1000000030

1002

here

lh~

propoGlic.o

J~J~,cJ

fromit, mull be !fue. If

then aoy pruVoGlioll is propofed 10

demooilraled, aod

offullle

:hc

cOlllro",(]~rJ

of lhal propoGlion, and

theoce Jiretlly infer lhe propoGlino 10 be demonUrmd,

by this "ery means \Ve know lha! lhe propoGlion fo io·

(med is lrue.

or fince from aoafTuOled propofilioo \Ve

have ¿edueed i"

conlradi,~ory,

we are lh<reby cemio

11m lhe aOumed propoGtion is falfe; aod if fo. l::cn its

conlraditlory, or 11w

d~duced

from il. which in lhis

cafe is lhe rame Wilh !he propoGlioD 10 be demoollmed,

mufi be true.

We have acurious innaoceof

thi~

in thetwe: flh propo–

fitioo of lbe ointh book of lhe elemeot!.

Eue/id

lhere

propofes to demonllrm,

Ihol in anJ forio

nUlJlberJ,

r!Jilig

frOIll

unil) ingmltelri,"/ progr:f:or., al/ Ihe prime

7IlIlIIb,,!

Ihol mlArure

/h,

/ujllmn in Ihe feria wi/l

iJlfo

T/Uefure Ihr nrxl afia IInilJ.

lo order to this. he

afTumes the comraollloryof lhe propoGtion

be demon–

Ilrated , namely;

Ihal

fo.ne

prillle n_ulJlber IIuafllrilll Ihe

lojl

1.,111

in Ihe forio . dou nol "{(.fu,, /he nrx/

aftrr

unÍ/y;

and theDce, bya coolioued traio of reafoning, proves,

that it atluaJlydoes meafure it. Hereupon he coneludes

the arTumed propoGtioo tObe falfe, aod lhal which is de–

duced from it, or its coomditlory, which is the very

prop,ofition he propofed to demoqllrate, to be true. Now

lhal lhis is 3 jull anJ concluGve wa)' of reafnoing. is

bunddotly mamfdl from what we havcfo clearl)

c1L~lifu

ed ,b'IVt.

¡-/Aviog lhus f"fficiently ev;oced Ihe ceminry of de–

monllration in all ilShranchcs, and Olewn the rules by

which \Ve ought to proceed, in order to 3rrive at a jull

cOllduGon. aecording 10 thevarioes ways of argui made

uf. of; il is needlcfs to enter upnn a panicular conGde–

ration of Ihnfe femal fpecics 01' f.lfe

r~afoniog,

whlch

logi,iaos diOinglll/h by the Dame of

fophifmI.

He thal

thl onghly uoderli.ods the form ,od Uruélure of a gocd.

argument, will of l.i.l\lelf re.ldily M.ero every devialion

from il. Aod al:hollgh

f lpbiJilll

have becn divided ioto

mioyclarTes. whic.h ore all called

foundlng oam,s. that

therefore earry in lhcm much aprear,nc. ollearning; yCl

are the errors lhem(e1v<s fo very p,lpable and obviour,

thal it is

100

I.bour tOwrite for a

0100

capable of beiog

miOed by thcm. Here lherefore we chufe 10 cooelude

this recond pan of logic, aod OlalJ io the neXI pan giv<!

fome accouO! of

",,/hod.

whlch, though iofeparable fronl

reafooing, is o.venhelefs alway' coofidered by logici,ns

adillintl operation oi the !'Iiod ; becaufe its influence is

not coofined

themere exercifeof lhe rearoniog

f.cu

!ty,

but eilteods infome degree to alJ tbe tranfaélions of the uo–

derflaodiog.

A1\

III.

E T H OD.

mr/hod in gendra/, and Ihe djvijion

il inlo analj–

,id and

f)'Tilh~/id.

have oow done with lhe IIVO6rll operations of the

miod, whofe oRice it is tOfearch after truth, aod eolarge

,he bouods of humao knowledge. 'fhw is yel a third,

which regards lhedifpo[aland arrangemeot

ourthoughts,

when we eodea.our fo tO put themtogtther that lh,ir

mUlual coonetlioo and depeodence mal' be clearly feeo.

