The CATECHISM.

"LET them ask him, whether he can conceive Velocity without Motion, or Motion without Extenſion, or Extenſion without Magnitude? If he anſwers that he can, let him teach them to do the ſame. If he cannot, let him be asked, how he reconciles the Idea of a Fluxion which he gives (P. 13.) with common Senſe? Again, let him be asked, whether nothing be not the Product of nothing multiply'd by ſomething? And if ſo, when the Difference between the Gnomon and the Sum of the Rectangles vaniſheth, [5] whether the Rectangles themſelves do not alſo vaniſh? that is, when ab is nothing, whether Ab + Ba be not alſo nothing? that is, whether the Momen⯑tum of AB be not nothing? Let him then be asked, what his Momentums are good for, when they are thus brought to nothing? Again, I wiſh he were asked to explain the Difference be⯑tween a Magnitude infinitely ſmall and a Magnitude infinitely diminiſh'd? If he faith there is no Difference, then let him be asked, how he DARES to explain the Method of Fluxions by the Ratio of Magnitudes infinitely dimi⯑niſh'd (P.9.) when Sir Iſaac Newton hath expreſly excluded all Conſidera⯑tion of Quantities infinitely ſmall? If this able Vindicator ſhould ſay that Quantities infinitely diminiſh'd are no⯑thing at all, and conſequently that, according to him, the firſt and laſt Ratios are Proportions between no⯑things, let him be deſired to make Senſe of this or explain what he means by 'Proportion between nothings. If he ſhould ſay the ultimate Proportions [6] are the Ratios of mere Limits, then let him be asked how the Limits of Lines can be proportioned or divided? After all, who knows but this Gentle⯑man, who hath already complained of me for an uncommon Way of treating Mathematics and Mathematicians, may (as well as the Cantabrigian) cry out Spain and the Inquiſition when he finds himſelf thus cloſely purſued and beſet with Interrogatories? That we may not therefore ſeem too hard on an innocent Man, who probably meant nothing, but was betray'd by following another into Difficulties and Straits that he was not aware of, I ſhall propoſe one ſingle Expedient, by which his Diſciples (whom it moſt concerns) may ſoon ſatisfy themſelves, whether this Vindicator really underſtands what he takes upon him to vindicate. It is in ſhort, that they would ask him to ex⯑plain the ſecond, third or fourth Fluxi⯑ons upon his Principles. Be this the Touchſtone of his Vindication. If he can do it, I ſhall own my ſelf much miſtaken: If he cannot, it will be evi⯑dent [7] that he was much miſtaken in himſelf, when he preſumed to defend Fluxions without ſo much as knowing what they are. So having put the Me⯑rits of the Cauſe on this Iſſue, I leave him to be tried by his Scholars."

III. In this CATECHISM I am firſt to be: asked, "Whether I can conceive Velocity without Motion, or Motion without Extenſion, or Extenſion with⯑out Magnitude?" Theſe Queſtions are more clearly expreſs'd in the 29th and 30th Queries of his Analyſt, where he asks, "Whether we can form an Idea or Notion of Velocity diſtinct from and excluſive of its Meaſures? Whether Motion can be conceived in a Point of Space? And if Motion cannot, whether Velocity can? And if not, whether a firſt or laſt Velocity can be conceived in a mere Li⯑mit, either initial or final, of the deſcrib⯑ed Space?" I anſwer, I can conceive Velocity and Motion in a Point of Space; that is without any aſſignable Length or Extenſion deſcribed by it, and ſo might he too if he had underſtood and conſider'd [8] the Nature of Motion. For Moti⯑on is an Effect of ſome Cauſe acting on the Thing moved; which Effect ſetting aſide all Reſiſtance, will ever be propor⯑tional to the whole Action of the gene⯑rating Cauſe: And therefore if a Cauſe acts continually upon a given Thing with⯑out any Interruption, there muſt be a con⯑tinual Increaſe of its Velocity. The Ve⯑locity cannot be the ſame in any two different Points of the Space deſcribed, however near thoſe Points may be to each other. For if it was, there muſt: be a Ceſſation of the Action of the moving Cauſe during the Paſſage of the Thing thro' the Space comprehended between the two Points; which is contrary to the Suppoſition.

