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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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and vet are OY CHIS LFODOIITIOM aS ThC AD-
fessa LL ai L, WetetOC LL 10IF
Ihe DF M ONSFR AFION os mhict
Practice depends upon ihis.
THac EN Beins = ~E COF F. F put ib.
0cC
ehen Mast. NF = ib-
5. iotiose Square is
2ibB -  0CCi  00CCCC
1660. Fo Wtich il Vou
add che Squate os G F, twhich in ehis Way oE
Oc L. ML, and lL. aec iA Collat
Proporrion. 8. E. D.
PROPOSFFZON VI.
Nocacion ras abore seed ro be oi cc, then in ehe Parabola the Parameter is ro the Sum os
the Square OF N C Will be i ibb -= di
1
DOCCCC
any o Ordinates, as their Difference is to the
Difference of the Abscista.
160B. Whole RooE in chis Nocarion will L CaY, PL. che Parameter, is 10 TH F= F C.
Be ib + . 50 chac a Line drann trom
he Focus rO the End oF the Ordinare will al.
Ways bc equal eo the Abscissa F F -  R Y
Thac is, (supposins F. O rakien equat 10 F. W
roche Linc FO.
PR OPOSLT FON I
::(Sec the last Fieure) ThatiS, tOFIO:: OC
cheix Difference, is 1OI F (OFR O) ehie Difte-
rerce ot hC Abscissae.
Let P F the Ereater Abscissa be called i b,
and che lesset P L, cb. Then, Dy Prop. L. the
Square ot che Ordinate R L will be occc,
axid consequeney cheOrdinate ir (etF= V: 0ec0;
(02(0 purtins i instead ot en V: oicc will be
che Ordinate P6.
Flarins thus noced them, IE YOU PeE TMC LATUS
In ehe Parabola FR CTI, the Squares os the Rectum, the Sum and Disterence oF the Ordi-
Ordinares are as the Abscis.
TLY HKFDCF: : EL. EF.
rhC Square ot LC tHC Ctdiate, WIH DC eqUa
0 che Paramerer mulriplied by i b che AbIcisa:
Ahat 15 = 0i cc: as hefore, ihe Square OF R
Wa5 == 0c60. But Rectangles harins the lame
Bases, are as their Alticudes; Wheretore chele
Rectangles vilt be as che sscsa: And chese
Rectanoles aee = TO InC SGuares OF the OF
dinares; Wwheretore the Squares ot che Ordi
mares are 25 C Abscissa. 8. E. D.
nates, and che Ditterence ot che Abscissae, alier
the manner ot tour Terms, in disjunet Geome.
trical Proporrion (25 belon) rou will sind the
Rectansles of the Exrreams and Means equal,
and consequently che tour Termsro be cruls Pro-
porrional. 2: li. D. AS,
Param.
Dcc. Sum oe ne Orc. . . DiR. OF chieOrd.. D. ABP.
Y: 0ice V: Deco V: Orcc = Y: occc. ib - eb.
Arid 10 avoid che Frouble os Mlulciplication
in Surds, wtich isthe Cale of the rwo Midale
Terms, vou need only consider chis Theorem:
Thac ehe Sum of any. Tuo Ouantities multipliea
hy their Disserence, is equal to the Disference es
their Squares. For (o vou vill casily find that
che Product in boch Cales ill be the same
Quarrirs 0106 = 0eC6.
15 in a duplisate RatiO OI L. F IB F HV
by che Construction ol chelsue, Il Wi
be che lame in l. O, wrtrick is parallel W0
chac is, EF. P N:: F N. F T. ANC
FOxIEE E F Be called ib, as F L was vet
called eb: Then che Parameter beine
LC. LAaC1d, L. 1s L... 1 l. 1a la
On Which our Famous Mr. Bater Founded
his Clavis Geomerrica Catholica, Which wras
untenown ro the Ancients, and communi-
cared cohim by Nr. Tho. Strode OE Maper-
con in Dorsetstire: And by wtrich he Chewe
how ro find che Value oF che Onknown
ROOt in all Eguations, noc exceedins Bi-
guadratiots.
Dec Construction and Centrat Rule-
N. B. This is ThaE PrOPerEy OE the Parabola
COROLL AR Y
IF a Line, 25 L O, be dravn parallet eoche
Diamerex or Aris ot the Section, aud be
cuc by che Transrerte Linc P C in B,
and By che Curre ot the Parabola in K;
hen all O L, ML, and R L, be in con
cinual Proportion
FOr the Triangles F FC and F NTM BC-
ne similar, and NM parallet 10 F C
Pec D BC che ParaMeteE OE any Parabola
2. C. TR.) BHE ChC SGNAEeS OF C F and sDectire Absoissae A and a. THeN T AIM EO prOVC
Lhis Properr ot che larabola, L ull DACI.
demonstrare in my Alsebra, Pas. 78.
 E muse BC EO FNF : : a5 F G. PY MI Wtose ro Ordinates are O and o, and their re
H are in a duplicato Rasio t L F 10 F. WV, seac P. 0 + 0.: O = 0. A = a. Wtiici