1000000030

bing,

&C.

of any decinlll fraaion by logarilhnil, it mufl

be obfemd, Ihat the firn fignificanl figure of Ihe power

be pUl fo manyplaces below Ihe place of unils, as IRe in.

dex of ils logarilhm wanls of 10, 100,

Óle.

multiplied

by Ibe index of Ihe power.

T••rlran Ih4 mIlo/powm

6j'LoGH1THMS.

To find mean prop,,¡iona/¡ ¡(/weln a.'!

I'IJH

nUlnh:rJ.

S\lbtr.a the logarithm of the lea(l term from the lo.

garilhm of Ihe greaten, and divide the remainder by

number more by one Ihan Ihe number of mean5 defired I

theo add Ihe quoticnt to Ihe loglrilhm of Ihe leafl term

(or fubtral1 it from Ihe logarilhm of Ihe greatea) conti.

n\laUy, and il will give the logarilbms of. all the meaD

D¡, ide Ihe

logarit~m

I~e

numbe.r by the index of pro¡iorfionals req\lired.

1he power, tbe quollenl

the Joganthm of Ihe root

Example. Lel Ihreo meaDproportionals be fought,

fougbt.

bClween 106 and 100.

LogarilAm of 106=

2.025~058

Log.aritbm of 100= 2.0COO"l'O

Logaritbm of Ih:

le~(l

lerm 100 added

Lo,gariihm of the 6r(l meaD

IC!lI'4673846

Logarilhm of the fecond mean 102'9563°14

Logaritlllll of. Ihe Ihird mean 1°44670483

Logarilhru of the grem(l lerm 106

2.0000000

2.0

06 316

4.75

2.0 t26p9·5

2.0

9794.

02 53°59.

OGIC,

the arl of thinking and reafoning junIYi or,

:i..J

it may be defiaed tlie (cieoee or hi(lory of Ihe hu·

/nao mind, inafmuch as it tracel the progrefs of our

knowledge froin our fir(l and

11)0(1

fimple Ihrough all their

Bifferenl combioation5, conception5. and all tho(e nume·

rous deduaions thal re(ult from varioufly comparing Ihem

one witb anolher.

The

pre~i(e

bufioefs of logie, Iherefore, i5

explain

die nature orthe' human.mind, and the proper manner

of conduaing it5 (everal

po\~m,

iD order to the attaio·

ment of trulh aod knowledge. lllays open .thofe errors

20d miflake5 we are 'apt, through inmenlion, to run in·

to; and teaches us how

dillinguifh between truth: and

whal oDly carries the appmance of il. By lhis .mean.

we grow acquainted wilb the nature and forceof tbe un.

derflanding i fee whal thing5 lie wilhio in reach i whers

\Ve may attaincertainlY and demontlralioD; aDd when ws

mufl be cooteoted Wilh probability.

Thi5 (cience is generally divided iOlo four pam,

viz.

Pmep¡ion, J.Jgmml, R'4foning,

aod

Mtlh,d. ·

This

divifion comprehends the whole hi(lory of tbe feoralions

and opemions of the humaD mind. But wemu(l refer Ihe

reader for Ihe 6rtl pan,

viz. P{rcep¡i,n,

and

Id,."

METAPH VS

tcs. where it will be more conveniently and fui,

Iy Irealed. and confine ourfelm in ,this place lO the Ihres

la(l,

viz. JudgmeRI, Rea/Ming, and MelhoJ.

PART

U D G M E N

1:.

miod being furnifhed with ideas, its nexl

(I~p

io.tbe way to knolVledge is, Ihe comparing thefe ideas

logelher, in order to judge of Ibeir agreement or dif.·

greemeol. In this joint view of our ideas, if tbe rela.

tion i5 (uch, ., to be iml]1edialely difcoverable by the

bare infpedion of the mind i the judgments tbence ob·

tained are called

inluilive;

for in. this cafe, a mere ato

tenlioo

Ibe ideas compared, fullices to lel us fee, how

far tbeyare conneded or disjoined.. Thus,

Ihal lhe wh.I,

grealrr Ihan any o/ il, p.rll,

is an iotuilive judg·

Ilieot, nOlhing more being required

convince us of its

• IrUlh. Ih. n an menlion

Ihe ideas of

whole

and

parl,

Aod Ibis

100

is Ihe mfon, why we call the aa of the

mind forming Ihefe judgmenls,

in¡l/ilion;

as it is indeed

DOmore, Ihan ao immtdiale perceplion of Ihe agreement

or difagreemcol of any two ide.,.

!JUI il is

be obferved, lhal our knowledge of this

kind refpeas ooly our ideas, and lhe relation5 betweea

them i aod tberefore can ferre only ., a foundation

fueh reafoniog5 as are employed in invetligating Ihefe

rdations. Now many of our judgments are converfaDI

aboul faéls, and Ihe real exitlence of things, which can.

DOt be traced by Ihe bare conlemplalion of Qur ideas.

does not follow, becau(e

havethe idea of acirele iD my

mind, Ihal therefore a figure

anfwering.to

Ihat idea, has

a real exi(lence io n'turé.

can form

myfelf the nQ·

tion of a centaur, or goldeo mounlain, but ncver ima.

gine on Ihat account, tbat eilher of Ibem exifl. Whal

then are Ihe grounds of our judgmenr in reladon to (.Iis

Experimce

and

IrflimMy.

e./,eritnce

we are io·

formed of Ihe exiflence of Ihe (everal objeéls which fur·

round us. and operate upoo our fenfes.

T,jlimony

i5 of

a wider eXtenl, and reache5 not only to objeas beyond

thc prerent (phm of our obfmalion, but airo

(,lis

and