[9] If the Thing moved be a Point, and the Space deſcribed by this Point ſetting out from a State of Reſt at A, be AD;

and if the Point be acted upon con⯑tinually by a moving Cauſe during the Time of its going from A to D, and the Cauſe act continually with the ſame Degree of Strength during that Time; the Velocity will con⯑tinually increaſe with the Time of the Motion, or with the Square Root of the Space deſcribed; that is, the Velocities in the Points C and D, will be in the ſame Proportion as the Times of deſcribing AC and AD, or as the Square Roots of AC and AD. Theſe are the Laws of Motion obſerved by Bodies falling from ſmall Heights to the Surface of the Earth, ſetting aſide the Reſiſtance of the Air, and ſuppoſing the Bodies to have exactly the ſame Weights during the Times of their Fall.

If the Cauſe acts continually upon the moving Point, but with different Degrees of Strength during the Time of the Mo⯑tion; the Velocity will not increaſe with the Time, nor with the Square Root of the [10] Space deſcribed; but will ſtill increaſe from the Beginning to the End of the Motion, and not be the ſame in any two different Points of the Space deſcribed, however near to each other. Let the Velocity increaſe with the n Power of the Time, that is, let V be as Tⁿ; and then V will be as [...] or as [...], putting S for the Space deſcrib'd: Whence it appears that the Velocity will not be the ſame in any two different Points of the Space deſcribed: For it muſt vary upon the leaſt Change of the Space S, and conſequently be different in every different Point of AD; which ſhews that this Author has been greatly miſtaken in imagining that there can be no Motion, no Velocity, in a Point of Space.

IV. The next Queſtions in the CA⯑TECHISM, depending upon each other, run thus. "Let him be asked, whether nothing be not the Product of nothing multiply'd by ſomething? And if ſo, when the Difference between the Gno⯑mon [11] and Sum of the two Rectangles vaniſheth, whether the Rectangles themſelves do not alſo vaniſh? that is when a b is nothing, whether Ab + Ba be not alſo nothing? that is, whether the Momentum of AB be not nothing? And let him be asked what his Mo⯑mentums are good for when thus they are reduced to nothing?" As to the firſt of theſe Queſtions I agree with him that nothing is the Product of nothing multiply'd by ſomething; but muſt know what he means by the vaniſhing of the Gnomon and Sum of the two Rectangles in the ſecond, before I give him a direct Anſwer. If by vaniſhing he means that they vaniſh and become no⯑thing as Areas, I grant they do; but ab⯑ſolutely deny, upon ſuch an Evaneſcence of the Gnomon and Sum of the two Rect⯑angles by the moving back of the Sides of the Gnomon till they come to coin⯑cide with thoſe of the Rectangle, that nothing remains. For there ſtill remain the moving Sides, which are now become the Sides of the Rectangle; into which Sides both the Gnomon and the Sum of [12] the two Rectangles are now turned by this retroverted Motion. And as the Gno⯑mon and Sum of the two Rectangles, up⯑on the Evaneſcence of their Areas by this retroverted Motion, are both con⯑verted into the two Sides of the Rect⯑angle AB, ſo in the Inſtant of that Con⯑verſion, their Motions are exactly the ſame; or the Motion of the Gnomon is the ſame with the Sum of the Motions of the two Rectangles, when they evaneſce, and are converted into the two Sides of the Rectangle AB.

