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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 806933011:0289
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E
chetormot PropostonalS, viz.
And mulriplyins che Fxcreams and MeanS; You
Produced boch ays; which hens hes alc. cus
proponrional. P. E. D.
WVHCrCTOre iE IC LaLAS RECrUM, AIII. LHC AIS
Transversus be giren in the EIlipsis, tis casie 1O AnC
cd
ehe second AXC. BY mating a5 ob:=
00l
(= Rectanele DC E) E0 20C d = Square AC. )
Wheretore A C is Hnomn, and consequentir its
double AB.
:
sum, Latus Rectum.
L
2 a 2. docL L. 10
AIsO sinCC C F. Square: A C Square : : ob:
0cd
5 chac is by chis Prop. AS Rectang C D LF:
SquareTK. ThereFOre SGNArE C R: Sgnare A C
:: Rectangle DI P: Square LR. ThariS alIO (b7
Cor. 3.) 25 Square C F: R ectangle DN F:: Rect.
ansle DTF: Square IK.
COROLLARY VI.
Wheretore chere wilt beFound a neu and uletul
way oE exprestins che Square oF che Ordinare LR
(wrhich we tound abore in Prop. T. W 25 00c d
cecd.) HYou mate aS C F Square (= 0 0bb
: Rectanele D N K = (o0bb. = m m, By Cor. 4
Prop. 2.):: 50 Rectangle D L F EO L FOUKTH, PFO-
porrional; Which orkins Algebraically by che
Rule of Threc, will be found co be oc bb -- e c bb
temm ammec
The Adramtase ot which Norarion will suffici-
EVhose Square must be 0oc d = Rectane le OP cheenuly axpear in thC next Proposion.
Larus Rectum into rhe Transversum; i. c. theFigure,
a5 Apollonius calls ir. WVheretore che axis secundus
and any Second Diameter, is a Mean Proporriona
becween the Latus Rectum and Transversum; OrrO
speale wich apollonius, is equal in Pomer eo the Fi-
Fure.
COROLLRKE 1.
voed
Since the Square OL A C = , and che Squ
OF C N (che Distance oF the Focus trom the Cen-
C) = 0 0 bb = 00C d v7 Corol. 1. 0f ProB. 2.
Pur them into one sum, and ches will matre
00bb
: wohich cheretore must De equal 10 Square
AN: And consequently che Line AN = Z, 1. c.
E0 haleche Larus Transversum.
Wheretore it rou hare che Axes in an ElliplIS,
eis eale ro find the Foci; For rou need only open
the Compasses to the Distance DC, and setrine one
Fioot in a, crossthe Transverse Diameter in the Point
N and N.
COROLLREE M.
Since bY Cor. F. ProP. 2. THC RectanelC DN F.
Ca
was prored equal to =, Wvtrich by Cor. Prece-
CT-) CN = =0b = eb.  m. BUL Ln wil
dine = A Cq. iis plain RectanssC D NF = AC sBC = Cn = Ct = m
SquarC.
2 0b + cb.
eec d: and che Rectanele DY F is cobB-
ee b, IH isb; as hach been evn in chie forme
Proposirions: Place cheretore chele 4 Ouanriries it
c
CDROLLARY IV.
The Square _ C F (- hallche Trantrerse Dia
meter) is to rhe Square oF A C halF che DiameTeF
snt. d5 Latus Lb sa C0 Latus Rectum.
::0d00. 8dd: : 0 bb : 0c 4
oc d
300c
tCt 
obb ocd
15 : ob: : 0cc d = cccd: 0cbb-
Wwill End che same Ouantier 00 cbc d =- occbca
COROLLRRY 
. 60
.t. b. Latuo Lrars oe
PRO P. V
In che xllipsis, ehe Aerexate, or Sum os che Rishra
Lines VN and Pn, drann from the same Point
R, in the Curve of the Ellipsis to boththe Foci Y
and n, is alvays equal to the Transverse Diameter
or AxiS D F.
THCPrOOFoF Which depende on che Contiderari.
on ot the Rectangled Friansles II NI and TR n
Where che Sides beins piven, che Hyporhenules
are easily tact
For il (25 in Cor. 4. Prop. 2. You callC N = m,
cher Will m BeV:
100a
AndLN =
Whetetcte