Mathematicks, Pure and Mixt

Neverthelesse there remaineth yet another part of Naturall Philosophie, which is commonly made a principall part, and holdeth ranke with Phisicke speciall and Metaphisicke: which is Mathematicke, but I think it more agreable to the Nature of things, and to the light of order, to place it as a Branch of Metaphisicke: For the subject of it being Quantitie, not Quantitie Indefinite: which is but a Relative, and belongeth to Philosophia Prima (as hath beene said,) but Quantitie determined, or proportionable, it appeareth to bee one of the essentiall formes of things; as that, that is causative in Nature of a number of Effects, insomuch as wee see in the Schooles both of Democritus, and of Pithagoras, that the one did ascribe Figure to the first seedes of things, and the other did suppose numbers to bee the principalles and originalls of things; And it is true also that of all other formes (as wee understand formes) it is the most abstracted, and separable from matter and therefore most proper to Metaphisicke; which hath likewise beene the cause, why it hath beene better laboured, and enquired, then any of the other formes, which are more immersed into Matter. For it beeing the Nature of the Minde of Man (to the extreame prejudice of knowledge) to delight in the spacious libertie of generalities, as in a champion Region; and not in the inclosures of particularitie; the Mathematicks of all other knowledge were the goodliest fieldes to satisfie that appetite. But for the placing of this Science, it is not much Materiall: onely we have endevoured in these our Partitions to observe a kind of perspective, that one part may cast light upon another.

The Mathematicks are either Pure, or Mixt: To the Pure Mathematicks are those Sciences belonging, which handle Quantitie determinate meerely severed from any Axiomes of Naturall Phlosophy: and these are two, Geometry and Arithmeticke, The one handling Quantitie continued, and the other dissevered. Mixt hath for subject some Axiomes or parts of Naturall Philosopie: and considereth Quantitie determined, as it is auxiliarie and incident unto them. For many parts of Nature can neither be invented with sufficient subtiltie, nor demonstrated with sufficient perspicuitie, nor accommodated unto use with sufficient dexteritie, without the aide and interveyning of the Mathematicks: of which sorte are Perspective, Musicke, Astronomie, Cosmographie, Architecture, Inginarie, and divers others. In the Mathematicks, I can report noe deficience, except it be that men doe not sufficiently understand the excellent use of the pure Mathematicks, in that they doe remedie and cure many defects in the Wit, and Faculties Intellectuall. For, if the wit bee to dull, they sharpen it: if to wandring, they fix it: if to inherent in the sense, they abstract it. So that, as Tennis is a game of noe use in it selfe, but of great use, in respect it maketh a quicke Eye, and a bodie readie to put it selfe into all Postures: So in the Mathematickes, that use which is collaterall and intervenient, is no lesse worthy, then that which is principall and intended. And as for the Mixt Mathematikes I may onely make this prediction, that there cannot faile to bee more kindes of them, as Nature growes furder disclosed. Thus much of Natural Science, or the part of Nature Speculative.