If a Point moves forward to generate a Line, and afterwards the ſame Point moves back again to deſtroy the Line with the very ſame Degrees of Velocity, in all Parts of the Line which it had in thoſe Parts when moving forward to ge⯑nerate it; in the Inſtant the Line vaniſhes as a Length, nothing of a Line will re⯑main; but ſtill the generating Point will remain, together with the Velocity it had at the very Beginning of its Motion. And the Caſe is the very ſame with reſpect to a Rectangle increaſing by the Motion of [13] its Sides: For upon the Evaneſcence of a generated Gnomon, there ſtill remain the Sides of the Rectangle into which the Gnomon by its Evaneſcence is converted, together with the Velocities of thoſe Sides that is, when the Gnomon eva⯑neſces there ſtill remains Ab + Ba.

To make this more evident to Senſe; let the Point which generated the Line AD,

move back again from D to C with the very ſame Degrees of Ve⯑locity in every Part of the Incre⯑ment CD which it had in that part in moving forward from C to D; and when the Increment CD eva⯑neſces and becomes nothing as a Line by being converted into the moving Point in C; there will remain that that Point together with its Motion in C; for neither the Point nor its Motion in C is deſtroy'd by the Evaneſcence of the Line CD.

[14] If the Rectangle CDK be generated by the Motions of two indefinite right Lines IB and IA, of IB down IA and of IA along IB, and from a Continuance of the Motions of theſe Lines, be in⯑creaſed by the Gnomon CGK; and if

the generating Lines return from L and E to K and C, with the very ſame Degrees of Velocity in the ſeveral Points of LK and EC which they had in thoſe Points in moving from K and C to L and E; it is evident, when the Gnomon CGK or the Increment of the Rectangle CDK evaneſces and becomes nothing as an Area, by being converted into the Sides DK and DC; that there will remain thoſe Sides and their Velocities in D; neither the Sides nor the Velocities of thoſe [15] Sides being deſtroy'd by the Evaneſcence of the Area of the Gnomon. But per⯑haps he will ſay, that when the Gnomon evaneſces it turns into ſomething more than the Sum of the Sides DK and DC: For the Rectangles LD and FC turn into thoſe Sides, and the Rectangle FH turns into a Point at D; and therefore the Mo⯑tion of the Gnomon in the Inſtant it eva⯑neſces, will become the Sum of the Mo⯑tions of the Sides DK and DC, and of the Point in D; that is, putting A and B for DK and DC, and a and b for the Velocities in D towards F and H, and p for a Point; it will be equal to Ab + Ba + ap + bp: Let it be ſo, and yet a+b × p will be nothing when compared with Ab + Ba, nor make the leaſt Augmentation to that Sum when added to it. For let a be to b as 3 to 2, and Ab + Ba + ap + bp will be 2A + 3B + 5p: But 5p or five Points added to a Line, make no⯑thing but the Line itſelf; a Point being no Part of a Line; and conſequently not in the leaſt increaſing its Length when added to it: And therefore the Motion of the Gnomon when it evaneſces and [16] turns into the Sides of the Rectangle CDK, will be Ab + Ba, as Sir Iſaac Newton makes it.

If the Curvilineal Area ABD be gene⯑rated by the Motion of any indefinite Line AH down AG, While a Point ſet⯑ting out from A moves in the Line AH from A towards H; and if from a Con⯑tinuance of theſe two Motions that Area be increaſed by the Augment BDFE,

