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alone were poffeffed of the right Method of Enquiry. Upon this, he applied himself to mathematical Studies; in order to fee whether, by making the proper Alterations, the mathematical Method could not alfo be accommodated to other Subjects.

11. In particular, he applied himself to Algebra; and found that this The Perfection Art performs even more than it promifes; and with the highest of Algebra. Degree of Certainty: when, having acquired a Habit of folving the greatest Difficulties therein, and examining the fecret Nature of its Method, or Manner of Procedure; he fays, he observed that unknown Truths may be discover'd, after the fame Manner, not only in Mathematics, but in every other Science.

12. He makes the Foundation of human Certainty to lie in thofe The FoundatiThings wherein the Operation of the Understanding is moft manifeft; on of Certainor those which may be conceived, without any Poffibility of a Contra-ty. diction; as that the Whole is greater than a Part; that the Radii of a Circle are equal, &c. whence numerous other Truths may be drawn: and, on the other hand, he lays it down for certain, that those Things which cannot be conceived, are falfe.

13. But here the Author cautions us against being deceived by the The Cautions Imagination; for, according to him, many Things are perceived by the required in Imagination only; of which Things no diftinct Notion, or Conception, laying it. can, by Words, be communicated to another; as in the Case of Pain, Light, Colours, Sound, &c. Hence he recommends two Ways of diftinguishing between the Perceptions of the Imagination, and the Conceptions of the Understanding. The firft is, by large and frequent Experience, and efpecially, by the Help of Mathematics, to acquire a Habit of finding the Difference betwixt them; and the second, is to confider the Equality there is in the human Understanding, which all Men have equally alike for what a Man truly conceives, he can communicate to another; as we fee in mathematical Demonstrations, which are equally understood by all Men; whereas thofe Things which are perceived by the Imagination, as he calls it, are perceived unequally, or more by fome, and lefs by others. And by juftly diftinguishing betwixt these two Powers, or Faculties of the Mind, he fuppofes many great Errors may be avoided.

14. We next proceed to the Author's Method of difcovering new The Way of Truths; wherein he fuppofes that any one may continually advance difcovering него Truths. to an indeterminate Length, without Danger of falling into Error. And here he advises us firft to procure, with great Diligence, a Stock of all the poffible Conceptions which the Mind, in the common Course of Studies and Occafions, takes Cognizance of. For, from these Conceptions, Definitions, in his Method, are to be immediately formed; then Properties to be deduced from thefe Definitions; which Properties he calls by the Name of Axioms: and from the Definitions, combined all Cccc 2

manner

That Men may

nitions.

manner of Ways, he difcovers fecondary Truths, or Theorems; thus making the whole Procefs algebraical.

15. He determines it to be in the Power of Men to form fcientifical form juft Defi-Definitions; and in order to form them juftly, advises us to confider the Manner wherein the Thing to be defined is itself actually formed: or, as he calls it, ftill in Allufion to Mathematics, generated; and from this Confideration, he directs us to derive the Definition. Thus, for Example, he defines Virtue to be the Power which Men have of preferving their own Nature, according to the Laws of juft Reafon; or of procuring to themfelves all the real Perfections both of Body and Mind; or, again, the Perfection, or Melioration of human Nature, according to the Laws of just Reafon.

Rules for 16. To facilitate this Bufinefs of forming Definitions, he lays down forming them. three general Rules. The first is, for reducing Things, in Thought, unThe firft. der their ultimate Kinds, or moft general Conceptions. And thefe highest mental Kinds, or Claffes, he makes to be three; relating to Things Imaginary, Mathematical, and Phyfical: under which Heads all Things that exift may be ranged.

The fecond.

The third.

The Elements of Things.

17. The fecond Rule is, when Things are thus reduced under their highest Kinds, or Claffes, to observe, either by Reafon or Experience, what Things thofe are which remain continually prefent in every Conception.

18. The third Rule is, that all the formed Conceptions be fo order'd, as to fucceed each other, according to what he calls the Number of Poffibilities, or Elements; or according as one Thing fuppofes the Exiftence of another: beginning with the fimple Cafes, and proceeding gradually to the more complex.

