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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 806933011:0426
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dietes are a0 che, Squares ot he Oidinates
The Larus Rectum may allo here, 25 vvell 25 in
he Pgrabola, be Ceomerrically foundo
LDKOELARE
N BC ThC FOcuS; ihen will L. N = 2 b ane its
HE che L atus Rectum L. MI, be applied (0 as rhar
EE vou sind srst EI F, a chird Proporrional 1d L
thie Abscissa, and 10 R I (OF F F) che Ordinare
(Sec Fraxis 2. in che Parabola.) Atcet Wnentind a
Fourch Proportional LL. ro DI, cheSun  C Lan
Transversum and Abscissa, 20 TIF, and toD P, etie
Catus Transversum. FOr supposins LS = II F (2
it misut casili hare been made by drawing ic a lit.
dle lorver) ac che end ot wrhich place S, and dran
D5; 25 2I(0 I E parallel EOFIF: TNeN MMAN L.S
beche emus ca. 2ct dd 1. 1d.. (6.
AE.) (oDF: L. F.
COROLLARY IV.
Erom wohich eis plain, chat tavinae EHC Latu
Rectum and Transversum, the Ordinares in any PTy.
perbolamas de  HC CC CuIr
casly described.
For cakins any pare ot the AXIS (a5 L I) Forthe
Abscissa, ana aking as D L: 10 L L :: 5001:
Square
4
.Bursby chis Proposicion) a
che Square R l: Square L NI :: Sois ihe ReCtan.
Se DLE: Rectanole D N P. That 16, 25 e 0C d
10ccd: 0ccda
00cd
4bb :: 0cbb + c cbb: 10
 Wohich will be found eo bethe Fourch Perm
bp chis way oE Noration. Also chis Rectanele
DNE (bcins made out oF che Whole Line D P
wich rhe part added P. NV, mulciplied by chac pare
added F N) cogerher wichche Square of C P, che
haltos D E, (= = O(00b b, 1. C. = OE0b 5quare) i5
equat 10  d = 00b
= C N Square, the taH
Line wichche parr added. Wheresore C. N is che
co a Tourch Proportional LS; and chen sindins a lDistance Trom che Pocus = 1. .0c d = 00bb
mean Proposctonal Berween IS and the Ablcista
F I (suxpote LK:) That Line PR righely applicd
Mall De the Ordinate soughe, chro Whole POint B
ehe yperbola W Pa(5.
OE lohick MC FOrmex Par dC, is che Court ac
Or he Rectansle ander e Lacus Rectum (20 d.
and Fransversum (0b): Or a5 Apollonius calIs it, the
tourch part ot che Fipure; and che orher parr Dob
der the Fines lyine betmeen the Ordinates and the chat from hence we may have a Canon co deter-
mine che Focus ot any Fyperbola, thus:
Add thC FOUTH ParE OF the Fisure (Or OF che
Rectangle under the Latus Rectum and Transver-
Lecthe Axis OF theSection E B bC called i b, 25 Sum) r0 che Square OF hals che Latus Transverlum:
and extract chie Square Roor oF che Sum, chai
Roor all be che Distance of the Focus from che
Centre, = CN. And iE trom C N vou tate
halt he Larus Transversum, C. F, ehie Remain-
der, F. Wd is che Distance ot che Focus trom che
Vertex.
Wrnicn Rule is vers eatie in Practice: FOr
90bb
+
is nochins bur ihe Squace Ot C F; anet
is onis L os D F mulripied ineo L. HI.
OP. II
In tne xyperbola che Squares os ehe Ordinates K Y ana
Vertices or Extreams of the Latus Tranlversum
and cheir respective Ablcista. Sec Fiβ. PrOp. 1.
belore L. L ivas called e b: Then by considerine
Prop. 1. eis plain, thac the Square of C F wilt BC
0i cd - ii c d; and che Rectangle DF F
Wviii (by Mulciplvins D F - = 0b -)  i bby F F =
i b) be tound r0 bcoi b b.  - ; i bb.
ABaI the Square oF FL I, will BC EO the Square
OFGF: : 25 0e0d -) = c cc d (By Prop. L. equal 10
11) i5 10 Di c d 1i i c d (nO proved = E0 thC
Square ( F.) Tharis, caleing awvay c d, which is
COIMMON, 25 0C-= 0 c, 151001-l i i. Bur in such
very Proportion are the Rectangles D L F and
Fior DI F =- e0 b b - 1 = e e bb (because
DF == ob and EI = c b) andD F L = 0i b b -
2Dd, a5 Was proved just abore. Nou there is
no dondt DuE e0bb 1 = e c b b: 0i bb - ii b
ec: 01-Y 1i. Whecctore chesc Rect.
GF, are as the Rectangles D IF and DF F, un- iS = OE che Square oF che Latus Transversum. S0
 EL
Wheretore