conſiſting of the Rectangle BC and of the Triangle CFD; the Motion with which the Increment BDFE begins to be generated, is the Sum of the two Mo⯑tions towards C and H in the Point D; which Sum, putting b for the Velocity towards C, a for the Velocity towards H [17] and p for a Point, will be BD×b + ap. Now ſuppoſe the Ordinate EF to move back to BD, and the Point F to move back in the Line HE to C, and that in moving back they have the ſame Degrees of Ve⯑locity in every Point of EB and EH, which they had before in moving for⯑ward; it is manifeſt, that when the Aug⯑ment BDFE vaniſhes and becomes no⯑thing as an Area, by being converted into the Ordinate BD, and into a Point at the Extremity of that Ordinate; there will remain BD and the Point in D, together with their Velocities in that Point; for the Motions of that Line and Point, are not deſtroy'd by the Evaneſcence of the Area BDFE, In the Inſtant EF coin⯑cides with BD, and the Point F with D, the Area BDFE will be converted into BD + p, and its Motion will become BD × b + pa, as before. But pa, being only ſo many Points as a contains Units, is real⯑ly and truly nothing with reſpect to BD × b; and conſequently does not at all increaſe it when added to it. And there⯑fore the Fluxion of the curvilineal Area ABD, will be BD × b; or as BD if b [18] be given, or the Line AH move down AG with a Velocity which is exactly the ſame in every Part of GA.

Hence it appears, that if mathematical Quantities be increaſed in equal Times by Motion, their iſochronal Increments muſt be made to vaniſh by a Retroverſion of the Motion, before we can obtain the Motions with which they vaniſh, or begin to be generated; that is, before we can obtain the Fluxions of the Quantities, the Name given by Sir Iſaac Newton to thoſe Motions. So then, this Author has been much out in ſuppoſing that upon the Evaneſcence of the Gnomon CGK, or of the curvilineal Figure BDFE, the Momentum or Fluxion of the Rectangle CDK, or of the Area ABD, vaniſhes. Conſequently, he has been greatly miſta⯑ken in every one of theſe Queſtions.

V. But he goes on. "I wiſh he were asked to explain the Difference between a Magnitude infinitely ſmall and a Mag⯑nitude infinitely diminiſhed. If he ſaith there is no Difference: Then let [19] him, be further asked, how he DARES to explain the Method of Fluxions by the Ratio of Magnitudes infinitely di⯑miniſh'd, when Sir Iſaac Newton hath expreſly excluded all Conſideration of Quantities infinitely ſmall? If this able Vindicator ſhou'd ſay that Quantities infinitely diminiſh'd are nothing at all, and conſequently that, according to him, the firſt and laſt Ratios are Pro⯑portions between nothings, let him be deſired to make Senſe of this, or ex⯑plain what he means by Proportion between nothings. If he ſhou'd ſay the ultimate Proportions are the Ratios of mere Limits, then let him be asked how the Limits of Lines can be pro⯑portioned or divided?"

As all this Part of the CATECHISM relates to the Meaſures of Fluxions by the firſt and laſt Ratios of iſochronal Increments generated and deſtroy'd by Motion, ſo I have taken it together, and ſhall anſwer the whole in one Section.

[20] Neither Sir Iſaac Newton nor I have ſaid, that Fluxions are meaſured by the Proportions of Magnitudes infinitely ſmall, nor by the Proportions of any Magnitudes whatever generated in equal Times; but that they are meaſured by the firſt or laſt Proportions of iſochro⯑nal Increments generated or deſtroy'd by Motion; which Proportions are the Ratios with which ſuch Increments be⯑gin to exiſt before they have acquired any Magnitude, or with which they ceaſe to exiſt and vaniſh after they have loſt all Magnitude. Theſe Ratios ſub⯑ſiſt when the iſochronal Increments have no Magnitude, for as much as the Moti⯑ons ſubſiſt with which thoſe Increments, juſt now, in this very Inſtant, begin or ceaſe to exiſt; to which Motions theſe Ratios are proportional.

For Example, the firſt or laſt Ratio of the Increments CD and EF generated in equal Times, has a real Exiſtence; for as much [21] as it is equal to the Ratio of the Motions in C and E,

which are the Mo⯑tions ſubſiſting in thoſe Points when the iſchronal Increments juſt begin or ceaſe to exiſt. The Exiſtence of the Motions preſerves the Exiſtence of theſe Ratios of the Increments CD and EF. If the Ratio of the Motions in C and E, be that of 4 to 3; the firſt or laſt Ratio of the iſochronal Increments CD and EF, will likewiſe be that of 4 to 3, even tho' no Part of thoſe Incre⯑ments has any Exiſtence.

