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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 806933011:0427
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the Distance C D, lettine one Foôr oF che Corripal-
ses in C, cross ineLxis ac N and NV; L0 Mall MHCK
Wheretore And a mean Proxorrional becween
oE DF = MtO and L. M, ihich ler bem l 
Poines be the Foci required.
LhIS FIBUIE.)
And rhen make ML C = C E oE itie Hyperbola.
For chen ail che LIyporhenuse N C, bc che Di-
Aance trom the Centre C, t0 the Focus H, se
quired.
GOROLLARN IL
Since che Rectanele DN F ]- Squate CF-
Square CN: Theretore theSquare CHI == Square
C. F = Rectansle D N F. Duc cheretore FOr BrC
vicies lake m == C N, andchen ivill che Rectangle
DNE =mm. -  in chis Noration, or wvtich
more belon.
P R OP. III.
En che Fyperbola (Sec Fis. of ProP. L.) ehe LatuS
Rectum is eo the Latus Fransversum:: A5 tBC
Square os any Ordinate IK, is to the Rectanst
BIF, contained under the Lines intercepted be
emeen it and the Vertexes of the Latus Franl
versum, and the Ablcisa.
Forhere (as abore)  = Latus Rectum, 0b
=Latus Fransversum, ando e c d  e ec d, vilt
bc = K ISquare, and the RectangleDIF, i5
0b b + co b b. Wheretore place chose Terms
accordins ro che Condirion oF he Propolicion
6,
COROLLARY I.
(bY Cor. L. Prop. 2.) ihe RectansICD N F.
: Cohich Ouanrier - = -, is also (BY
Cor. T. OF this Propoposition) proved equal 1O A C
Square: Jis plain che Rectansle D N P = AC
Square, ot 10 a fourth part of the Fisure, 25 Apol
COROLLAEY MI.
Elence cis plain, That rhe Sgnare OF (C F) tiale
che Fransverse Diameter, is Forhe Square OF (AC
OF P F) HalF che second Diameter, 25 tis called: :
ASche Latus Fransversum ro chie Latus Rectum.
For 0bb 00cd
cd: : 0b:
t
:: 00bb: 005 d: : 0bb:
COROLLARY I.
Axain, Since C F Square: A C Square: : ob:
B (by Cor. 3.) chac is, :: AS he Rectangle
DTE: TK Square (bY chis Proposition) elie Square
OF halF che Transverse Diameter, is ro chie Square ot
talE che Second Diameter; (Ox by Cor. 2.) 10 the
Rectansle DNE = A C Square):: AB che Rect
ansle DLE, 10 EC Square oF chc Ordinare
E
COROLLARY V
Fence che Square oE che Ordinare FE L, (Prop. 3.)
Which hicherro in che LIyperbola hach been deno:
ced by 0ecd  eecd, (lec Prop. 1.) may receire
a netr and asetul NToration, etus: SincC C F =
: 0b : : 0ccd = cccd: cobb F ccbb. ies Square will be o . Sax cheretore, aS C F
Squate: 10 etie Rectatigle D NF:: Rectonele
And ervins by mulciplication oF che ExereamS DLB: e02 Fourrh Pertm, ertrich will be etie Square
and Means, vou will sind che Came Ouanciey
00cb d -1- e0b0c d arise trom bocti. And
cheretore che Terms are cruls Proportional.
P. F. D.
COROLLARY I
Inche Hyperbola (Sec Fiz. L. OE Cor. r. OF Prop. 2.)
IsAC Square, Or its equal F F. Square (- 0oc d
extrichis = OF D P mulciplied inEO L NI) bC Fatret
OnE OF CF Square, or ies equal C H Square, (1. c.
OnE OF 0OCd1 00bb
bY Cor. T. ProP. 2.) chere
willremain  uotiole Square Rodt is
C D = hale ihe Lacus Fransversum DF.
Wheretore here, it che AXes be giren, che FOci
arC (O 10O: FOr draw thro the V erTCZ L, R F per.
oF ehie Ordinate LR: and in chis Nocation ic vil
Aand chus.
45d0b
b
:: 50150cbb F. ecbB
cotemm, deomm = 0cbb = cc bb. 50
hat ehie Squate L K, is equal E0 + c m m,
4eemm =o c bb = c cbb. The V (e oP vtiete
pendicutas 10 L. D, and egual 10 C A, and wieh
vill Follon in che nent Propohaion.
Sine
00c
eRC
lonius callS ic.