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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 806933011:0079
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Denominator or Divilor is ro be 2 a (the double) Vn.) Tochis Numeracor, il (For che Denomi-
Roor ot the substracted Square) Or 2 a F c. (thaE
double Roor increaled by one) checrue value (al-
lins becween chele rvo; Comerime che one, (ome-
time che ocher, beins nearest to che rrue value.
Bur (for avoidins ot negarire Numbers) thelac
ter is commonly directed
The erue ground oE rhe Rule is chis; aa beine
(by Construction) che srealest Incezer Square
nacor or Dirisor) re Tubjoyn 30a, che Resule
will cerrainly be 100 grear tor e, becaule che DC
vilor is. 100 lirele: (P’or ic Mould be 3aa f 34c +
ee, to sire che rrue ralue ot e.) It For theDi
vilor, we cakre 3aa + 34 f 1, ic Will cerrainty be
co0 lierle, becaule the Dirilor is 100 ercat. (For
e by construction is lels chan r.) Ic must chere.
fore (berveen chele L imiEs) be more chan chis
concained in n, ris evident chace mus be sels 
chan e, (ocherwile noc aa, bur thesquare ot a L 1,
Patrex; and cheretore rhis larrer Resiile being ad-
ded to a, will pire a Rooc Whole. Cube may be
or lome oreater chan ic, ould be the srearest subsracted trom the Non Cubick propoled in
mainder b= 290 f ee be dirided by 2a, che resule
Will be e00 ereat tor e, (the Dirilor being 100
order ro anocher Rep.
Buc il for the Divilor, we take 304 f 3a, (OF
even lels than (0) che Resule may be t00 great:
liccle, tor ic Mould be 2a F c to make che Ouori or (in case b be (mal1) it may be r0o lieele, ane
enc e:) Bur il (co rectitie chis) ve diministi che
Ouoriene by increatins che Divilor, addins LtO
ic ic becomes 100 licele, because che Diritor i
nou c00bis. Por (e beins lels chan X) 2a f X is
more chan 22 =c; and cheretore t00 big.
e
AS For instance; IF che Non-quadrar propoled
n-5, che Ercarest Inreger Square cherein
concained is aa =-4 (the Square OF a == 2.) Whiet
beine substracted, leaves n aa--5. 4 -- 1 -- 1
2ac = ec; wrtuch beins divided by 24= 4, sives
: bur divided by 2a f 1 == 1 = 1=- 5, gires 5
OFE 15 (0.)
noueh, che lame Procels may be again repeated;
Which comes co pals trom hence, becaule
(by Construction) is less chan L; and cheretore 3aC
lels chan 32; and perhaps l0 much, 25 chac che
Addirion ot ee will nor redress ic. And wvhen ic
(0 happens, 30a f za is a berrer Divisor chan
Thac t00 ereac, and chis c00 licele for c. And
cheretore che crue ROOr (a f e-= Yn) is lels chan
24 = 2, 25, bur greater chan 25 =2, 2. And chis
wras ancienely choughe an Approach near enough.
IEchis Approach be nor nou choushie near e
3a4 f 3a =F, COr even Comewhat lels than ei-
Cher.) Buc because it doch noc alivays (o hap.