T his is whu logicians

"lI lt/e/hod,

and place always the

h ll in order in explainiog lhe powers of the uoderUand·

iog ; becaufe it oecelfuily

rnppof~s

a previous exercife of

ou r olher faculties, and fome progrefs made in koow–

Jedge, before \Ve cao exm it in aoy eXlenGve degree.

ID lhis view it is plaio, lhat we md l be before-haod

well acquaioted with the trurhs IVe are to comhioe toge–

Iher ; otherwife how could we difcern their feveral con·

neélions aod relalioos, or fo difpofe of lhemas lheir mu–

tualdependeDce may r<quire1 BUl it oflen happeos, that

(he underfiandiog is employcd, 001 io lhe arrangemeot aod

compofilion of

koo\V~

truths, but io lhe fearch and difco·

very of (uch as are unkoown. Aod here th. manoer of

proceeding is very d,ff«ent. We aITemb!e al ooce our

whole Uock of koowledr,e rclatiog tO any fuhjetl; and ,

after a

~er.eral

(urvey of lhioes, begio Wil h examining

Ihemf'P'lrdlel y and by pa m. Eence it comes 10 pafs,

that whereas, at our f"JI fwiog OUl, we wereacquaimed

only Wilh fume of lhe gr,lnd I!rokes anoontlines of trulh,

lhus purfuiog her lhrough

fcveraI wiodines anJ

recclres \Ve gradually clifenv", thofe 0I0re inward allo G·

ner lOuches wheoce /he derives

,11

her nrenglh, f)'OIlII e–

Iry, ,nd beauly. And hereit is, lhat when, hy a lIarrow

fcruliny inlo thioss,

\'IC

hJveuDI.yc

!l,o

~oy

p.11

t of J.oow-

'ledge, aod lraced it tOits firO aod original principies, in–

fomuch that the whoJe frame and coO!extore of it lies

opeo to lhe view of lhe miod ; here ir is. that tlking it

·lhe.contrary way, aod beginoing \Vilh Ihefe priociples, we

can fo aJjull and put togelher lhe pam , as the order aod

methodof fcieoce requires.

BUl as thefe things are bell underfioodwheo illuOratcd

by examples : lel us fuppofe aoy mael,ioe, for inllance a

watch, prefeoted tO us, whofe llrullure . od compofilioo

we are as yet uoacquainted with , bUI waO! if pollible to

difcovcr. The maooer of proceeding io this cafe is,

takiog

th~

"hole to pieces, and ex,mioiog the pans fepa–

rately one afler aoolher. Wheo by fuch a fcrutioy we

have Ihroughly informed ourfelves of the frame and con–

textureof each,.we lheocompare them IOgclhtf, in order

to judge of their mutual aétioo and influence. By this

meaos \le gradually trace out the ioward make and com–

poGlioo of ¡hc whole, aod come al Icngdl tO difcern , how

pans of fueh a form,. and fo put together, as \Ve fouod io

unra,;elJing aod taking themafuoder, CooOiHlle that par–

ticulor machioe called a watch, aod cootrihute to all the

feveral motions aod phxnomeoa obfefl'.ble io il. This.

difcovery being made. we

C.10

take

t1.1I0~S

theconu arywa)',

and, bcciooing Wilh lhepal

IS,

fo difpofe.and con?c,'l lhem,

as thtir feveral "fes and Jlru/lures reqtllre, 110,,1

lenglh

\Ve arri,'c at lhe\Vhole itfclf, flom the

uoral'ellin~

of whieh

dlefe pm, I'clilhcJ.

And as il is io trariog and

exaO\inin~

lhe works of art,

fo is il in asreal mea!i" c in unf"ld:og any pan of humao

knowlcdge. For die rel.nions and IIIII:u,1 habiluJ,s uf

things do not always immcdiately :lpp,ar upon COlnr·

l -

ring lhcm one Wilh

allodl~r.

Heoce w. hare

rccuu~fe

intcrlll,Jiatc iJ as, ar.o by

r.:

30S

Ihc~1

are rurr.dhr.1

\Vi,l.