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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 806933011:0290
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 L. Y
And the Square ol Li 100DVL 0cbb
cc bb - 0 b m -) - 2 e b m-
Square OF LK, Wuhich (BY Cor. C. OF the precedent,
aSocbb = ecbb- + emm, 4mmec
0c
Sum will BC K PT Square, Cor Ehe Square of che
Ftyporhenuse) which i5 = = 0 0 b b =- o b m -
2 cb m  mm-+ emm 4eem m
And Square HE n = 200bb = ob m - - 2 ebm
Imm (temm, +ec m
And consequently Fxtracting Fhe RLOOES OF thole
Equations (Which is very casic) rou illtiare RV
= = 0b  m - =  and K n = = 0b = m
2em
Wrhich evo added cogether, are manisets egu
200b, the Trantverse Diameter. Q. F. D.
Way uled Dy Gardeners, Xc. to describe Ovals Or FI
lipsis sby truo Pins in ehie Transverse Diameter at 
andn, and a Serinsmordabouchembr a tin ast;
Wheretore the Square oF LN = = 00b b -
LL Compasses, IS an Intrumenemade
isi BraIS, 10 dra at one Rerolurion oF ce LICI.
2nY ECPLSOT Oval.
ELLIELLCAL Dial, is an Instrumene macie
commonly oF Brals, ich a Joyne ro Fold tosether
ance Chomons co Fall Aac, commodioussy con-
trived to tatce licle room in che Pocket; by id
tmar befound che erue Meridian, Llour of che Day
Rilins and Serring ot the sum; irh sereral orter
Lroposirions ot cheGlobe.
TLLIETICAL Spacc, is che Area conained
wichin the Curre oF the Fllipsis.
The Elliptical Space d a cb, is to a Cirele deseri
bed on che Tranlverse Axe dC, as the Conjusare
Diameter, Ot Axis Rectus ab, is co che Transvexle
Are d c.
oc bb -  = ce b b - - 0 b m =- 2 c b m - m M
Nou is ro cach oF these Squares pou add thS
COROLLARET
From whence arites the Realon Ot che C
For by ehis means the Point F willalways Be inehe
illipus; and since a Circle is delcribed by a ol
imorins ound onc Pin placed in the Centre, ris
plain a Circle isan Ellipsis, wotiole Foci are cet
dent.
Draio so, 5n, perpendicular 10 C
Tlen vill 50: fc: : 5,n: 8 c.
2
2
C.  bMA
COROLLARY H.
Elence also ris eatie ro describe an Elixsis on
Plain Geometrically; Oy os Sealé und Compass
b: Al. 9201913) (W
Butchis Proporrion olfo: 5n:: ab: de, wiltue
erue wherever che Perpendiculars fo and 5 n Arc
drawon; chacis, OE aII ehie Indirisible OE ME OHLEI
CMCsC ana FsipIIS: Pherctore che llane spaces
made our of chem must in che ivhole De in etre lame
othe Circle, is as che Conjugare ab, r0 the Prari(
verse Diameter dc. D. F. D.
COROELARES
Proporrion to one aotet. LMar iS, The FIlipsis
WMeretore the Ouadrature oF the Fllipsis ill. be
hac, wohen chac et che. Ciscle io cound, qod vise
versa.
LDROLLARV, H.
Eor havins dravon etie Axis Fransversus D F, and
in it catceri che Foci n and NI; ac a distance nOE
chan hals che Transverse Axis, Wich che Compasse
in A Arike an Ak, 25 f, and sex ctie lamie discance
FrOm L1OG
Then openinsche Compalses to the remainine di
Stance C L, wich one foor in n crols the Ark F, anc
char Fomewill be inthe Elliphs, and thus roumaz
hindt temanu Conto ne poupteale, nieh all icadineto
milar Figuse on a b,  de Wee of che late
The Ellipsis is a Mean Proporrional Berween che
kind on des 25 a b eo a chird Proporrional; 1. c. A5
che Edipsis is ro che grearer Cirele, s0 is the lesser
Ciecte 10ie, vir. 30 ab10 dc.
ereater and lesser Circle. For a Circle, or any Si
as abte.