The Motions in C and E, are as the moving Quantities and Velocities taken together; or as two Points and their Ve⯑locities, taken together; or as the Veloci⯑ties, all Points being equal. And the firſt or laſt Ratio of the iſochronal Incre⯑ments CD and EF, is compounded of the firſt or laſt Ratio of theſe Spaces, and of the Ratio of the moving Quanti⯑ties. For the Velocities in C and E be⯑ing in the firſt or laſt Ratios of theſe [22] iſochronal Spaces, the Motions, which are as the moving Quantities and Velocities taken together, will be as the ſame moving Quantities and the firſt or laſt Ratio of the iſochronal Spaces taken together. If Q and q denote the moving Quantities in C and E, V and v their Velocities, S and s the iſochronal Spaces CD and EF, and Ṡ and ṡ the firſt or laſt Ratio of thoſe iſochronal Spaces; then QV will be to qv, as QṠ to qṡ; and in this caſe V will be to v, as Ṡ to ṡ, becauſe Q and q are equal.

Again, the firſt or laſt Ratio of the iſochronal Spaces FD and DH in the augmented Rectangle EGL (See the Fi⯑gure in Page 14.) has a real Exiſtence; for as much as it is equal to the Ratio of the two Motions of two Points in D, of one towards F, and the other towards H; which Motions, ſubſiſting when the iſo⯑chronal Spaces FD and DH are nothing, preſerve the Exiſtence of the firſt or laſt Ratio of theſe Spaces, or keep it from being a Ratio of nothings. If V and v, denote the Velocities in D towards F [23] and H, Q and q the Sides of the Rect⯑angle DK and DC, and Ṡ and ṡ the firſt or laſt Ratio of the iſochronal Spaces FD and DH; then Q v will be to qV, as Qṡ to qṠ; but Qv + qV is the Fluxi⯑on or Motion of the Rectangle CDK, as I have ſhewn before; and therefore the Moment or Meaſure of the Fluxion of the Rectangle will be Qṡ + qṠ. This is a full and clear Anſwer to this Part of the CATECHISM, and ſhews that its Author has been greatly miſtaken in ſup⯑poſing that I explained the Doctrine of Fluxions by the Ratio of Magnitudes infinitely deminiſh'd, or by Proportions between nothings.

VI. I come now to the laſt Part of the CATECHISM, which ſtands thus. "I ſhall propoſe one ſingle Expedient, by which his Diſciples (whom it moſt concerns) may ſoon ſatisfy themſelves, whether this Vindicator really under⯑ſtands what he takes upon him to vindi⯑cate. It is in ſhort, that they wou'd ask him to explain the ſecond, third, or fourth Fluxions upon his Principles. Be this [24] the Touchſtone of his Vindication: If he can do it, I ſhall own my ſelf much miſtaken: If he cannot it will be evident that he was much miſtaken in himſelf, when he preſumed to de⯑ſend Fluxions without ſo much as knowing what they are. So having put the Merits of the Cauſe on this Iſſue, I leave him to be tried by his Scholars."

I do not wonder that this Author ſhou'd have no clear Ideas or Conceptions of ſecond, third or fourth Fluxions, when he has no clear Conceptions of the com⯑mon Principles of Motion, nor of the firſt and laſt Ratios of the iſochronal Increments of Quantities generated and deſtroy'd by Motion. For Fluxions, according to Sir Iſaac Newton, are the Motions with which the iſochronal Increments of Quantities be⯑gin or ceaſe to exiſt, or the Motions of the generating Quantities in the very Limits or Extremities of the Fluents: Thus the Fluxions of Solids are the Motions of Surfaces; the Fluxions of Surfaces, the Motions of Lines; the Fluxions of Lines, [25] the Motions of Points; and the Fluxions of Points are nothing, for Points in their own Nature are invariable, and therefore incapable of being generated or increaſed by Motion: And if the firſt Fluxions of Quantities be Motions, it follows, that the Mutations of theſe Motions and the Mutations of thoſe Mutations, which are the ſecond and third Fluxions of the Quantities, muſt likewiſe be Motions.

