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in the fmalleft Corpufcle, fay they, is to fuppofc it infinitely extended : For infinite Parts placed externally to each other, as the Parts of Bodies doubtlefs are, inuft make an infinite Extenfioti.
They add, that there is a World of Difference between the Divifibility ofPhyfical, and Mathematical Quantities. For every Mathematical Quantity, or Dimenfion, they grant, may be increas'd and dimintfh'd infinitely : But Phyfical Quantity, neither the one nor the other.
AnArtift, dividing a continued Body, arrives at certain minute Parts, beyond which he cannot go ; which we may call Minima Artis. In like manner Nature, which may be- gin where Art ends, will find Bounds; which we may call Minima Nature : And God, whofe Power is infinite, be- ginning where Nature ends, may fubdivide the Minima Na- tWtPj but he will at length come at certain Parts, to which there being no other Parts continuous, they cannot be taken away. Tnefe minute Parts are Atoms.
All we can fay to the Point, is, that on the one hand 'tis certain, every extended Corpufcle muft have two Sides, and confequently is divisible ; tor if it had not two Sides, it were not extended ; and if it had noExrenfion, an Aflemblage of divers fuch Corpufcles would not compofe a Body. And on the other hand, the infinite Divifibility fuppofes an Infinity of Parts in the minuted: Corpufcle : whence it follows, that there is no Body, how fmall foever, but may furnifh as many Surfaces, or Parts, as the whole Globe of the Earth can ; nay, and infinitely more ; which, to fay no worfe, is a vio- lent Paradox.
The infinite Divifibility of Mathematical Quantity is thus prov'd, and illuftrated by the Mathematicians: Sup- pofe a Line AD {'Tab. Geometry Fig^fO perpendicular to BF, and another, as GH, at a fmall Diftance from A, alfo per- pendicular to the fame Line ; with the Centres CCC, ££c. and Diftances CA, CA, Eifc, dcfcribe Circles cutting the Line GH in the Points e, e, &c. Now, the greater the Radius AC is, the lefs is the Part e G : But the Radius may be augmented in Infinitum, and therefore the Part e G may be diminifli'd in the fame manner 5 and yet it can never be reduced to nothing ; becaufe the Circle can never coincide with the right Line BF. Confequently, the Parts of any Magnitude may be diminiflVd in Infinitum.
The chief Objections againft the Doctrine, are : That an Infinite cannot be contain'd by a Finite; That it follows from a Divifibility in Infinitum, either that all Bodies are equal, or, that one Infinite is greater than another : To which it is anfwer'd, that to an Infinite may be attributed the Proper- ties of a finite, and determined Quantity. And who has ever proved, that there could not be an infinite Number of Parts infinitely fmall in a finite Quantity ; or that all In- finites are equal : The contrary is demonstrated by Mathe- maticians in innumerable Inftances. We are not here con- tending for the Poilibility of an actual Divifion in Infini- tum, ■ we only affert, that however fmall a Body is, it may be ft ill farther divided; which we imagine may be call'd, a Divifion in Infinitum^ becaufe what has no Limits, is call'd infinite. See Infinite.
True, there are no fuch Things as Parts infinitely fmall ; yet the Subtilty of the Particles of feveral Bodies is fuch, that they very much furpafs our Conception ; and there are innumerable Inftances in Nature ot fuch Parts actually fepa- rated from one another.
Mr. Boyle gives us feveral Inftances. He fpeaks of a filken Thread 300 Yards long, that wcigh'd but two Grains and an half. He meafured Leaf-Gold, and found by weighing it, that 50 fquare Inches weigh'd but one Grain : If the Length of an Inch be divided into 200 Parts, the Eye may diftinguifti 'em all ; therefore there are in one fquare Inch 40000 vifible Parts ; and in one Grain of Gold there are 2000000 of fuch .Parts ; which vifible Parts no one will de- ny to be farther divifible.
A whole Ounce of Silver may be gilt with eight Grains of Gold, which is afterwards drawn into a Wire thirteen thoufand Foot long. See Gold, and Ductility.
In Odoriferous Bodies we can ftill perceive a greater Subtilty of Parts, and even of fuch actually feparated from one another; feveral Bodies fcarce lofe any fenfible Part of their Weight in a long Time, and yet continually fill a very large Space with odoriferous Particles. See Ef- fluvia.
By Help of Microfcopes, fuch Objects as would otherwife efcape our Sight, appear very large : There are fome lmall Animals fcarce vifible with the befl Microfcopes; and yet thefe have all the Parts neceffary for Life, as Blood, and other Liquors : Flow wonderful muft the Subtility of fuch Parts be, which make up fuch Fluids! whence is dcducible the fol- lowing Theorem :
Any Particle of Matter, how fmall focver, and any finite Space, how large foever, being given ; it is poflible for that fmall Sand, or Particle of Matter, to be diffuied through all that great Space, and fill it is fuch manner, as that
there /hall be no Pore in it, whofe Diameter mall exceed any given Line ; as is demonftrated by Dr. Keil. IntroduSf. ad Ver. Thyf.
