1000000030

991

tae

ide¡ is fuund to correCpond with the particulu objeél.

Havinc thus explained the rules by which '\Ve are tO

we .theo without líeGtation apply the genéral name ; but conduél ourfelves io ranking panicular objcas under

i( ho fuch corrcfpoodence intervenes. the conelufion 'mull general idw, and Ihewn their conformity to the

praaic~

necdrarily take a contrary turno Let

U5,

for infiance, anJ manner of the mathematicians; it remains only t.o

lake the number.

,ight,

and coofider by \Vhat lIeps we are obferve. thal the true lVay of rendering this pan of

I~d

to pronounce it an

,um

number. Firfi thcn we call knowledge both eafy and certain, is, by habituating our·

t9 mind the idea fign[ficd by the exprdlion

'utTl

Celves ro elm and determina te ideas, and keeping them

nO/llh",

viz. Ih.t it isa

numh" diuijib/, inlo Iwotqua/

fieadily annexed to their refpeélive names. For as al!

la"I.

We then .compare Ihis idea wilh the number our aim is, to apply general 1V0rds aright; if thefe words

tighl,

aod, finding Ihem' manifefily tO agree, fee at once fiand for invariable idm, that are perfcaly knolVn to the '

the omllily of admitting Ihe conelufioo. TheCe Ceveral mind, and can be readily diltioguilhed upon oceaGon,

judgmeots thmfore, traosferred into language, aod re· there wil! be liltle danger of mifiake or error in our rea·

duced

the form of a fyllogifm, appear Ihus :

fonings. Let us fuppofe, that by cxamining anyobjeél,

Eu,ry numó" Ihal n/al h, dividid inlo l'lJJOiqua/

and carrying our

~ttenlion

fu ecellively from one pan to

/3rll

EVEN

numh,r.

anotber, we have acquainted ourfelves with Ihe feveral

7'h,

numótr

EIGHT

mal

é,

dividd inlo two ,qU4/'

particulars obfervablé in it. If among theCewe find Cuch

}ti

rlJ,

as confiitule fome geoeral idea, fralned and Cettled before-

Thmjm th, numo"

IG HT

ÍJ

EveN

numd,r.

haod by the uóderfianding, and diflinguilhed by aparticu.

Herc it may be obCerved, that where the geoeral idea lar name; Ihe reCemblance, Ibus known and perceived,

tp wh,icb particular. ohjeéls

ate

referred is very familiar necetrarily dmnnioes the fpecies of Ihe objcél, aod there-·

to the mind, !his refereoce, aod Ihe applicatioo of the by gives il a right

the oame by which that fpécio! is

geoeral name, Ceem to be made withoul any apparalus of cal!ed. Thus four equal fides, joined together at right–

reafoning. When we fee a horCe in the fields, or a dag angles, made up the

o~tiaa

of a fquare. As Ihis is afix–

jo the. fireer, \Ve readily apply the name of the fpecies' ; ed aod invariable idea, without which the geoeral oame'

habir, aod a familiar acquaintaoce wilh the geoeral idea, canoo! be .pplied we oever cal! aoy panicular figure

¡ .

fuggefiing it infiaotaneouily to lhe miod. We are OO!

jqlla",

uoúl il appears

have thefe feveral conditions

¡:

however to imagine on this accounr, that,the uoderfiand- and cootrarily, where·ever a figure is found \Vith thefe–

i~g

departs from the uCual rules of jufi Ihinking. A freo conditioos, il necetrarily lakes the oame of a

[qua".

'1uent repelilion

oE.

afu begcts a habi!; aod hahits are ato The fame wil! be fouod

hold

in.al

! our other reafon-.

lended wilh'a cmaio promploeCs of execulion that pre· ir.ogs of this kind; whm oOlhing can male aay'dilEcul–

nnlS our obferving the feveral fieps and gradarions by ty but Ihe want

fettled .ide~s.