19. The first Elements of Imaginary Things, perceived by the Senfe", he makes to be Fluidity, and Solidity; the firft of the Mathematical, he makes to be Points, ftrait Lines, and Curves; and the first of the Phyfical, Matter, Motion, and Reft; without which nothing farther can be conceived. Thefe Rules he explains and illuftrates by many Examples, especially of the mathematical Kind: and then proceeds to fhew the Way of forming Axioms from thefe genuine Definitions; which he fuppofes to be the Elements, or firft Principles of Truths. And by confidering thefe Definitions, either fimply, or comparatively, and in all their elementary Relations, he deduces thofe Truths from them, which he calls Axioms. And thus, by confidering the fcientifical Definitions of a ftrait Line and a Circle, or the Relations arifing from their Generations; large Number of Axioms may be deduced. For Example, from confidering the Generation of a Circle, by the Revolution of a strait Line about a fixed Point, this Axiom arifes; viz. that the Motion is flower

Sce above, f. 13..

flower towards the Centre, and quicker towards the Circumference. And fo in other Cafes.

20. After the requifite Definitions are formed, and compared together, The Method, the last Thing is to combine, or join them with each other, fo as to algebraical.. conftitute what the Author calls Theorems, or new Truths. For two or more Definitions, or Natures, being thus joined together, there may hence arife different Natures, or new Poffibilities, depending upon each other: as we fee in compound Machines, &c. And this the Author again illuftrates with a great Variety of geometrical and phyfical Examples. The whole Procedure he declares to be the fame that is used by the Mafters of Algebra, for folving fuch Problems, as at firft Sight might appear unfolvable, by any human Genius. For a Problem being propofed, the Thing is reprefented to the Eye, as if it were already known and discover'd; fo as clearly to fhew what Particulars are here joined together; whilft the Natures, or Definitions, thereof are either already known, or actually exhibited. Then each different Nature is feparately confider'd, and expreffed by a different Equation, in the most fimple Characters poffible. And now thefe feveral Equations are varioufly compared, or combined together, till a fingle Equation thence arifes, and includes the Natures before exprefs'd by different Equations; fo as clearly to demonftrate how the Queftion propofed may receive a Solution.

Viz. (1.) by

correcting

21. The Author afterwards fhews how his Method of difcovering Truth How to be famay be eafed and in order thereto, firft removes the Impediments in the cilitated. Way; among the chief whereof he places Falfhoods, Prejudices, and Errors; enquires into their Origin; and produces Inftances thereof, in his Errors. three Kinds of Subjects, viz. Imaginary, Mathematical, and Phyfical. He accounts thofe the moft fubtile and treacherous Errors, when imaginary Matters are confounded with real, or physical ones; which he obferves to be done even by the molt acute Philofophers among the Moderns, in laying down the Principles of Nature; and fhews how various Sects and Prejudices have thence arifen, and spread themselves.

22. Thefe falfe Philofophies, and reigning Prejudices, he apprehends (2) Diftin may be corrected two Ways; viz. first, by exactly diftinguishing be- guishing be twixt the Operations of the Understanding, and thofe of the Imagina- twixt the Untion; and, fecondly, by affifting the Understanding, in the Discovery of derstanding and Imagina Truth, with the Imagination directed by a good Method of Inveftiga- tion; and tion. And this Help is afforded, (1.) by a juft adapting of Words to making them Things (2.) by proper Characters for different Ideas; (3) by Motions, co-operate. or moving Engines, and Contrivances, to aflit the Mind in its Operations; and, (4.) by new Experiments, which give new Conceptions. And by this Means he fuppofes the Imagination may be brought to co-operate with the Undertanding..

1 See above, §. 1.3..

23. The

to Utility.

Valuing what 23. The fecond Impediment, he makes to be this; that we do not duly is known; and regard, nor attentively confider, the Things already known: and the having no immediate regard third, that we too much regard the Usefulness of Knowledge, and Difcoveries; whereas, he fays, we ought to content ourselves with the bare Discovery of new Truths: otherwife we block up the Way to the most useful Things of all. For a very fmall natural Power, which in the abstract Conception, appears of very little Significance, may yet prove infinitely useful in its future Applications; as in the Cafe of the Magnetic Needle, Printing, Gunpowder, &c. For numberless Inventions of this Kind may be derived from trivial Experiments.

Work; and ob

taining Time

Helping the 24. The fourth Impediment, he makes to be a natural Indifpofition Indifference of in Men; whence they are not always fit to go upon the Enquiry the Mind; after Truth: and for this Indifpofition he propofes feveral Remedies. Shortning the The fifth Impediment, is a too long Series of Investigation; which he endeavours to remove by a proper Distribution of the Work, and establishing a proper Order. And the fixth Impediment, he makes to be this; that the Affairs of Life often prevent our enquiring after Truth: which Hindrance he proposes to remove, by directing us to follow our own Inclination in Purfuits.

for it.