For Naturall Prudence, or the part Operative of Naturall Philosophy, we will devide it into three parts, Experimental, Philosophical and Magical, which three parts Active have a correspondence and Analogie with the three parts Speculative: Natural History, Phisicke, and Metaphisicke: For many operations have bin invented sometime by a casuall incidence and occurrence, sometimes by a purposed experiment: and of those which have bene found by an intentionall experiment, some have bin found out by varying or extending the same experiment, some by transferring and compounding divers experiments the one into the other, which kind of invention an Emperique may manage. Againe by the knowledge of Phisicall causes, there cannot faile to followe, many indications and designations of new particulers, if men in their speculation will keepe one eye upon use & practise. But these are but Coastings along the shoare, Premendo littus iniquum, For it seemeth to me, there can hardly bee discovered any radicall or fundamentall alterations, and innovations in Nature, either by the fortune & essayes of experiments, or by the light and direction of Phisical causes. If therfore we have reported Metaphisicke deficient, it must followe,11Naturalis Magiasive Phisica Operativa Major. that wee doe the like of Natural Magicke, which hath relation thereunto. For as for the Natural Magicke whereof now there is mention in books, containing certaine credulous and superstitious conceits and observations of sympathies, and Antipathies and hidden Proprieties, and some frivolous experiments, strange rather by disguisement, then in themselves, It is as far differing in truth of Nature, from such a knowedge as we require, as the storie of King Arthur of Brittaine, or Hughe of Burdeaux, differs from Cæsars commentaries in truth of storie. For it is manifest that Cæsar did greater things de vero, then those Imaginarie Heroes were fained to doe. But hee did them not in that fabulous manner. Of this kinde of learning the fable of Ixion was a figure: who designed to enjoy Juno the Goddesse of power: and in stead of her, had copulation with a Cloud: of which mixture were begotten Centaures, and Chymeraes. So whosoever shall entertaine high and vapourous imaginations, in steede of a laborious and sober enquirie of truth shall beget hopes and Beliefes of strange and impossible shapes. And therefore wee may note in these Sciences, which holde so much of imagination and Beliefe, as this degenerate Naturall Magicke, Alchimie, Astrologie, and the like, that in their propositions, the description of the meanes, is evermore monstrous, then the pretence or ende. For it is a thing more probable, that he that knoweth well the Natures of Waight, of Colour, of Pliant, and fragile in respect of the hammer, of volatile and fixed in respect of the fire, and the rest, may superinduce upon some Mettall the Nature, and forme of Gold by such Mechanique as longeth to the production of the Naturs afore rehearsed, then that some graynes of the Medecine projected, should in a fewe Moments of time, turne a Sea of Quick-silver or other Materiall into Gold. So it is more probable that he that knoweth the Nature of Arefaction; the Nature of assimilation, of nourishment to the thing nourished; the Maner of encrease, and clearing of spirits: the Maner of the depredations, which Spirits make upon the humours and solide parts: shall, by Ambages of diets, bathings, annointings, Medecines, motions, and the like, prolong life, or restore some degree of youth or vivacitie, then that it can be done with the use of a sewe drops, or scruples of a liquor or receite. To conclude therefore, the true Naturall Magicke, which is that great libertie and Latitude of operation, which dependeth uppon the knowledge of formes, I may report deficient, as the Relative thereof is; To which part if we be serious, and incline not to vanities and plausible discourse, besides the deriving and deducing the operations themselves from Metaphisicke, there are pertinent two points of much purpose, the one by way of preparation, the other by way of caution: The first is, that there be made a Kalender resembling an Inventorie of the estate of man, containing all the22Inventarium Opum bumanarum. inventions, (being the works or fruits of Nature or Art) which are now extant, and whereof man is alreadie possessed, out of which doth naturally result a Note, what things are yet held impossible, or not invented, which Kalender will bee the more artificiall and serviceable, if to every reputed impossibilitie, you adde what thing is extant, which commeth the nearest in degree to that Impossibilitie; to the ende, that by these Optatives and Potentialls, Mans enquirie may bee the more awake in diducing direction of works from the speculation of causes. And secondly that those experiments be not onely esteemed which have an immediate & present use, but those principally which are of most universall consequence for invention of other experiments, & those which give most light to the Invention of causes; for the Invention of the Mariners Needle, which giveth the direction, is of noe lesse benefit for Navigation, then the invention of the sailes which give the Motion.

Thus have I passed through Naturall Philosophie, and the deficiences thereof; wherein if I have differed from the ancient, and received doctrines, and thereby shall move contradiction; for my part, as I affect not to dissent, so I purpose not to contend; If it be truth.

The voice of Nature will consent, whether the voice of Man doe or noe. And as Alexander Borgia was wont to say of the expedition of the french for Naples, that they came with Chaulke in their hands to marke up their lodgings, and not with weapons to fight: So I like better that entrie of truth which commeth peaceably with Chaulke, to marke up those Mindes, which are capable to lodge and harbour it, then that which commeth with pugnacitie and contention.