If, for inllanee. we have

~hich

any cou,fe of aaioo is accomplilhed: Bul' io other' OO! determined withio ourfdves Ihe precife norioo de·.

lpfiaoces, where we'judge nOl by pre'contraaed habits, noted

by.th'

e 1I'0rd

/IIanjlauglt,,;

it wil! be impollible ror

as wheo the general idea is very complex, or lef. familiar' us to decide, whether ¡ny párticular aélioo ought to bear.

the miod: we always 'proceed according

the form that name: becaufe bowever nicdy we examine the ac·

-cf reaConing efiablilhed above. Agoldl'mirh, for inllance, tion itCelf, ye! being lIiangers

the geoeral idea Wilb

,:,ho js in doub! as

any piece of mml, whether it be of which ir is lO be compared, weatC ulle"y unable to judge

I.he

fpecies cal!ed

gold;

firfi examines ils properties, and of Iheir ag,eement or difagreemeot. But if we take me–

Ibeo comparing

th~m

wirh ¡he general idea fignified by 'lO remove this obfiacle, and difiinaly trace thetlVo idm.

\hat n,me, if he fiods a perfeél correfpondence, oolonker uñder confidemion, al! d.lEcu!ties 1'30ilh, and Ihe reCo-

befitales under ",hat claf. of melals to rwk il.

lution becom;s both ea[y and cenain·.

But lbe gre'l importance of Ihis branch of reaCooing.

Thus \Ve Cee, of what importance it is, towards the

and the oecemly of care and circumfpcaion io refmiog improvemeat aod certain.y 01' human knowledge. tha! \Ve

particular objeai to general idtas, is Jlil! fanher evident

ace~fiom

our[e!ves to clear ar.d determinate ideas, and a

from the

pra~ice

of Ihe matbematician!. Every One who fieady applimion of words,

has rcad

Ellclidkoows,

Ihat he frequemly r,quires us to

O R

tafollillg, a, il rrgar

Iu pO'lJim alld pl'0p"liu

drawIlnes through cenain points, and according lO Cuch

oj lhillgl, and

Ir.,

re aliollJ

our gm"a/ idm.

and'fuch direaions. The figures then:e refu!ting are

often Cquares, parallelograms, or reaangle.. Yet

E.,

VfE comenow

the fecondgreal end which meo have

e/id

never fuppo[es this from their bare appearance, bu! in view in Iheir reafonings, namdy, Thedifcoveriog aod

always demonfirales it upon tloe filiadl priociples of afcri:irg tO diings their feveral amibulr! and propenies.

~eomclry.

Nor is Ihe melhod he takes in anythinC diF· And here it will

necetrary tOdiflinguilh bClween rea·

fmOl {rom that deCcribed above. Thus, for iollance, foning as it rcg1fds Ihe Ccicoces, and as it conceros (om·

having d,fiocd

fquarc

be a figure boundcd by four . mon life. lo the fciences, OUr rcafoo is cmployed ehief·

tqu,1 fidei, joioed together al riEht ¡oglcs; when fuch Iy aboul uoiverfal trulhs, it being by Ihcm alonc Ihat

a "gule ,rifes in any coofilua ion "reyions tOlhe demon· the bounds of

hU~13n

knowledge are eol!l ¡:cJ. Hcnce

Ilr'tio~

of a propofilion, he

ytt

ncver calls il by Ihat tJle divifioo of Ihingsinto v.arious ela(fes, called olherwi/e

naOle,. unlil he has Ihewn Ihat il! fiJesare ' qual, and all cenero aoJ fpecies. · For Ihele univ,rfal ideas, beinr. fet

il! .nblts

rip.ht

ones. Now Ihi! is arrmndy lhe fJme up as the rlprefeomives of mlny pmicularIhmgs. 1I1·,t.

(",m of rtlfoniog \'le have before exhibllerl, in pro.iog eyer is alli rmcd of IhlOl may be alfo ,/Ii tm. d of a!l lhe

~ighl

tn be an eveo nlllllb,r.

iodividuals

"hich th,y beleng.

lIIurdrr,

for

ina~nce, .

VQL,

11. N°

63.

¡l .