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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 806933011:0233
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Ouancicres A and E, itole summ 15 Z and L
etie Ablolure Number, Was the Summ ot cheir
Cubes in che tormer, buc x cheDitference oF them
andX che Ditterence ot cheir Cubes in che latrer.
L.nd he tound allo, chac aII Cubick E quations mixhE
De reduced ro one of chele two Forms; Por as Por
chele 1NO, Zc 3 A Z Z. and Xc + 3 C. X
Xc, Where Z and X are Nepacire Ouanciries
chey omly ditter lrom cheformer, in wtich che
are Astirmacive, in ehiis, ehiat here X and Z will
be Weparive Ouanciries, whereas chere chey will
De Posicive.
So rhac all Cubick Equarions beine reducible re
chiele cmo Forms, che only Disticuley remainine i
etiis: Flavinque ihe Rectanele of eruo Duanticies, wich
ehe summ or difference of cheir Cubes, to finst the
duantiries chemselves, and consequentys, their
Summ and Difference.
Wstict is performed by relolvine a Ouadrarict
Aiguarion ot a Solid ROOr (or one Wwhole ROOT i
aCube or lome hixhee POWCT.)
FOr  =F.  =E C. AC+  = Ac-
Eo = Z, and (0 = = 4 C = A0 and 3
EAC L F CZ; Wheretore (multiplvins by
AC Or Ec, and chen cranspolins che Terms
Acc  AC=  c B CC  E C, wtrole
RODES ace : Z +V: Z Z.95 R -
And Dy che lite Process it will be sounc, rhar
Ac
=eX-
EC E0; and consequenaty
AcC X AC=  C FCC + X F. C, intiote ROOI
are V: i. X 9, + R 0 +. Y = Ac
And etlen will ehe summ or Disserence oF cheir
Cubicke Rots BC A + F = Z, and A F= X thC
RoOrS Couphe in rhole cabicke Equarions: That is
V6  =Z LV:  29, cFV: C, + =Z V.
Cq F c A + F Z V: C + = X + V: 2 X93 F
BCC XFY: + X q3 FC A F. X.
Ouamay be NegacM, as -Z Or = X; ihe
AS I5 plain scom bare Algebraieat Mulriplicaci
on in che followine Example.
4a + 2a6 +00
firom wtience ris very easie ro understand, borh
ehe Componition ot any Cubick Number, and aIIC
the Reason oF che Method For excractins ehe Cubc
Root our oF any Number siven-
Thus, luppose 28 vere provoled ro be cntred.
eire is doin (0 chac chere may be so0m co rire
Fixures berween cach
Place; 25,
20 15 8 ct 6000, 11
(wilen 15 t2) mucis
wilen place orderty un
Nexr Z riimes the Square
Ot. 8 15 192, and thac
allo ordexly, as vou sec: And lakly, the Cube o
8 i5 512, Wrhich must De wriccen dovn so rhac che
trk Kixure ot ic ro che Righe Cland may Aanc
ander 8; and ehen addins all cogerher vou have
IP che Number eo be cubed hact conilted ot 3
Nou must procced as betore ca snd eie Cube OF
28, che 2 sirst Pigures roward che, Letr.hand
eetich is 21952; chen atcer char vou are 10 ac
conne char Number 25 rhe Cube oE a. and B0 on
eo find che orter Members as foIIOWS.
and lec charbeb, and 20
Non eo construet Cubicke L quarions atcer MF. sfOrC thuS, 3 tmes IBC
Daters Way by che Parabola, Sec Construction os Square ot 28 is 2352
Equations.
Mr. Ealley (nou oux Learned Savilian Protel.
males 11760 44ab
EOF OF Gcometry 2E Oxon) in Philos. Fransact. N. 190, vorire chac doon there
sires 2 po0d vray co exrract che Roors oF all Cubick tore as vou lec: ltien
aquarions by ehie help ot rhe Tables oE hines:
By che Mulciplication ot a square Numter by IES
21952=Cube ot a + B
oc moie places: L5 (uppole 285.
oure 5 10 Hand 2 places
Roors ihen will be - 1. F- Z. and - A Tarrher corhe Riphehand
b
Or Ot 280
mulriply d by 2 eires 334== Z abb, wtrich Wrire
21952, chetrue Cube of 28.
2
21952= a a.
24149143.
5, Which is 125 = b bb in iis proxer order, a5 Was
ROOE Thus S4 is a cubick Number, and is made Memed above, and rhen addins ail rogecher, chc
By mulriplxins 16 che Square oF 4, by che ROOT4
In Alrebra the chird Porver in a Serieo oF Geome
rrical Proporrionals concinved, is called a Cube:
25, a is cheRooE, a a che square, and a a a che
Cube: And all Cubicke Numbers may be ranged
Summ will bc 23149125, che Cubc oF 285.
And atrer ene lame manner son mult proceed
on, les che Number robe cubed benever lo large.
Andctiis Mechod et etie Componiion it a Cubc.
Number beine well understood, the Extraction oE
Mo che form OF Cubes, 25 8 or 27, Whole Sides )etie Cube-Root ill be very eatie and incellixible
erc zand 3, and cheir Bases 4 and 9
by che sollormine Directions.
Suppole sounere lo exract he Cube-ROOt OUF
_t the Hoor, and ot z times the square ot the for Lom over elie Arit Fieure 5, and hen over e
ereacer pare mulciplicd by che leller, and ot very chird Pisure atcerwards; 25 many Poinrs a5
 reo che desdate b de telet una  schere arcus 1o many Rigures will jon trave in vour
he BCcater
aobt.
. P inet
adFLaab
e act habeecdo
aad+ 34a0+ 3000+ 606.
aa
d em 2E10
db
12
C
11760=3a ab
2100 3
125 = bbb
Lla 3, l Cube oF 20r
rimes the Square oF:
by 8 Bives 96=3 a a b
der che 8 25 you sec.
Imaxine che ned et.
Or 280, a; proccedrhere.
rhick ulcixls d by
N. B. IF, 25 Was Paid above, the Abloture
Cay. J rimes che Square oF 5 i5 25, Which mulei
COBICAL Number, is thac which is produced don as sou sec: sna lalels, eire the cubc ot
ply d by 28 eires 2100=3 b ba; vrrite thac also
Lbeorem. Frery erue Cubical Number prou
acut a nominal Hooc consiles ot chele Parrs, oF chis Number 2314912)
8Z. Lhe Cubes ot the ereater and leNer parrs
2. Beximmine at heRiptic harid, mate a Prick