Firſt, ſecond and third Fluxions do real⯑ly exiſt, and may be clearly and diſtinct⯑ly conceiv'd by attending to the Motions of the ſeveral Parts of a Cube, namely, of its Surfaces of their Lines and Points, in the Inſtant it begins to be increas'd by Motion. For if A denotes the Side of a Cube generated by an uniform Motion, whoſe Velocity is expreſs'd by a; the firſt Fluxion of the Cube, according to theſe Principles, will be expreſſed by 3aA²; its ſecond Fluxion, which is the Fluxion of 3aA², will be expreſſed by 6a2A, or by 6aA × a; its third Fluxion, which is the firſt Fluxi⯑on on of 6a2A, will be expreſs'd by 6a3 or by 6a2 × a; and its fourth Fluxion will [26] be nothing: But all theſe Fluxions or Mo⯑tions do exiſt, and may be clearly and diſtinctly conceived in the Motion of a Cube, at the very End of its Generation, or at the very Beginning of its Augmen⯑tation, by Motion; for it begins to be augmented by the Sum of the Motions of three of its Squares comprehending any one of its ſolid Angles, each of which Squares being denoted by A² and their Velocity outward by a, the Fluxion of the Cube or the Motion with which it begins to increaſe or to be enlarged, will be 3aA²; and this is the firſt Fluxion of the Cube; and the three moving Squares begin to be augmented, in the very ſame Inſtant wherein the Cube be⯑gins to enlarge, each by the Sum of the Motions of its two adjoining Sides, and conſequently the Motions of thoſe Sides to augment the cubic Surface, will be expreſs'd by 6aA, but that Surface at the ſame Inſtant of Time moves outward to augment the Solid with a Velocity which is alſo denoted by a, and there⯑fore the whole Motion of the fix moving Sides of the three Squares for increaſing [27] or enlarging the Cube, will be expreſſed by 6aA × a or by 6a2A; and this is the ſecond Fluxion of the Cube; and when the three moving Squares begin thus to increaſe, ſideways and outwards, for the Enlargement of the Cube, their ſix mo⯑ving Sides begin to be augmented by the Motion of ſix Points; and the common Velocity of thoſe Points in order to in⯑creaſe the Sides of the Squares, being the ſame with the Velocity of thoſe Sides to increaſe the Cubic Surface, and with the Velocity of that Surface to augment the Solid; the whole Motion with which thoſe Points begin to enlarge the Cube, will be expreſs'd by 6a3 or by 6a3 p; and this is the third Fluxion of the Cube: Theſe three Kinds of Motion do all ne⯑ceſſarily exiſt and may be clearly and diſtinctly conceived in the Syſtem of Motion whereby a Cube begins to be augmented: And therefore the firſt, ſe⯑cond and third Fluxions of Quantities may be diſtinctly conceived, and fully ex⯑plained upon the Principles of Sir Iſaac Newton.

