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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0648
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Position E
Double 16
Position fase. Conctus. crue
l. 28li 3: 220l. : 20l. 1
40 B
160 C.
Ducat pa 64
boch - J) andche Remainder 28 is cheDiridena.
and the lesser Frror r substracted tromthe srearer
ErrOr 3, leares 2 For the Dirisor; the Ouorient
oE which Dirision ill be 14, che. Numibet
TOUBHE FOT A. and then by consequence B. HIIIIC
have F0: For2 taken trom 10, and added ro 14
220 ProOF. make 16 = twice 8; 2 raken From 14, a
Pur 10 50, makies r2 boch alike.
Fixst
Positio.
Ar01
20 Position.
3. I- Error.
Ouection, then For more lacilur in Proccedine
calce such a Number for the Position as may bc
equally parted by che Paris exprest in the Oue-
stion.
In Ouestions propounded, ic happens some-
imes thac a Number Aands unalterable by the
Fractions siren, and s0 mar be subtracted trom
the sum siren, and set by till che Operarion bC
made writh the rest, and then restored again.
Parrition in the Numbers to makce a Proportion:
Theretore rou must makie a Supposirion tvice
proccedins cherein accordins ro The Tenor ot
the Ouestion; and it cirher ot the Cuppoled
umbers happens eo solve che Propolition, chc
Wock is done; bur il not, obserre ThC PFTOFS.
and whether cher De sreater or lesser than che
Relolution requirech, and marke the PFrONS aC.
cordinslr, wich che Signs -1 Oe-
Then Mp conlassise che one Position
by che other Peror; and if che Frrors be boch
100 great, or boch e00 licrle, Cubrract che onc
Product from che other. and the one FrrOF From
the ocher, and divide the Difference oF the PrO-
duets by che Difference of thC FrrOrS.
But il the errors be unlike, as che onc - 1
and the ortier -, add the Products, and divide
the Sum chereof by. the Sum oF the Frrors ad-
ded rosether: For the Proporrion of the PrrOrS
is the lame wich che Proporrion of che fixcesses
or Detects. ot the Numbers supposed, 10 che
Numbers soushE.
B. replies,  L’had emo of jours, i sould have
just as many as vou have: ITo mans had cach :
Bur cher Tould BC CGuat, CHCICIOTCche Position
artrich is noc egual; cesciere a e again
15 3 t00 nuch.
by  ThC SII LTOT, IHC LIOUMIL 26 1S CaCM
Products 24 = 20 = 14 ( 14 A
Errors 2. = 2 = 2 10 B.
Bur il che Suppositions are 20 and 10, theri
the trrors beins tound unlikce; the Sum oF che
Producto must be che Diridend, and che sum
oE c too che Diritor.
First
Second
Posicion 20  x20 Posirion.
Frror 3. ]  2 2 - Error.
30
40
Products 30 -] 40 = 70 p 24 A.
Frrors 3. ] 2 = 5 10 B.
O
2
-
28
14 st
10B.
e
10
Products 48-
Etale
Frrors
20  2 = 12 sequal
ddtC.
EE che Supposicions hadt Been F2 and 50, che
Aood inuo, as atore, because hC LTTOIS atE
Errors being Doch -, ue Spetation wouldhave
First
Costobi.
Error 1.
HE there be a Fraction or Fractions in che
POstLIOL Double, is Wrhen there can Deno
oatole.
Second
20 Position.
2 C11d1.
Noce, T. That ad well in che Sinele a5 in che
Double Rule of Posion, ho che. Numbet
suppoled be nerer (0 Falle, a Relolurion
mar be had cherebr: Xec, tor more Palc
in cheOperation, suppose a Number rhac
mas De parred equallr into (o manr PaFES 25
are necessary co che Relolucion of che ne
Rict
Tuo Mem L. and B. discoursins of cheir NO-
ner; A. PaYS CO B.. I P had tuo os jour Pieces,
Esoula hade Turce as many as you habe; eo ertrich
Srippose L. had 16, 20 wrhich 2 beins alueul
makes 18, Wrhich is twice 9; bur havins raken
e Trom chelce, it must de by chis dupor
thac B. had sL: WHesciore 2 lakea Irom 16,
and added W 1L, Atakes 13 i1 b. and A. +4.
iS erroneou, a  LOL COD MHCHB) L.
Asain, Suppole A. hacl20, theM 20) 2 = 22.
that is tvice FT; bur From thence L Deins Fa-
ken, B. must have x3. Now 2 From 20, and puc
10 +3, Sres 1 1OI b. and lcares 18 FOr H.
Then mulcipirins r6 che GrA Posrion, bY 3
2. Tet the Second PositiVi D aL Wa)S LIdMo-
seneal, or oF che lame kind wich che firit:
That is, belons boch LO OnC MTan, OnC
t Et
ehe second FFrOK, and alto 20 the second Polition,
crom che Product 48, (becauie ihe LrrOro atc
 2