DIVISION, the Act of feparating a Whole into the Parts it contains. See Part.
If the whole be compofed of Parts really diftinct, call'd In- tegral Parts, the Divifion made thereof is properly call'd Partition : As when a Houfe is divided into its Apart- ments. See Partition.
If the Whole be compofed of Parts, call'd Subjeblive, that is, if the Whole be only one common Term, the Sub- jects comprized in the Extent whereof are the Parts, the Divifion thereof is what we properly call Divifion : Such is the Divifion of a Genus into its Species, &c.
Division, in Phyficks, or Divifio Contimu, is the Parti- tion, or Separation of the Parts of a Quantity ; whereby, what before was one, is now reduced into feveral. See Continuity.
This Divifion is effected by means of Motion, without which there can be no Separation of any Continuum, or even Contiguum.
This Motion is performed divers Ways, by FraMion, Scif- fion, Setlion, Fiffion, Refolution, 'Dilution, Maceration^ Difperfion, Effiifion, Difiratlion t &c. See Divisibi- lity.
Division, in Logic, is the feparating any Thing into di- vers Parts, or Idea's : or more ftrictly, it is the Diftribution of a Whole inro all it contains. See Distribution.
The School-men define it a Difcourfe, explaining a Thing by its Parts; In which it approaches near to the Nature of a Definition, whofe Character is to define a Thing by its Parts. See Definition, Part, &c.
Divifion, we have faid, is a Diftribution of a Whole, S?c But the Whole has two Significations, whence two Kinds of Divifion.
A Whole is properly what confifts of integral Parts ; as the Human Body, which contains divers Members : And a Diftribution into fuch Parts, is properly callW Partition : Such is that of a Houfe into its Parts. See Parti- tion.
But there is another Sort of Whole, which is properly no other than an abftractldea common to more Things than one, as the Univerfah : Or a compound Idea comprehend- ing the Subftance, and its Accidents, or at leaft moft of its Accidents.
This Whole admits of a triple Divifion. 1. When the Genus, or Kind, is divided by its Species, or Differences ; as when Subftancc is divided into Body and Spirit ; or into Ex- tended, and Thinking. Theiecond, when any Thing is divided into feveral Claffes, by oppofite Accidents ; as when the Stars are divided into thofe which mine by their own Light, and thofe that only reflect a borrowed Light. 3. When the Ac- cidents themfelves are divided according to the Subjects in which they inhere ; as when Goods are divided into thofe of the Body, the Mind, and Fortune.
The Laws of Divifion are, 1. That it be full, and ad- equate, that is, that the Members of the Divifion entirely exhauil the whole Thing divided : As when all Numbers are divided into Equal, and Unequal. 2. That the Mem- bers of the Divifion be oppofite ; as Equal, and Unequal; Corporeal, and hot Corporeal ; Extended, and Thinking. 3. That one Member of the Divifion be not contain'd in an- other, fo as the other may be affirm'd of it. Tho', in other refpects, it might be included without any Fault in the Di- vifion : Thus Extcnfion, Geometrically confider'd, may be divided into a Line, Surface, and Solid 5 tho* the Line be included in the Surface, and the Surface in the Solid. 4. The Divifion not to be made into too many, or too general Parts. Laftiy, the Members, unlefs the Subject require it, not to be too unequal ; as if the Univerfe were divided into Heaven and Earth. *
The Division of a Word, is a Difcourfe explaining the Latitude, or Comprehenfion of a Word : The Latitude when the Word is univerfal ; as when the Genus is divided into Species, and Differences : The Comprehenfion, when the Word is ambiguous, ^s'Taurus, Bull ; which fometimes denotes a Conitellation, fometimes a Beait, and fometimes a Mountain.
TheDivisioN of a Mode, divides a Quality into its De- grees. The Philofophcrs, after the Phyficians, fuppofe 8 De- grees of every Quality : Hence when a Quality is faid to be in the 8th Degree, it marks, that it can be no further intended, or heighten'd. See Degree, and Quality.
Division, in Arithmetick, is the laft of the four great Rules ; being that whereby we find how often a lefs Quan- tity is contain'd in a greater ; and the Overplus.
Divifion, in Reality, is only a compendious Method of Subtraction ; Its Effect being to fake a lefs Number from another greater, as often as poflible; that is, as oft as 'tis contain'd therein. There are, therefore, three Numbers con- cern'd in Divifion : 1. That given to be divided call'd the
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