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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 806933011:0425
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the midale FOInE OL THAL LIHC LL, LoCateU M
Centre os ihe dection, oc rdeher ot ihe opposic
Sections. 
 let
1
Square oF IK: Wheretore etie Rectansle F E
=PK Square; Wtrich in Ehis Nocation Will BC
oc cd=  eeca
Or Conracteals,
This done, procecd (as directed in Cor. Y. Prop. 1.
Ot the Parabola, eo firid che LatUS Rectum) by C2y-
in8, 25b: c: : 0d: , in Words, as che ParaI.
let tothe Section is IO ThC PaFE OE the Diameter et
the Base intercepred:: So is che Latus Primarium.
toa toureh Proportional; ris plain, che Courrti P exm
vill BC OonC ParE OF the Line TS, or in ehis HIOca-
tion = = Lavus Rectum R L (oT L. F.) snd hC
Ortrer will be Coune chus: AS b: c: : 8 d: E
Or accordins c0 Apolloniuss ay of Exprestion in
chis Provosrion: AS ob:   : :) cb:  : 502
thac Will be Tound io De ehc Fourih Proporrional as
besore: Whien is non found oue according c0 chc
Fermis ot ihe Proposuion, becweenitié Lacus Trans-
versum (0 b) andche Ladus Rectum =, arie THC
Abicista eb.
Wheresore decd  cecd, the Square ot Htie
Ordinate LR, is manilestly equalto the Rectanole
uneer che Latus Rectum and che Abscisse; ayd al(0
to anorher under ihe Abscissa, and rhe tourrti Pro.
porcional. 8. F, D.
res EOROL L AR Z si dor ecor
Hence ihe. Realon ot. itie Name Hoverbola-
Wrhich Apollonius sare i0 ihis Section,, is apparent,
viz. Becaule che Square ot che Ordinare exceeds
che Rectanele under the Parameter and Ab-
scissa. ait 11
MEDROLBARY H.
IE vor mulciplys che Lacus Rectumlo c d, (wtieti
is nored here as in the Parabola) bort. abore and be
lo che Line by b, che Parallet r0 che Section;
chere will arise ehiis Ouantity
b
Which beins reselred inco Proporionals chus:
A5bV: Cd: :b0: ; eires exactiY Apol-
loniuss Canon For fincirs he Lacits Rectum, (in
Prop. 12. Lib. 1.) viz.
ASthe Square oc ihe Bide os ehe Cone in whictu
che Section is made, is to the Rectansle berveen
the Scoments oF cheBase made by a Parallel co che
Section, and deaun etiro ehie Verrex of the Cone
ii dois che Latusi Transversum 10 che L acus Re
dum.
Thus in ehe anmexed FiBure, che Curi  L17L
it
qi
is an Hyperbola
:acts ct cit B3i
Wherc The Line P. D, Beins che Conrinuation
OFthe Axis rilI ie meer with the opposire Conc, or
opposice lide oF the former Conc C B produced, i
called by che Name oF che Latus Fransversum; ane
ek D
En an Hyperbola GP FL F, ibe Square of. Ie Or
nate LK, is equal botheothe Rectans le L. L mac
andor ihe Parametes L. B, and tho Abscilla L
and also 10 the Rectanele LS, made unuer +h
Ascissa P L (Or L. R) and anoiher Lin BR
ste is a fourth Proportionat eo D) F the L atu
Tralretsum, P. P ihe P arartierer (or LAtus RC.
clams ada ts t ehs Absetta.
blos gicique sde stius sti
Tet the Bde OF the Core AB, in Whick chie Se
ction is, becalled à; andctiro B che Verlex oFche
Conc, deaW B MI parallet co the AXis ot iE Secti
on, and which call b. Pet The inTETCCPECE ParF Ot
che Diamerer oF che Ba(C A M, bC calledc. Let
LL = cb. Then by comparino chesimilat Prian-
sles A B AP and P IN, IN, in this was oF Nor2
tion, will BC = ec. And il vOU PuE MC =
and che Transverse Diamerer D L = ob; CHeB
ob -) e b. ANd BY TCRION OF THC M.
milarier oF che Trianeles B MIC, DE P alc
DIO, rou will sind thac P P must be exprelles
Oy odq atid IO, by 0d-) ed; and consequeney
DO == od. (The Ceneral Reason of all whas Wa)
es Potation, and the may of morteins to obtainu, sou
vill sec in ihe Parabola.
This done, tis plain chat I L Square must be =
10 che Rectansle NIO; chatis, in this Nocati.
On = occd -) = e ec d, 25 7 ou ill sind by MuIE
plicacion. Wheretore iF occ d - ecc d, tll
Square oF LK, bC dirided by che Abscissa P. L = ed
ehe Duoriene must be such a Linc, wtich loBecer
il D.
Wvick F I, cam mie a Rectansie equal 10 he