Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	demonstration_n	proposition_n	quantity_n	1,827	5	13.9195	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A35986	Of the sympathetick powder a discourse in a solemn assembly at Montpellier / made in French by Sir Kenelm Digby, Knight, 1657.; Discours fait en une célèbre assemblée, touchant la guérison des playes par la poudre de sympathie. English	Digby, Kenelm, Sir, 1603-1665.	1669 (1669)	Wing D1446; ESTC R20320	50,741	64

forth It may haply seem impossible that there can be an emanation of so many small bodies that should be spread and carried up and down so far in the air by a continual flux if I may say so and yet the body whence they come receive no diminution that is perceptible though sometimes t is visible enough as by the evaporations of the Spirits of wine musk and other such volatil substances But this objection will be nul and the two precedent Principles render themselvs more credible when we shall settle another viz. That Every body be it never so little is divisible in infinitum not that it hath infinite parts for the contrary therof may be demonstrated but it is capable to be divided and subdivided into new parts without ever coming to the end of the division And it is in this sense that our Masters teach us that Quantity is infinitely divisible This is evident to him who shall consider with a profound imagination the essence and formal notion of Quantity which is nothing else but divisibility But in regard that this speculation is very subtile and metaphysical I will serve my self of some geometrical demonstrations to prove this truth for they accommodate best with the imagination Euclide teaches us in the Tenth Proposition of his Sixth Book that if one take a short line and another a long one and the long one be divided into divers equal parts the short one may be divided also into as many equal parts and every one of those parts also into others and these last into so many more and so on without being able eve● to come to that which is not divisible B●t let 's suppose although it be impossible that one might divide and subdivide a line so that at last we should come to an indivi●ible and le ts see what will come of it I say then that since the line resolves it self into indivisibles it must be composed of them le ts see whether that may be verified To which purpose I take three indivisibles and to distinguish them let them be A B C. for if three millions of indivisibles make a long line three indivisibles will make a short one I put them then in a row First A then B so near that they touch one another and I say that B must necessarily possess the same place as A or not possess it If it possess the same place they both together make no extension and by the same reason neither 3 nor 3000 will do it but all the indivisibles will unite together and the result of all shal be but only one indivisible It must be then that being not both in the same place yet touching one another one part of B must touch one part of A and another part not touch it Then I add the indivisible C wher of one part shal touch a part of B. which touches not A and by this means B is copulant lying between A and C to make the extension To do this you see that we must admit that B hath parts as the other two also which by your supposition are all indivi●ible and this being absurd the supposition is impossible But to render the matter yet more perspicuous let 's suppose that these three indivisibles make one extension and compose one line the proposition already cited from Euclide demonstrates that this line may be divided into thirty equal parts or into as many as youplease insomuch that it must be granted that every one of these three indivi●ibles may be divided into three parts which is point blank against the nature and definition of an indivisible But without dividing into so many parts Euclide shews by his Tenth proposition of his First Element that every line may be parted into two equal parts but this being composed of indivisibles of unequal number it must necessarily follow that being parted into two there must be an indivisible more on the one side than on the other or the middle one be parted into two halfs So that he who denies that Quantity may be divided in infinitum entangles himself in absurdities and incomprehensible impossibilities And on the contrary he who assents to it will find it no impossibility or inconvenience that the atoms of all bodies which are in the air may be divided stretcht and carried to a marvailous distance Our very senses make faith hereof in some sort There is no body in the World which we know of so compact so solid and weighty as Gold yet to what a strange extent and division may it be brought Let 's take an Ounce of this massy mettal it shall be but a button as big as my fingers end A beater of Gold will make a thousand leavs or more of this Ounce Half of one of these leavs shall suffice to gild the whole surface of Silver of three or four Ounces Let 's give this gilded lingot of Silver to them who prepare Gold and Silver Thrid to make Lace and let them draw it to the greatest length and subtilty they can let them draw it to the thinness of a hair and so this thrid may be a quarter of a league long in extent if not more and in all this length there will not be the space of an atom which is not cover'd with Gold Behold a strange and marvailous dilatation of this half leaf Let us do the like to all the rest of the beaten Gold it will appear that by this means this small button of Gold may be so extended as to reach from this City of Montpellier to Paris and far beyond it into how many millions of atoms might not this gilded line be cut with small Sciffers Now 't is easie to comprehend that this extention and divisibility made by such gross instruments as hammers and Scissers is not comparable to that which is made by the light and rays of the Sun And it is certain that if this gold may be drawn into such a great length by spindles or wheels of iron some of its parts may easily be carried away by those winged Coursers we spoke of before I mean by the rays that flie in a moment from the Sun to the Earth If I did not fear to prove tedious to you by my prolixity I would entertain you with the strange subtility of little bodies which issue forth from living bodies by means whereof our Dogs in England will pursue the scent of a mans steps or of a beasts many miles and not only so but they will find in a great heap of stones that which a man hath touched with his hand Therfore it must needs be that upon the Earth or upon the Stone some material parts of the touched body remain yet the body doth not sensibly diminish no more than Ambergrise and Spanish skins which will send out of them an odour during a hundred years without any diminution of skin or smell In our Country they use to sow a whole field with one sort of grain