The Discovery 25. In the laft Place, he comes to deliver the Method of discovering of unknown unknown Truths, with refpect, (1.) to ourselves, in following our own Truths, to reInclinations; (2.) with refpect to thofe Sciences, the Knowledge whereof gard three Particulars. is the moft neceffary, or moft pleafing; and, (3.) with refpect to Natural Philofophy, which, when known is, according to him, the most delightful of all Science. For by Natural Philofophy he understands a Knowledge of the Universe, demonftrated a priori, in exact mathematical Order; and confirmed a pofteriori, by manifeft Experiments, fufficient to convince the Imagination.

The Medicina

ganum.

26. Such is the general Plan of the Medicina Mentis; wherein we may obMentis com- ferve much Sagacity and Ingenuity: but perhaps, when clofely examined, pared with the the Work will appear a little too much influenced by the Notion, which Novum Or the Author at firft efpoufed, of fitting the direct Algebraical Method to univerfal Philofophy; and that he has thus endeavoured to found an univerfal Art of Investigation upon one, which, tho' extremely noble and excellent, is yet limited or confined: or that, at beft, his Method is not fufficiently general, or fitted for univerfal Practice; but rather formed. according to the Model of Man, than the Model of Nature. It may also, till farther improv'd, appear to be more mental than practical; and to be better fitted for folving Phænomena in the ordinary Manner, affigning probable Reasons of Things, and making all fquare with the human Mind; than to discover, and fuch actuating Caufes as fhall enable Men to fubdue and conquer Nature by Works: in which Light, it feems to fall vaftly fhort of the Novum Organum, or Art of Investigating Forms.

27. But

27. But tho' in this principal View, the Medicina Mentis may not be for ufeful as the Novum Organum, yet they have a remarkable Agreement in numerous other refpects; and may be made greatly to affift and promote each other: efpecially the Medicina Mentis will prove ferviceable to the Novum Organum, in the forming of Notions; which M. Tfchirnhaus terms the forming of Definitions. Thus much is certain, that they both deferve to be farther improved, and reduced to Practice for the Field of Nature is fo large, as to require all the Engines, and artificial Helps, that can any way be procured. And if this Method of M. Tfchirnbaus fhall be brought to Perfection, or commodiously fitted for Practice; it will then, perhaps, be found to coincide with the Novum Organum, so as to constitute a Part of that general Engine, from whence, it feems in great measure, to have been derived: for, as the Medicina Mentis is the Algebra of Men, applied to Things; fo the Novum Organum may be called the Algebra of Nature, applied to herself.

who have en

28. Amongst the later Philofophers of our own Nation, who have The English endeavoured to improve, or find out, Methods of making new Discoveries; Philofophers the Principal feem to be Mr. Boyle, Mr. Locke, Dr. Hooke, and Sir Ifaac deavoured at Newton. Mr. Boyle has given us a particular Account of the Method he Methods. purfued, in his Philofophical Enquiries; which plainly appears to be formed upon the Model of the Lord Bacon; and is no other than a loose and imperfect Kind of Induction, proceeding upon certain Tables of Enquiry, or general Heads of History. For in every regular Enquiry, Mr. Boyle firft propofed Mr. Boyle's to himself three Kinds of Orders, Ranks or Claffes, under which he Method. ranged all the Particulars relating to the Hiftory of his Subject; whether it were a Body, a Quality, an Operation, or a Procefs. The firft general Order, or Place, was deftined to receive all fuch Titles, or Heads of Enquiry, as readily occurred upon the firft deliberate View, or general Survey of the Subject; the Titles being made fufficiently numerous and comprehenfive, and not accommodated to any Hypothefis. His Titles of the fecond Order were fet down, after a careful Confideration of the Heads of the firft; trying the Experiments, and making the Obfervations there propofed; and after reading Authors, converfing with Philofophers, and meditating upon the Subject; fo as thus to have procured a full Information with relation to the Whole thereof. This Set of Titles will, of course, be more exact, more full, and better ranged than the first; whence the Materials here contained or indicated, will, with the proper Introduction, Alterations in Method, Connections, Tranfitions, Additions, farther Directions, &c. begin to form a Natural Hiftory of the Subject; that may be improved, from Time to Time, or from Age to Age, till it arrives at Perfection. Laftly, where the Enquiry was difficult, or large, the Author thought proper to form a middle Order of Titles, interpofing betwixt the two former; and this by carefully examining and comparing the feveral Particulars ranged under the Titles of the first Order: fo as thus to difcover many new Directions, and

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