[28] As firſt, ſecond and third Fluxions are explained by the ſeveral Motions neceſ⯑ſarily exiſting in the very Inſtant a Cube begins to be augmented, ſo they may like⯑wiſe be explain'd and distinctly compre⯑hended, by conſidering the naſcent or evaneſcent Increments of the ſeveral Parts of a Cube, generated by Motion; pro⯑vided always that by naſcent or evane⯑ſcent Increments be underſtood not gene⯑rated Increments of any Magnitude what⯑ever, but only ſuch Quantities or Mag⯑nitudes as are proportional to and Conſe⯑quently Meaſures of the Motions with which thoſe iſochronal Increments begin or ceaſe to exiſt. For if a, which before denoted Velocity, be now put for the firſt or laſt Ratio of the Space deſcribed by that Velocity in a given Time; 3aA² will denote the naſcent Increment of the Cube generated by the Motion of three of its Squares comprehending any one of its ſolid Angles; and 6aA will expreſs the Sum of the naſcent Increments of the three moving Squares, which Sum mul⯑tiply'd into a will be the Increment of the naſcent Solid 3aA²; conſequently [29] 6a2A will be the ſecond naſcent Incre⯑ment of the Cube; and the naſcent In⯑crement of 6Aa, or of ſix Rectangles each denoted by Aa, will be 6a2, which multiply'd into a gives 6a3 for the naſcent Increment of 6a2A, and therefore 6a3 is the third naſcent Increment of the Cube: All this may be clearly conceiv'd and made evident to Senſe by the Figure in Page 14. For let CDK repreſent one of the three moving Squares compre⯑hending any of the ſolid Angles of a Cube increaſing by Motion, and then three times CDK multiply'd into a, or 3aA², will expound the firſt naſcent In⯑crement of the Cube; and 3FC + 3LD or 6Aa (which is the naſcent Increment of the three moving Squares) multiply'd into a, will be the ſecond naſcent Incre⯑ment of the Cube; and, the Rectangle FH or a2 being the naſcent Increment of the Rectangle FC or LD, and 2FH or 2a2 the naſcent Increment of FC + LD or of 2Aa, and 6a2 the naſcent Incre⯑ment of 6Aa, it follows that 6a2 multi⯑ply'd into a, or that 6a3, will be the naſcent Increment of 6Aa2 and conſequently [30] the third naſcent Increment of the Cube. And theſe three diſtinct Orders of Incre⯑ments, all begin to exiſt together, in the very Inſtant the Cube begins to be aug⯑mented by Motion.

This may ſerve as an Anſwer to the laſt Part of the CATECHISM, concern⯑ing the Author's Touchſtone of my Vin⯑dication: Whether he will own himſelf miſtaken I know not; but I think he ought after his unjuſt and ſhameful Treat⯑ment of Sir Iſaac Newton; who in the Introduction to his Quadrature of Curves, in the ſecond Lemma of the ſecond Book, and in the Scholium to the firſt Section of the firſt Book of his Principles of Philoſophy, has deliver'd his Doctrine of Fluxions in ſo clear and diſtinct a Manner, without the leaſt In⯑conſiſtency in Terms or Arguments, that one wou'd have thought it impoſſible for any Perſon not to have underſtood him, particularly for this Author, who ſays, he had long and maturely conſidered thoſe Principles, and taken as much pains as [31] any Man living to underſtand and make Senſe of them.

I have now done with the CATECHISM; but beg leave before I conclude this Pa⯑per, in order to prevent my being CATE⯑CHISED any more by this Author, to give the World a ſhort Account of ſome Part of my Faith in Religion. I believe that there is one ſupreme, incorporeal, ever⯑living, intelligent and omnipreſent Being, called GOD, who made and governs the World. I believe that GOD is endued with infinite Power, Knowledge, Wiſ⯑dom and Goodneſs; and that to deny or limit any one of theſe Attributes, is in Effect to deny a GOD. I believe, that to ſay GOD cannot create Spirits with a Power, inherent in themſelves and reſult⯑ing from their own Frame and Make, of perceiving and knowing. Things of a quite different Nature from their own, by Ideas and Senſations; is in Effect to deny a GOD; for as much as by this Principle his Almighty Power is denied. And laſtly, I believe that this Supreme Being has revealed his Will to Mankind [32] by Moſes, the Prophets, Jeſus Chriſt and the Apoſtles; and that the Doctrine by them deliver'd is therefore divine, and cannot be altered by any Power or Authority upon Earth, nor even by an Angel from Heaven, who is pronounced accurſed ſhou'd he preach any other Goſ⯑pel than what is delivered.