But there remaineth a division of Naturall Philosophy according to the Report of the Enquirie, and nothing concerning the Matter or subject, and that is Positive and Considerative: when the enquirie reporteth either an Assertion, or a Doubt. These doubts or Non Liquets, are of two sorts, Particular and Totall. For the first wee see a good example thereof in Aristotles Problemes, which deserved to have had a better continuance, but so neverthelesse, as there is one point, whereof warning is to be given and taken; The Registring of doubts hath two excellent uses: The one that it saveth Philosophy from Errors & falshoods: when that which is not fully appearing, is not collected into assertion, whereby Error might drawe Error, but reserved in doubt. The other that the entrie of doubts are as so many suckers or sponges, to drawe use of knowledge, insomuch as that which if doubts had not preceded, a man should never have advised, but passed it over without Note, by the suggestion and sollicitation of doubts is made to be attended and applied. But both these commodities doe scarcely countervaile an Inconvenience, which wil intrude it selfe if it be not debarred, which is that when a doubt is once received, men labour rather howe to keepe it a doubt still, then howe to solve it, and accordingly bend their wits. Of this we see the familiar example in Lawyers and Schollers, both which if they have once admitted a doubt, it goeth ever after Authorized for a doubt. But that use of wit and knowledge is to be allowed which laboureth to make doubtfull thinges certaine, and not those which labour to make certaine things doubtfull. Therefore these Kalenders of doubts, I commend as excellent things, so that there be this caution used, that when they bee throughly sifted & brought to resolution, they bee from thence forth omitted, decarded, and not continued to cherish and encourage men in doubting.33Continuatio Problematum in Natura. Catalogus Falsitatum grassantium in historia Naturæ. To which Kalender of doubts or problemes, I advise be annexed another Kalender as much or more Materiall, which is a Kalender of popular Errors, I meane chiefly, in naturall Historie such as passe in speech & conceit, and are neverthelesse apparantly detected & convicted of untruth, that Mans knowledge be not weakened nor imbased by such drosse and vanitie. As for the Doubts or Nonliquets generall or in Totall, I understand those differences of opinions touching the principles of Nature, and the fundamentall points of the same, which have caused the diversitie of Sects, Schooles, and Philosophies, as that of Empedocles, Pythagoras, Democritus, Parmenides, and the rest. For although Aristotle as though he had bin of the race of the Ottomans, thought hee could not raigne, except the first thing he did he killed all his Brethren; yet to those that seeke truth and not Magistralitie, it cannot but seeme a Matter of great profit, to see before them the several opinions touching the foundations of Nature, not for any exact truth that can be expected in those Theories: For as the same Phenomena in Astronomie are satisfied by the received Astronomie of the diurnall Motion, and the proper Motions of the Planets, with their Eccentriques and Epicicles and likwise by the Theorie of Copernicus, who supposed the Earth to move; & the Calculations are indifferently agreeable to both: So the ordinarie face and viewe of experience is many times satisfied by severall Theories & Philosophies, whereas to finde the reall truth requireth another manner of severitie & attention. For, as Aristotle saith that children at the first will call every woman mother: but afterward they come to distinguish according to truth: So Experience, if it be in childhood, will call every Philosophie Mother; but when it commeth to ripenesse, it will discerne the true Mother. So as in the meane time it is good to see the Severall Glosses and Opinions upon Nature, wherof44De Antiquis Philosophijs. it may bee every one in some one point, hath seene clearer then his fellows; Therfore I wish some collection to be made painfully and understandingly de Antiquis Philosophijs out of all the possible light which remaineth to us of them. Which kinde of worke I finde deficient. But heere I must give warning, that it bee done distinctly and severely; The Philosophies of every one throughout by themselves; and not by titles packed, and fagotted up together, as hath beene done by Plutarch. For it is the harmonie of a Philosophie in it selfe, which giveth it light and credence; whereas if it bee singled and broken, it will seeme more forraine and dissonant. For as, when I read in Tacitus, the Actions of Nero, or Claudius, with circumstances of times, inducements and occasions, I finde them not so strange: but when I reade them in Suetonius Tranquillus gathered into tytles and bundles, and not in order of time, they seeme more monstrous and incredible; So is it of any Philosophy reported entier, and dismembred by Articles. Neither doe I exclude opinions of latter times to bee likewise represented, in this Kalender of Sects of Philosophie, as that of Theophrastus Paracelsus, eloquently reduced into an harmonie, by the Penne of Severinus the Dane: And that of Tylesius, and his Scholler Donius, beeing as a Pastorall Philosophy, full of sense, but of no great depth. And that of Fracastorius, who though hee pretended not to make any newe Philosophy, yet did use the absolutenesse of his owne sense, upon the olde. And that of Gilbertus, our countreyman, who revived, with some alterations, and demonstrations, the opinions of Xenophanes, and any other worthy to be admitted. Thus have we now dealt wt two of the three beames of Mans knowledge, that is Radius Directus, which is referred to Nature, Radius Refractus, which is referred to God, and cannot report truely because of the inequalitie of the Medium. There resteth Radius Reflexus, whereby Man beholdeth and contemplateth himselfe.