by the Motion of the most tenuous Matter of what he Terms a Third Element which he supposes so very pure that even to Transparency it may cause Bodies tho' appertaining to Earthly Composition very clearly to Shine And thus we have the Earth according to the Doctrine of Des-Cartes both a motional and illuminating Planet But should I account the numerous diversities of the fictitious Motions and shifted Inventions by which this Author confers a shining Capacity on some Particulars of the Earth's Substance I might more than fire if not abuse the Patience of an indefatigable Reader Neither could I do other than impertinently load my Pen with repeated Objections and manifest Confutations of his Theories of Motion as they have been diversly apply'd by him on this or other Subjects The Movements of Things in his Method as he annexes their Qualities and Motions being neither exactly agreeable to streight Lines or their proper Tendencies or to such Curv's as might be of Mathematical Construction and therefore inconsistent with the Geometry of Nature Which as to her Works must proceed from a regular Process to which purpose enough has been already written by me I will therefore in this place briefly Inspect the Fond of the shining Attributes that he confers on some Particulars of the Earth as they are stated by him The principal Reason that he offers is That 't is experimentally found that pure Liquor in the Earth of tenuous Consistence is also pellucidous or shining Which cannot be true if by clearness he means an Illuminating Quality No more than the purest Water that can be Imagin'd may be said to Shine because it is clear And who ever beheld any shining Part of the Earth otherwise than by diffus'd Beams of the Sun ' Moon or Stars it might be enlightned tho' without any Illumination as to its own Capacity Where are the Eyes that in a gloomy Day or Night ever observ'd the shining of a Mole-Hill on the Surface of the Earth Or such little Morsels of the Ground as Worms deject which might be compos'd of such Materials as he describes his diminutive Globuli to consist of for any reason given by him to the contrary To confirm these Objections this one that includes many may pertinently be added If as he imagines the diaphanous Parts of any of his Celestial Elements as they are defin'd by him should by any intelligible Movement so operate as they might be so qualitatively Constituted as to embue any particular Substance or Places of the Earth with a shining Capacity since he has undertook to Metamorphose our terrene Habitation into a Planetary Composition How can it be probably apprehended that his Fluid Globuli by their feeble Commotions should be conjoyn'd to the Surface of the Earth notwithstanding that the condense or crusty Parts of her Surface are thickly harden'd and nourish'd by the Roots of Grass Trees Minerals Stones of all kinds diversly temper'd and not possibly penetrable by any compulsive Motion of his diminutive and impotent Globuli unless so much of the gaping Superficies of the Earth could be suppos'd to receive their Fluid Descents to no other purpose than she does Rain when distill'd by the Dissolution of Clouds Which being done there could but a dewy gloss appear on the Ground that might not more imbrighten any Part of the Earth's Figure than when in some moist Seasons the Glow-worm with her Light is engender'd So that whosoever would persuade himself that the terrene World or any Part of it was ever primarily compleated or motionally dispos'd by the Globuli and Vortices comprehended in the Diagrams and Theories of Des-Cartes may as readily believe that the Globe of the Moon was originally produc'd by the efficacious Seeds of a Carret-Bed Nor does he deny in some respects the incongruity of his Principles as in his 18th Particulars he confesses The Materials by which he moulds the Frame of the Earth's Composure and first Existence to be confusedly operative by granting that the liquid Parts which he Attributes to the prime Formation of the Earth were disorderly complicated with his Celestial Globuli Yet might by their Operations in his judgment upwards downwards or transversly be separately distinguish'd by the Similitude he Porduces of a Glass of Wine in the Must having Dregs not only on the top and bottom correspondent to Gravity and Levity but also on the sides of the Glass When afterwards the Wine being clear notwithstanding that it before consisted of various Particulars it becomes pellucidous or shining and not more gross or thicker in any one Part than in another Here he presents his Reader with a Philosophical Weather Glass by which he would determine the temper of the Season when the Earth was forming by his diversified Globuli and whirling assistance of his Vortices Which petty Operators as he states the Metaphor of their Condition and Conduct might be as drunk as Flies may be suppos'd when some of them are as it were giddy on the top of a Glass of strong Liquor or lean to its Sides for supportance whilst others more ebrietously replenish'd heavily sink to the bottom All which may be assimulated without any wrong to the Brain of this Author unto the giddiness of his Phaenomena's It being impossible to conceive from what rational Course of Nature he could produce the Substances together with the Movements of his debauch'd Globuli by which he constitutes the Being of the Earth Considering that he deduces their original Descent from what he Terms his first pure Element In his 19th Head he positively assures us That the Third and main effect of his Celestial Globuli are so perfectly operative that they convert liquorous Drops residing in Air into rotund Figures the reason as he
