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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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 The. Line C. d. _. Hill. lessen uxwards, Vet thes sit = verero be dirided by 2 he Quotient L5 will
cannever become nothine, because no Line drann
Trom a ca any pare ot de thouph never (o remore
ean postibly erer coincide wich che upper Paralle
Sec also che Learnea Mr. Keit S, act Philosopbica
Lecture, reda In cul Onivertier ot Oron, and lare
Ana Chac ihC Lails, ot Solid Bodies are almos
infinicely (maII, and chac cher are capable oF be
ins divided wondertul minurely, cho II. MIF. Boyl
Mens by chese Instances.
. A Piece oF Silver Wire was dramn (0, snallo
chac che Weiphe ot bur a Crain vould. re2ch 10
27. F0or or 324 Inches in lensch; and since an
Enelist Inch can casily be divided into 200. cquat
Pares, one Crain ot rhis Wire may be dividod in
20 64800 ParrS. And since ehis Dirision relaret
only co che Surtace of che Wice, ies Solidiey may
exsilys be conceired ra conist, oF many Millions, o
tuch. PaFES.
2. One ot ihe Oval. Cases os silk. vorms vas
dramn our inco a Lonpch char much excoeded 300
Vards, and ver weixhod bur cuo Grains and a1
halt; (0 char cach Cylindrical Crain oF ehar Silt
vas ac leaA 120 Vards in lengch.
3. A Grain ot Leat Gold was extended into an
Arca ot above 50 Inchess and chen supposins che
Area reduced ro a Square, and irs sides divided
alcer rhe manner vetore menrioned, 1. e (0. chav
chere be 200 dirisions in an Inch: PF Paralsel Lines
be luppoled ro be dravn chroueh chole subrile di
vitions, che Area will be dirided inro na tels chan
ruvo Millions ot lirele Squares
At vou suppolo che Silver Wiro montioned a
bore co be eilr wich Gold sand allovn for ch
Gildins 8 Grains of Gold 1o an Ounce ol Silver,
Which ver is more chan is commonty ulcd) vor
will tind an Ounce ot Cold may. cover as muct
Nire as will reach c0 r55? Miles in lenech.
5. By dissolrins onc Crain ot Crude C opper in
pood Provorrion oC Spirie oC sal armoniac
dcep Bluc Colour was produced, and alcor chis:
800d Ouancier of distilld Wacer was pur coic, re
dilure ic, ver (0 25 thar rhe Blue C olour did Aill re
main vilible; and on che comparins che WeiphEo
be much bisger chan che Diridend 3, hecause 25
1.400 165. (1. e.) 25 one is eo che Dirilor:
Co is che uorienz co the Dividends buc I, is ereat.
the Liquor vich che Crain ol Copper hrc distol.
ex than = Or =, Wheretore LS must. al(o be PrCatEF
thon 3.
thereducins che Dividend and Divilor eo che torm
Thusit ab ivere robe divided by cd, ic must DC
Placed chus, , ane MHac Fraction is che Onori-
enr; chouph some choole ro vrire ic chus, 0d) a b
Or ab=cd. Wrtich last Mark  is che commori
Character For Division.
parrins a sensible Colour c0 abore 5i3620 times
eins or parcms et ans me ma us propet Larts
and is onty a Compendium et substraction, tor ehe
Divisor is (o many rimes concain d in rhe Dividena
as chere are Dnits in che Ouorient; lo thac lub
Aractins concinually che Divisor trom che Divi
DIVTSION in Species oe Mlebra, is in penerat
ot a Fraction, whieh Fraction is rhe Ouoriene.
ved, ic Wwas found, chac Grain was capable of im
irs Bulk ot Liquor.
Por the performine the Worte of Division Alcebrai-
cally observe these RuIes.
Ist. Rule. Wten ihio Dividend is, equat. 19 etie
Dirilor, che Ouocient is Onicy, and must bc
placed in che Ouoriene, because everr chins
contains it selF once.
2d. Rale; Wstenche Duorient is exprossid tiractin
on vays (a5 in Simplee Division) is eHe Came
Lecters are tound equally rexeaced in every
Member oF che Numerator and Denominator
cast amar chose Lerrers, aud che Remainder
ab. le. 8c
3d. Rule, Wten chere are any Co esticients, dix
vide ehem as in Common Arichmeriek, and
ro he Ouocienes annex che Quancicies ex
pressi d by Lerters, hus, 360 ab (- 15 a
24. b
gth. Rule. The general way ot Division ot Com
Pound Ouancicies is likre che ordinary ivay in
Common Arichmeriek, respect being had id
etie Rules of Algebraick Addirion, Subduction
and Mulciplication, a5 allo, phar like Siens
sire F, and untike= in iho Ouorient; ta-
kins care r0 divide erery part ot che Diri
dend by ies correspondins Divisor (i. c.) chac
whole Lerrors Me il os ete lame Kinc
wich ihe ocher) 10 prevent a Fraction whict.
vould orhermise arile
chus, a +b) a a + a b c a cb (aie
dend, and accouncins an Onice For each rime, the resolvino che chins inco irs PaerS) cheretore since
vided is Lallea the oacna Chac by itnch jou
divide ehe Bo, a  Muriber oF cimes Mac could produce che Diridend; etieretore, it theDi
y sublised.
DErISIONY in generat hsmnes ene aucribu-
Sunm ot ore Onus is che Duatient:
he: Dioraena CaM lHe Boyor so caceu  feu
Thae thie Pame Reason for litee Sipris sivine 
posicire and untike à nesarive Duoriene, must holg
in Division as Wellas in Mulriplication, is clear Feori
consderins che Nacure of Division, (Which is only
every Dividend is nochine else bur rhe Produet ot
the Guoriene muct consist ot such siens itrich
vicen de causMantiey chac hach a limi-
rient or Duore. And lomerimes rho Parabola, che lar Sien wichu, ce Olibelehe muut be policire:
Reale et irhich lec under thac mord.
Ih all Division, as one is ro cheDivilor:: (0is
ee Ouoriene ro che Dividend; Wheretore chouph
 ler Numbers che Ouorient must alivays bc
it by L Quancicy tavins a dissimilat Sien, ic must
be Hegacives
It may be a Gegerat Rule in Compound Divi
non in Algebra, alivays ro place suck a Lerrer ir
less chan che Diraen, vec in Fractions ic mule ehie Ouorierie, as will, irtien mulciplicd into che
alvass be greater
Thus, lec 36 be divided by 4. the Quorient is
3, le(s chan 36. because, since L. 4.. 5. 5. 
Divilor, produce che Dividend; Por thar is a)
pisor lecarere ede pe egitee ade de don
riege.
In D: Disto. InC LIL et Canciry ro b0 di cheDivisor and Guocient mylriplied by eacti orter
ins tels Man 4: 9 must also be lels rhan 367 bur