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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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ELLLPSIS (in Crammar) is that Figure, where-
by lome Paltos Our Discourse is letr our or rerret
CHCa; ad IIthe Latine Fxprestion, Paucis te volo;
rieure is vety common in che Oriental Lal-
Thi
6. Wner
ce ehe Square oF rhe Ordinate
BUaGCS.
thus.
in which Wecuo, verois aidgut dic sest oul.
DO (= D B x DS) is equal +0BD X DF-
FLLTESI, in Geometry, is an Oral Figure, tis
Produced trom che Section of a Cone, by a Plane
che Balc, For then ic produces a Circle) and meet.
ins wich ele Base produced, asFDK F.O in chi
secont sure Folloving.
But Art L will sive vou DE. WVallis S Geheral ane
Ceometrical Was e demonstrarins che Gener
Propetis oF che Fllipse, and which he expresso
e n= CCCNOP. 3.) L LCDBi to Platio
COROLLARY I.
Flence tis plain, Thac is rou have che RietE
Lines B D and DS, yoU HaVC INC Ordinare DO
OuE e contran becaule the LeS BD, DS may
vary infinicely, and ver makre a Rectangle equas W
DOg. Wheretore the Conick WVriters thoughE
eo determine che Ordinates aocher war; For in-
Read oFB D, chey rook in the SCCCC, CHC CMC
A D, Or the Abscilla; and instead ot A S, etier sub-
Cicured anocher Imaginary Linc, Cuppole L A
(Wrhich cher called che Latus Rectam) and ordered
and consequemdy ihe Latus Rectum = AF X AS,
and A d
e 2a 100
it(0 schac ic Mould be 2 4 proportional recipro
cally 10 the Lines AS, BD, and D A. S0 thac e
very wrhere ic Mould bc B I X AS == D AXL A
cuttins boch Sides of che Cone (bur nor parallel 10
The Square os any Ordinare (TK) in ehe Fllipsis, 15
equal tothe Rectanele (IL) under rhe Lacus RC
ctum (P. L) and the abscissa (F. I) Less, or adia
tine out of it another Rectansie made ) ihe san
Abscissa P. D, and a fourth Proportionat (R S) 10
the Lacus Francrersum, the Larus Rectum (D F)
and the Abscissa.
In the Fllipse the Squares of the Ordinates are equat
1o the Disserences betroeen to Rectaneles, os rhict
the greater are as the Abscissae; the lesser, as the
Squares os the Abseissae.
For,
r. ThC Squares OF DO, are = Rectangles BD
X DS every where, because S B is the Diameter
Ot a Circle.
2. Dramins then S F Parallet 10 A a, The LarUS
Transversum, and producins che BSSerery where
t0F; che Lines D S will erery where bc =DF
FS, Where che D FS are all equal, because SF
Parailet Aa.
3. Nou ill And also char che Rectangles under
BD and DS (= D O 9) will bc = 10 che Rect.
ansle under BD and D F, deductins chac undes
BD and F S. Thac is, BD X DS = BD. 
DF = BD X F5.
4. AIso Becaule the D FS are all equalthe R ect.
anoles BDF, wil Aill bc a5 che BDS: And those
B DS, because oF che Similar Tr. angles ADB, wil
Rill be as the D RS, Or the Abscissae. WVheretore
ehe Rectanoles B D F will erery where bc 25 chc
Ablcis A O; eohiich is ihe ProOt ot ehe tirs
PAIT.
5. BuF thC SqareS BD L F S, MIIICO WOEI IIC
BDS and F S5 are cvery where 25 che A D:
must be in a duplicare Rario ot, or 25 che Square.
et ine plscettae aB.
Drav a Parallet rorhe Section, as MB, Which
Nore wich B, and continue che Axis oF che Section
illir meer wich rhe Diamerer oF the Base oF che
Cone produced in che Poine F, and draw it On 1O
i, and calI AM, c.
Draw also the Latus Primarium F P, and paral
el to ir N O, chrough any oiven POIME, L. Call
che Side of rhe Cone, in wrhich the upper Verrex ot
che Section is, a. Let che Abscissa F I be nored
Nich eb. And rhen (working by che similar Tri
angles BC A, and P IN, accordins corhe Rule ot
Proportions, NVI will be expressed in chis Nocari-
On, by ec. Let the produced parr ot theBale MC,
De called d; andche Latus Transversum, Or Tran-
verse Diameter F D, becalled o b: Then will ID
be=
Sincerhe Triangles BM C, DED, and DFO,
are all Similar, Work For a fourth Proporrional 10
expre(s F P, and vou ill sind ic to bc o d, and 10
in this Nocarion (by che Came way ol ortins)
will be od = e d
Here