pen, (Though for the most part ic doch) che
Rule doth racher direct the ocher; as wrtrich
doch cerrainly sire a Roor sels than che rrue va-
luc, Whole Cubemay always be substracted trom
the Non. Cubick propoled. The delion beinsre
have, such a Cube a5 (beins substracted) may
leare anorher b ro be ordered in lihe manner for
a new Approach. Buc for rhemost parr zaa may
be Patelr taken for che Divilor: For chouoh che
Resule will then be Comehac 100 bis, vet the
excels may be (0 (mall as ro be neglected; Or ar
A, 84 a (nou conue a5 an Inceper in che leas, e may chence casily judse irhar Number
second place ot Decimal Parrs) ehis substractea
From 5,00. COl, Wisel che lamc, 0. 84, ThC ex
cels et ehis Squale above the Former, From 1
orhich tras chettene Lemainder,) lcares a neur re
dires 4. 45-=53= -0. 65636 f, t00 much: Bur divi
ded by 2a f 1 = 4. 5 IE Bives 450225=0,0355
F, c0d lucle. Iie ulle ralue (borween chese
ivo) being 2. 256 proxime, Whosc Square i
rhar e00 bis; but 2, 236067 F would be muct
(ComeWhar lels chan ir) may be sately caken ;
and il ve chance ro cakce ic Comenhar r00 bis
ehe Inconrenience will be buc chis, thar b For che
nexe Rep will De a Nepacire; ot Which Case e
Mall speake anon.
Thus for instance; il che Non Cube propoled
be g=n: che prearest Inceper Cube cherein con-
rained i5 8- aaa (Whole Cubick ROOE 15 a =2.
Wtrich Cube substracted, lcaves 9. 8-- 1 -B.
3040 f 340c 7 eec. This dirided by 3aa == 12
sives 13=0. 08333 f, 100 bis For es bur che
Came divided by 3aa f 32 = 1 == 12 f6 f 1= 19
eives 23=-0,05263 7, e00 licrle; or it bur by
3aa f 34== 12 f 6- 18, IEgiVes, 3 960,05555+
vet roolicle. For che Cube ot a f0, c6, 2,06
is buc 8, 742, which is More oF 9: And (0
much BOrE ot ie, thac we may Pately rake 2, 07
a5 nor e00 bis; Or perhaps 2,08, (Wrhich il il
chance eo be roobis, ic will noc be much c00 big
(25 MaII be Farther Bewn:) And uxon eryal ie
will be found noc r00 big; For the C ube OF, 2,08,
15 8,998912
IF ehis Scep be nor near enoueH, this Cube
substracted From 9,000000, leaves, a new b
0,001085, Wtich divided by 39a =- +2,9796.
Dires 0,000084, Which vill be Comentat 100
big bur noc too much (For e is nou (o (mall, 25
chac zac may be Pately neglected (and ee muctu
From che Non Cubicte proxoled, (suppole n) miore;) (0 rhar it t0 2.08, Wve add 0,000084.
the RelulE 2,080084 will bc r0obis, bur 2,080085
vill be more r0o licele; (a5 will appear it We
cake rhe Cube ot each,) (0 char cicher oF chem
at etie econd Scep, sives the erue RoOE wichim
an Onire in che siniti place oE Decimal P r1S.
and rhar as oc as is choushr necessary.
Lake non For a, 2, - 2,. 2, Whole Square is
mainder b= -0, 16; Wtrich divided by 2a = 4.4
4. 999696
Ethis DC nOE chouxhe near enouxt, substrae
ehis Square From 5. 000000: The remainder b
0.000304, divided by 24 == 4. 472, Or by 2a f Y
A. 473, Sires (cicher way) 0.0000683 Wrhict
added 10 a== 2. 236, makes 2, 236068, Tome
moretoo licele
And by rhe lame method, it be chouehenecd.
Tul, we may proceed furthet.
Ie ere eatie ro compound the Proce(S OF L
or more Sceps intoone, and sive (tor che Rule
ihe ResulE oF such CMPOnEION, Wrtich evoulc
Which gires us the Square RoOc oF 5, adjustec
10 the sixch place oF Decimal ParrS, at chree Aeps
make it leem More seau ante mysterious, re
amule the Reader.
tick) ehe Rule is this:
substract the greacest Cube in Incegers cherein
concaind, (Cappole aaa) che Remainder (sup-
Pole b= 3aac f 3acc f eec) is to be che Numera-
Tor ot a Fraction for delignine l Value ot e
In the Cubick RooF, (contonane to the Ouadra-
(che remainins parc ot che RoOE Conelc, a + e