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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 806933011:0146
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a
Whecetore C +]- 2 a2 t22 and E F =D H-
2aC + ZE b. BNI EEg; t FCq. = CFg. -CY. g
=CDgi + F D9;. 1hat i5, 4 a a 2 2. + 4 a 2 + 2.
4ba2- 2b 22 + bb + 22 + 22d + d a = Bb. + dd
Expunioe bB F d d and chere will remain
aa2 Eraax ta 40a 2022 +22t 2 d 2
0. nr
Then it vou ArA mulcipIy aIl ehat Equarion b3
PP. and divide ic alcerards by 2 you willbrine
ix c0 chiis, 4a a2 f 4a 22+ 2- 4∞b a 2pb27
DZ + 2 p p a =0.
Or to reduce it ro a more Regular Form,
Z = 4a ZZ + D P Z 4 p b a
+ 4aaZ + 2 P p
2
Or il von hac called che whole Line C a by che
Name ot a (25 Baker calIS ic p) che Equarior
evould cand thus,
X +2a22 + P p Z 2bP a -0
F a a Z + 2 pb a
-2b
Nou compare ihis Equation Member by Mem.
ber wich one siren eo be solved in che ulual form;
a5 suppolC, Z + m Z Z +r 2 +5-0.
Drawins any Parabola tatee DC-m Decaule
2 a=m) and apply ic inco che Parabola at rixir
Anoles EO ThC AX AO. Nexe comparine the Co.
efficients in the rvo next correspondent Perme
Vou havep p +aa 2 p b =r Or p P + = mm 2pC
=r: And consequeny, 1 - PP + nm-
BY
Ertich is che Rule 10 Aind C D, Or 10 deter.
mine che Poine D, nearty the Came (chansins on-
Iy The L EEterS) Wich Bater S first Rule.
Then again, compare the nexE ro correspon-
dine Terms in Boch Rquations roserher and vou
have 2pp8 2b p a = 53 Wheretore d F 2bpa
Wrhich beins all a Hnovon Ouanrier, che L ine FD
is knoun, and consequener che Cenrral Poine L
ot the Cirele ro be described, Whole Radius ill
BC F C. Or FO, and which will cur che Parabola
50 25 ro sire you che Poines C, T and N; from
extience lertine FaII Perpendiculars eo che Diame
rer C FF, chey MaII bC the 3 real RoOrs oF chis
Cubick Equarion, ZZ Z L m Z Z Fr ZF5 --O.
And ertich are Nesacire, and wrhich AMrma
rive vou will sind in the Constrution ot chese F
quations by che Parabola: Which lec.
IF rhe Liquarion had been 2 Biquadrarick, 
suppole,
(1 + m Z - n ZZ + r Z 5--0:
Then che Circle vould nor have passed chrouetr
the Verrex oF che Diamerer, bur chrouxh anocher
Point eo be tound accordins ro che Rules menci-
Polirion et    aet  
rected more calie, simple, or universal; secine
any Parabola beins once tor ale acleliou, l
sire au che Loors true or talle, ot any e quation
vichone Reduetion, oe ans Alleratton unalio.
ever.
ened in Des Cartess Construction of Fiquarions; rilt be pataes lo che Scyle, and t0 one ano.
ewtich is, 10 let V: sit s reprelenr che absolure
Number ox siteh Perm in luch an Eiquarion, and
have a Negacive Sign) ac righe Aneles 1O PC
on che Verrex oF the Diamerer; buc it ic be L. 5,
chenthat Line V: must De inscribed in another
ther.
Semicirele made on che Line EC; Whict beins cowards rhe Aphelion, as che sun is trom che len-
et trom che Vercex ot che Diameres C, Will Bive ere os che Liccentrique cowardo rhe Poribelion.
CENTHI
in the PeripherY Ot CMaL SCMMCL OH LC, 
Poine chrouph which che Incerlectins Circle re-
quired Mall PaIS. Sec the manner ho the cen
erat Rule is investisared in che last Term ot a BI
quadrarick according eo this Merhod OF MF. Ba-
Per, under che Word Construction.
Erom which appears.
The Analticte Mertod by wohrich NI. Batiet
ddeo a Lde; Tor a Parabora ven atetDea
and a Point in is plain siven in Position, ne ex-
Prestes ln ays, the Radius ot a Cirole pastine
chronge Verrex ot any Diameter, chac is, by
ehis neu Property, (That the Rectanele made of the
Parameter and Difference ol us scssu, is equat
to the Rectansle made ot the summ of the ro Ordi
aates into their Differences,) ro express rhe Ratio
oF the Radius co che siven Line ot che Parabola
lo hat aEquation oE tour Dimensions, and re-
jectins lc Liquals on boch lides, he depresses ic to
a Cubict. de adjoinins c il a quatsels set inC
Fsomosum Comparationis, chereby makins the
utsble equal co nochins. che equation lubsilts in
a Biquatraticse, havins all irs Terms: IE the Circle
be supposca ro pals noc chroueh the Vertex ot che
Crametes, Vol Chrouph d Lo WICA BeMB OIM
ed vich che Vertex and center, may terminate a
Risbt Ansled Triansi
L Lquation he compares with anocher lke
Ic, and equal l  chen by equatine che C0-eff-
cients ot chele cu Equations he prelencly disco.
vers che Central Rule; Whole univertal Exrent
appears in andraticte Equations, adtected under
al Parodicte Decrees; Tor al che orher Cases
wrhere any ocher Perms are mancins are bucCo-
rollaries, or more compendious Constructions de-
rived trom rhe generalRule. S0 char che Inven-
tion ot che ue scems as much due rothe last F
quation ot che C0- efficient 25 ro the atorelaid PrO-
perries, whicl is demonstraced by archimedes in
the Section oF a Parabolicke Conoid by a Planc p2.
rallet corhe Axis, and es particas uleu oy siu
sius in his Anyticts, wrho chereby constructs a
Biquadraek Equation, Keepins aIl ies TermS.
Buc chen the Analysis oF Slusius by breakins che
quation into no orters ro sind cvo Places is ve-
ey disterene trom char whereby our Aurhor tound
his Centrat Rule ) CAAA HESLCLE BOLHLLM CAL NL CX
CFNI of a Cirole, or oF a Sphere, iS chat
Poine From Whece all Rignes ctan l ine
Circumtelence or Surtace are equal. T0 tind che
ntre of a Circle, sec Chord.
CEATRE os a Dyal, is chat Point where thC
Axis eF che World incerlects che Plane oFtheDyal;
and rom chence in chose Dyals charhave Centres
all che Four Lines are dravn. YF che Plane ot
che Dyal Be parallel ro che Axis ot the World, ir
can bare no Cenere ac all, bur alt che LTour Lines
CENTRE os an Eltipsis or Oval, iS chaE POInE
wohere the cvo Diamerers, the Transverse and the
Conjurare intersect each other.
CENTRE of ihe Equant, in actronoms, is a
Poine in che Line of che aphelion, beins exactly
distant (0 Par From che Centre of the Rccentrique