OCR Text |
Show Numbet. Book II. CHAP. XVI. Of l{umber. § r AMong!\: all the Jd<as we have, as there is none fuggelled to the · ' Mind by more ways , fo there is n':'ne more limple than t~at. of 'lJnity, or One; it has no fhadow of Vanety nor Com~olitlon m 1t: every ObjeCl:our Senfes are employed about ; eve_ry /Jea m our Undertlandings; every Thought of our Minds bnngs thiS Idea along With 1t : And therefore it is the moll: intimate to our Thoughts, as well as It IS m its Agreement to all other things, the moO: univerfal Idea we have: _For Number applies it felf to Men, Anr;els, Acl:lons, Thoughts, every thing, th•t either doth exi!l:, or can be imagined. §. 2.. By repeating this Idea in our Minds, and adding the Repetitions together, we come by the complex Ideas of t!Je Modes of it. Thus by adding one to one, we have the complex Idea of two ; by puttmg twelve Unites together, we have thecomplex/dea of a dozen; and fo of a Score, or a Milion, or any other Number. §.3. The jimples modes of NNm~er art of.all other t!Je mojl di(li•El; every theleafr Variation, which is an unite,makmg each Co~bmauon, as clearly differe~t from that which approacheth near~fr to 1t, a~ the mofr re-. mote ; two being as difrinCl: (i-om one, as Twd hundr<;d; a(ld the Jdear of Two as di!linCl: from the Idea of Thtee, as the Magmtude of the whole Earth is from that of a Mite. This is not fo in other limple Modes, in whicH it is not fo ealie,nor, perhaps, poffible for us to difringuilh betwixt two apprilacbing Ideas, which yet are rea~ly diffe~ent. For who will undertake to find a difference between the wlute of thiS Paper, and that of the next degree to it 1 Or can form di!l:inCl: Ideas of every the leafr excefs in Extenf1on ~ ~. 4• The Clearnefs and Di/linEl~6fl of •ac!J mode of Num~er from all others, even tholi: that approach nearefr, makes me apt to think, that D~ monfrrations in Numbers, if they are not more evident and exaCl: than 10 Extenlion , yet they are more general in their ufe, and more determinate itt their Application. Becaufe the idea• of Numbers are more prec.fe,and difringuifhable than in Extenfion; where every Equahty and Excefs are not fo ealie to be obferved, or meafured, becaufe our Thoughts cannot in Space arriveatanydeterminedfmallnefs beyond which it cannot go, as in an Unite; aad therefore the quantity or proportion of any the leall Ex· cefs cannot be difcovered, which is clear otherwife in Number, where, as has lleen lilid, 91 is as diftinguilhable frotn 90, as from 9000, though 91 be the next immediate ExcelS to 90. But it is not fo in Extenlion, where whatfoever is more thanjufl: a Foot, or an Inch, is not di!l:inguifhablefrom the Standard of a Foot, or an Inch ; and in Lines which appear of an e· qual length, one may be longer than the other by innumerable Parts: Nor can any one allign an Angle, whicb lhall be the next biggeft to a right one. 9. ~. By the repeating, as has been faid, of the Idea of an Unite , and joining it to another Unite, we make thereof one colle&ive Idea, mar· ked by the Name j,.;,. And whofoever can do this, and proceed on, frill adding one more to the !all colleCl:ive Idea he had of any Number, and give a Name to it, may count, or have Ideas for feveral ColleCtions of Umtcs, Chap. XVI. Number. Unites difringuilhed one from another, as far as he hath a Series of Na~es for followmg Numbers, and a Memory to retain that Series, with the~r feveral Names_> . All Numeration being but frill the adding of one Umte more, and g1vmg to the whole together, as comprehended In one Idea, a new or d•frmCl:_ Name or S1gn, whereby to know it from thofe before and after, and dllbnglllfil 1t from every finallcr or greater multitude of UMes :_ So that he .that can add o~c to one;, ~nd fo to two , and fogo on w1th hiS Tale, talnng frdl With hrm the d1fbn8: Names belonging to every Progrellion; and lo again by fubtraCl:ing an Unite from each CoilcCl: i<;m retreat and l effc~ them, is capable of all the Ideas of Numbers, Wltlun the compafs of Ius Language, or for which he hath names, though ~ qt, perhaps, of more. Forthefeveral fimple_ Modes of Numbersbeing 1n ourMmds but fo many CombmauonsofUmtes, which have no variety, nor arc capable of any other difference, but more or lefs, Names or Marks for each d1fhn61: Combmauon, feem morc·neceffary than in any other fort of Ideas. For without fuch Names or Marks, we can hardly well mal<c ufe of Numbers m reckoning, efpecially where t\JC Combination 1S made up of any great multitude of Unites, which put together "tVIthout a Name or Mark, to dJfl:mgulfh .th,at precifc ColleCtion, will hardly be kept from being a lwap in Confulion. . ~- 6. This, I think, to be the rcafon why fome Americans I hive fpoken With, (who wore othcr\\~(c of qu1ck and rational Parts enough,) .could not, as we do, by any means count to rqqo; ,nor had any difrinCl: Jclea of that Numbe1! though th!'Y could reckon very well to 20. Becaufe their L1nguage bemg fcamy, and acco_mmod~ted ~nly to t)1e few neqeifaries, of a needy limple L1fe, unacquamted e1ther with Trade or Mat,hematicks, had no Words in) t _to 11and for~~; fo ,that ;y~en .they whe difcourfed with of thofe g'reater Number~, they woufd".ll!ew the Hairs of ~heir ~ead,, to exprefs a ,great multitude which th,ey C\lljld, not numper; wh1ch mablhty, I fuppofe, proceeded frorn their.want qf ~ames. . The '(ououpinam6os had no Nai1)CS for Nu.mb<;rs above ~; a~y Number poyond that, they made out by lhewing their F~ngers, and th5 Fingers of others whowcreprefent: H.:,ffoire d'un 1/qiage fait en !a ierre dg Bniftl, par Jean de Lery, c. w. ~- A~d I doubt not bu~ we. our, felves mig~t di, J1mCl:Jy number m Words, a great deal farther than w,e ufually do would , we find out but fome fit denominations to lignifie them· by 1 wh~~<;as in the way we take now to name them bY. .Millions of Millions of Millions tt is h"d to go beyond eighteen, or at moO: four an<;l tw~nty decilpal Pr~ greflions, Without confulion. But to lhew how much di/linEl Names cond. ce to our well re~i·oning,_ or having ufeful Ideas of Nu111bers, letu~ f~t all thefe followmg.- F1gures 1,0 one continued Line, as thp Marks;;of Ql\C ~umber: 't'. g. , , ,} .. -' · ·1 1 \ l j ·' :. • .) ' .,· s~;~·;~: /6~~~6. ~r;~~~. ~;;~;'6.~~~·;!";~ f:8~6d;~~·;·. i)~~~;l~~~~. rJ;tr~j) The ordinary way of naming this Number in Eng lifo, will be the oftert repeating of Millions, of Millions, of Millions, of Millions, of Millions of Millions, of Millions, of Millions, (which is the denomination of fi; fccond Figures.) In which way, it will be very hard to have any di!lingUlnllng Nouons of th•s Number: But whether, by giving every fix Figures anew and orderly denomination, thefe, and perhaps a great many more F1gures, m progreffion, m•ght not eaf1ly be counted diflinctly, and !tleas of them both got more ealily to our felves,and more plainly fignified to others, !leave it to be conlidered.This I mention only to lhew how ne- 0 2 celliu-y 9?. |