States it is because those Celestial Globuli find more Passages into a watry Drop than into the Circumjacent Air And by that means as near as may be Move in right Lines or in such as most approximate unto direct lineaments whence it is manifest in his Opinion That such Globuli that are in the Air are less motionally hinder'd as they meet with a watry Drop according to the continuance of their Motions in a streight Line or nearest unto it if that Drop of Liquor be exactly spherical than if it had taken any other Figure But if any Part of the Superficies of that Drop be extended beyond a spherical Figure the Celestial Globuli by their more forcible discursions made in the Air more strenuously assault the watry Drop than were it other Substance and immediately thrust it downwards towards the Center The Reader I presume will excuse me if in this Place and some others of his Writings I deliver the Notions of this Author in more uncouth Accents than I would willingly commit to his Perusal It having been my care no less than necessary Diligence to render as genuinely as might be his Latin Expressions into English If my Remarks on his precedent Praticular had any sharp Allusion dress'd in a plain and familiar Application I cannot rebate on this occasion the point of their tendencies Wherefore if prov'd by me in the foregoing Head tho' by a comical Similitude that his Hypothesis had inebriated his Globuli I may as judiciously Assert That his Sense in the Particular I now Treat of may be by no extravagant Similitude term'd unnatural or Philosophically and Mathematically Intoxicated unless I could Affirm in his behalf that his Globuli which as he supposes might by the force of their whirling Vortices so dispose their Materials to the Constituting of the Earth that the very Grapes that caus'd drunkenness in the Head of the Patriarch Noah were engender'd by some of their giddy Compositions And as sure as the Earth is now in Being Nature might be deem'd out of her Wits if according to his disorderly Process she could be thought to Design the Production of the earthly World Or what can be more improbable than the Tale he tells of his Celestial Globuli converting of liquorous Drops hanging in the Air into round Figures And what Reason does he give why no better than as he supposes That his Globuli may find more passage in watery Drops than in the circumjacent Air But does not common Experience confute this Imagination Let a strenuous Hand fling a smooth Peeble-Stone into the Air and afterwards into Water will it as soon pass any Part of the Superficies of Water as of the Air Or will it not the Water being of a more condense Substance than Air have proportionably a longer Motion and Passage by the ressistance of its thicker Body than might be given by the Tenuity of the Air A Truth so practically evident that it could not be unknown to many of the young Contemporaries at School with Des-Cartes wherefore I wonder to find him of a contrary Opinion here As little concentring in any kind with sound Principles are the Proprieties that he annexes to his Globuli which if in their Motion engaging with any Part of a watry Drop that is extended beyond a spherical Figure they immediately with greater force assail it and by compulsion enforce it towards its Center But if any Part of it be nearer its Center than another his Celestial Globuli contain'd in that watry Drop forthwith imploy their utmost Force to expell it from its Center and next altogether concur to make one spherical Drop Here by a perverse Contradiction he notoriously thwarts the surest Maxims of Philosophy as they pertinently Relate to the Nature and Motion of Corporeal Beings Nor is there any Thing more irrational if not Philosophically absurd than to define as he does globulous Materials and debar them of Motion natural to their Figures It being not possible to imagine that whatsoever is rotund should be more propense to Move in a streight Line or the nearest unto it than in a circular Revolution If a Ball be let fall from the Hand will it it not rotundly Move suitable to its Figure And could this Author imagine That a Demonstration so experimentally obvious would be wav'd by any Principle of his Geometrically Inconsistent or that the exactness of Things circularly Mov'd of all others most perfect should incline to deviate from their Centers Or if that were granted is it at all probable that they could have freer migrations according to this Author through any one of his suppos'd watry Drops than in the tenuous Substance of the Ambient Air Which being done they are in his Sense sometimes compulsively enforc'd towards their Centers if their Figures be not absolutely spherical but if exactly round as forcibly remov'd from their Centers And thus he Implicates if not so crosly Involves Contradictions that he determines the operations of Nature more consonant to the exerting of a Step-dame's Arbitrary Conduct than suitable to the comely Effects by which she regularly produces the Motion and Being of Things All which must be conceded as Principles of Nature incident to her Rule and regular Intention as surely as some of her Materials are more substantially heavy or lighter than others and will therefore have a natural Recourse upwards or downwards to their Centers accordingly Wherefore it may be admir'd in what Fit or Heat of Fancy the Brain of this Monsieur was Inveigled when by so many perplex'd Words as also opposite Terms and Methods he did in a manner angrily Impose the Limitations of his Measures on the stupendious Productions of the Works of Nature Insomuch that his Maxims if soberly consider'd signifie little other than a design'd Rape committed on the Grandeur of her Figure and Beauty together with the providential Facility by which she compleats and preserves her Legitimate Conduct and Operations So that his Invented Elements with all his Diagrams of Vortices and Globuli seem fictitiously devis'd or appertaining to the Imaginary System of some other World since not at all probable that they could belong to the Composure of this But enough has been in this Place and occasionally before I believe satisfactorily Inserted on this Subject that it were impertinently tedious if more be added There remains one Particular that ere I conclude on this Head requisitely deserves a considerable Remark because it Includes a very curious and subtil Mathematical Problem Which he thus expresses the Angle of Contact by which the Tangent Line touches a Circle and by which only it is distant from a right Line is less than any Rectilineal Angle whatsoever and in no Curve Line besides the Circle is every where equal Wherefore he Affirms That a streight Line cannot more equally and less every where inflect or bend from its Points than when it degenerates into a Circular I have read in the History of Algebra written by Dr.