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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 806933011:0080
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HIe (ays, tatins the Cube of each, (Wvtich he) No, wrhac is laid ol the Cube, is calils ap-
does; chac che chine may be more clearty appre-
hended) ic is nor necessary chac ve crouble Our
selres with che Whole Cube: FOr, aa2 being al.
ready substracted, For finding b-- 3aac = 3ace + ece
ve have no more ro ery, buc Whecher 3200 
3rec f eec be crearer or lels than b, accordins 25
Wve rakee 0,0000840r0,000083. FOr c.
WVhich may be convenienely done in chis man-
ner: Pake 3a =c, and mulciply chis by c, (OrC
by ic) so have we 3ac F ee; ro chis add 3aa.
and mulciply ele whole by e, ((0 have we
394c f 3aec = eec) ro see whether chis be sreater
OF lels chan b.
Thar is, in che prelene Case, it we cake
0,000084, and add cochis, 34 ==6, 24, chen i
6, 240084 = 3a fc: This malciply d by e-
0,000084, 15 300 + ec ==0, 000524 +5. c0 Which il
we add 344 = 12, 9792, ic 15 304 + 3ac + ce=
c2.979724, erhich mulciply d again by c=
0,000084, 15 0,0010902 f, = 3440 + 34cC F ece.
exhich is more chan b==0, 001083.
Bur it Wve Take c 0,000083, and proceed a
betore, We MaI have 3aac F 3aec f ecc=
plicabie co che higher POrers..
Thac ot che Biguadrare mray be omited, Le
canse here perhaps ic may De rhongBE most ac-
rilable ro extract rhe Square ROOE OF che PILH
ber propoleu; and then the Souare ROOCOF EtAF
ROOF.
Buc if we vould do ic aconce, We are From n
Ithe Number propoled, beins nor a Biguadrate)
eo substract a (the greacest Biquadrare contain-
ed in ic) e0 Aind che Remainder b=- 420- + 6a702 f
42c3 4. +, Wrtrich Remainder, il ve divide by ae
the Quorient ill certainly be c00 biz For 0, (cho
perhaps noc much.)
IFBy 442 + 6a F 4a + F, ic will cerrainly be 200
licrle (for reasons betore mentioned.). And We are
couse our Dilcrecion in caking lome incermediare
Number. And il ive cherce chance noc to ssicom
the nearest, the Inconvenience vill De bur chis
char our leap will noc be (0 great as ochervile ie
mishebe, which will be rectify d by anocher b
aE ThCNCXL SceP.
For che Sursolid (oF ehe Are Dimensions) WBE
are, trom n (che Number provosed, being noc 2
0,001077 F, wrhich is lels chan b, and cheretore pertect Sursolid) 1o substract a: (the grearest Sur-
(it eve substract chac trom chis) the Remainder solid cherein contained) ro Aind che Remainder
0,00002r, will be anocher b for the nexE SceP,
it ve please to proceeu Furrher.
b 542C- + 1043 02 f 104203 +5401. + e5.
Wrhich (a5 before) it we divide by 5a2, the RC
Fricherro we hare pursued che Method most sule will be lomenhar 100 bis, (becaule che Di
affected by che Ancients, in sectins a Square or vilor is 200 licrle.)
Cube, land rhe like of ocher Povers) alvays lels
IF by 5a2 + 1043. F 1042 F5a F P, The Relule Wwill
than che just Valve, chac ic mishr be substracted certainly be lels chan che erue e. The jus
From the Numiber propoled, learins b a pohcire Value ot e beins lomenhar bermeen chelé rvo
Remainder, chereby aroidins Nepacire Num-where we are ro ule our Discrerion, what inter-
DerS.
Buc since the Arichmerick of Nepatires is (0
Wvell underscood, ic may in chis (and acher Ope.
rations of like narure) be adrisable ro cale che
mediare Number ro cake; wrtich accordins a5 ic
prores r00 grear or 100 licele, is to be rectits dar
the REXE StCP.
IE ro direet us in the choice of such interme:
next greacer (in case thar be nearer 1o cheerue diare Numbers, we ould mulriply Rules orPre
Value) racter rhan ene next lesser.
Accordms eo This HNotioH, For rhe square ROOF
OF 5, l ivould (ay, ic is (2 f) Comermhar more
cepes for such choice, che crouble ot oblervins
s
xhem vouid be more than the advantage 1o be
sained by ic. And for rhe most parr it moule
chan 2, and enquire, ho much more : Bur For be late énoush (and lcas crouble) co divide by
EhC Square RoOr ot 8, I vould (aY, ic 15 (3
Tomehat less than 3. and inguire, hou much
at. Which sires a Ouoriene Lomewhac 100 Bis;
Wrhich e may cicher rectity ac Discrerion (by
less. Fakins in boch Cales char which is nearest cakins a Number Lomewhar le(s) or proceed se
ro che just. Value
anocher b, Catrmarire or Nlesacive as che Cale
Thus in ehe Cubick Rooc before us, Prake For Mail require) and (o onward to whar exactnels
(in ehie las Enquirr) 0,000084, (nhere For ne pleale (Which is, tor substance, in a manner
ehe nexe Aep we have b=0,000002,) rather co-incidene ich Mr. Raphson S Method, even tor
chan 0, 000083. F, (Where tor the nexr Aer we
Mould haDe b-=- f0, 00COTF.) In this lacter Cale
ve are co divide b== +0, 60001I, by. 3aa
12,980236-, 10 find (by che Ouoriene) hon
affected Rquarions.
Thus, in che presene Case; if che Number
proxoled be n-- 33, chen i5 a == 32, and b = 33
32= 1 = 54 C + (04 C = 104202 +54C2 + e, Wwtrict
inuch is ta be added r0 0,000083. In cheorher il re diride by 5a1=5X16=-80, che Relulr
Casc, we are 10 divide b= +0,000002, by
52F=0, C+25, is Comenhar t00 bis For c, buc noc
32a == 12, 980248, 20 find (by che Ouorienr) vetrat much. And it e examine ic, by cakine che
is eo De abaced oF 0,0000843 (0 have We Sursolid oF 2,0125, Or OF 273, Wwe MMaIL And 2
3 20,00000085. +, 10 be added 10 Desarive b, (For che REXE ScCP) bUE nOE very
6, 240083: Or 4535585970,00000015+ 10 bC considerable. Or it we rhink ic considerable re
abared oF 6, 240084: (Or ic may sustice in cirher, may proceed Further co anorher Scep, Ox more
2o divide by +2,98 F, Or cven 0) 13, Wichour chan 10.
beine incumbred ich a lons LiTOF) etet O1). Lhe like Mechod may be axplyd (rich morc
evhich sires us, For the Roor (oughe, 2,08008385 advancasc) in che Eligher Porvers, accordins a5
proximé. True (ac che chird Srep) roche eiehrh che Compolition ot cach Porver requires. Anit
Place oF Decimal ParEs. And il this be nor near sche lame Mechod may be oF ule (wich 800d Ad-
enouph, the Cabe oF. ehis compared wwich che vancase) in lone DTumbers (it duly axplied) c
umber proxoled, will. sive us anocher b, For ven betore e come ro che place ot Vnits, For
pans ec. ane lo onnacdo ad Eac a0 e he laure roul equalls hola phere do.
eo