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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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In ie Second Form, Wotrieh I5 a a d a == R 2,C
Grearer OE tlie evo ROOES,
Coethcieni, or ot= d, en sire rou che guare
OFIT, O. ot =d Fa: Frous im oc ot Which, a
lalt Caking =d, chere v
Make BC. =A
lremain a che letler ot
checno ldors CoughE.
In che Second Form, WHere a a - d a =R.
Lec Z x be suppoled =a, chen will Xy=-a d
eli Cali chinss beins constructed as
a dR (By 14. C. 6. FuCl.) ana ACrC
and contequ
Defore) a a
as betore,
8. 2d F Xr,
As cortie Third FOrm, viz
Saa a=  WBCrC
the Co. efficient is. the Summ oF the ROOES; On S
a5 a Diamerer, draw the Circle d pbz: then appls
adicilariy asbetore; and cher
lure Number, per
Sus e iHC Lobes, it elher be a che ocher muse
bc5- 4) and theretore S a aa ==R
But it X B be suppoled equal 10 a Ce lette
ROOE) chon wist R F -5.- a.
d L R. FY HI, erhich is equal re
in 2 Line equal ro rheSquare RoOT OF R, che ab(0
n, wetrich is S a-
Let F b --5, and C B Or L
S
BuE By 36, 8. 3. F.UCl.
NCBK OFKFC =D BH OEFF:
1 R
then will L C. Or
Thac iS Sa
vare Roor oF which addins
Ed youhare Z X OF p V = a.
And D F Or D T= = = d (hals che Co esticient) cher
will AIBCL = B FC, (by 36. 6. 3. ) OE aa
d= R.
In the T
Will 5 a. V: R:: : V: R. a ; (FOr BBCC S 1o Eti
Arst caken away. Floverer, because ic was that
extrich sare che trst rile ro Bakers Admirable
Rule, and eo whacever Improrements have becm
since made in ir, ies prover io sire jou an AC-
conneot ic in ehc Arst place.
CONSTRDCTION Os Cubicte and Diguadra:
tick Equations in Alcebra.
BIC IIR FC-=CI F L, ThaE 15, da  a
Y 36, 6. 3. Fucl
TDC 3 Forms oF Ouadraricks may allo be con
Arusted aniocher way, atcer che tollovine
manner; Wvhich aprees rery ell rich par
riocs Mechiod ot Solurion by complearins che Fiquarions, bur such as had rheir Second Perrr
Square.
Thus luxpole a a F d aR.
Dean a Line ac pleasure, and on ie set the C0.
etticiene a and bisect ic; at any end ot ic erect
perpendicularly a Rishe Line equal ro rhe D. l.
Then wich ehe distance beciréen he rop oF the
Line and rhe midale ot d. delcribe a Cirele whicta
rill sire sou a, 25 you lec; For chen i: R W
be a mean Proporrional, and a a f a d==RR, 
Phis,  believe, was sirst done by Des Cartes.
aho (in the Third Book oF his excellent Geome
erus) hach siven us a Merhod tor rhe constructins
and findins chc eruC ROOIS OF alL Lquations no
exceedins tour Dimentions, by means, ot a Para
bola and a Circle; bonch Mechod vas indees
noc perteet, becaue Il tould nor construct an
Wvtienthe Second Ferm is Wvancine, Des Carres
Latus Lectum. t Latanetet et als siven Para
bola, and is suppoled equal ro r. thac ies PoWC
inay produce no rrouble in Operation: By wrhict
means ehe former Equarions vill Aand thus
Z. 2. P2. 9-0, 2nd Z1. . PZ2. 42. 1 =0.
Pex then any Parabola, a5 F A C BC suppoled 10
be described, Wwhole AZ iS ACD KL, and iIS Pa
rameter 1=a, inate AC equal 10 :: a, (0 rhac rhe
Poinr C Will alivays be wichin che Parabola
Then cate in che Ax (donnuards tron C iE I
hare a Necacire Sien, buc upvards in rhe AX
produced when ic hach a Poscive onc) CD = e
P. Lhen trom che Poine D (or C, iP the Ouan
pendicula
reduces all Cubicte Equations eo chis FOrm, Z3.3
a pZ. aa g =0, and Biquadratiotes r0 Etis, Z1. 7
a pZ2. a a 92. a a a r= 0, Where a cands For che
140. 6. Lublia.
And here ris plain, thac it c0 R, the Hnown od
absolure Number, you add chie square ot hale che scuy p be nains in che Equacion) erect a Per