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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 806933011:0287
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F L
Here also, as in che Parabola and Fyverbola,
the Square L HE = Righr angle NVFO, prhich jou
ill sind in the Fllipss, must be noced by o cc d.
cec dus 25 in che Hyperbola (pou may (ec) ris
0ec d  = eCcc
IF theretore vou divideocc d = eec d == the
Square OF the AbScisa Ordinate TF, by FF thC
AbsCissa in this Nocation =e b, ic Wwill Aand thus,
0c0 d - 00Cd, or   utichis equal
Eo che Line TS; and wtich wichr che ABScissa
E I = eb, will make P S, a Rectanele =- 10 LK
Square.
and it von ork here 10 tind the Larus Rectum,
accordins to the Canon siren in tlie Parabola, by
(apine a5b: c. : 0d: , vou will have
FOr chC LatuS Rectum; Wtich vou sec is plaints
one parr of che Line LS; and che orher, viz.
=is a Fourch Proxorrional eob, 0 and e d. That sind 2 l Proporrional (F FI) rO F L and R L
15, in Apolloninss way, eo ob che Larus Transver-
sum, = he Larus Rectum, and e b che Abscissa,
(For the Pame Ouancirr -,. comes out bort ays
Wheretore the Square ot the Applicate F L, i5 c-
qual co che Remainder of the Rectansle IL, con-
Fained under the Latus Rectum and Abscilsa, wvten
Out oF chat Rectansle anocher is catren wtich is
made by the same Abscissa, and a Fourth Proporrio-
nal R S coche Larus Transversum, Latus Rectum,
andthe AbsCiNa. Q. F. D.
COROLLARLES.
1. Hence che Reason ihe Name Fllipsis giren co
chis Section, is evidene; because the Square of rhe
end K, When rixtuls applicd, will alvars be inthe
Ordiriate is lels chan, or defectire oF the Rectangle Curre o che Fllipsis.
under rhe Latus Rectum, and rhe Abscisa.
COROLLARY H.
ThC Latus Rectam LCLC, as  ad s  La
bola and (Iyperbola, is here found by malcins 25
b: Parallet ro the Section: is t00, the produced
Diameter oC che Base oF che Cone:: 50 is o d, the
Larus Primarium: E0 =, che Latus Rectum F. L.
And hereil che Ouantiir abore and belon ehe Line
be mulcixlied by b, rou will have =  a guan.
rity equal to the Former, bur more agrecable to
apolloniuss way ot Exprestion; Who gireschis Ca-
non FOr the Latus Rectum, 25 bb == che Square ot
che Parallel eo the Section, is 10 cd == to a Rishe
anele under the whole Base and che pare produced
:: C0 is ob = Latus Fransversum, 20, (Or
P.) che Lacus Rectum.
DLLARY III.
Wrtich Lacus Rectum max be had C eometrically
truo.
Ftavins che Ordinare R L, and che ABSCINA F I.
li L.) And ihen tind a tourch Proporcional 10
ID, (che Difference beteen che Latus Transver-
sum and che AbIcissa) eo the chird Proporrional
E FI, betore found, and roche Larus Transversum
and chen char Fourch Proxorrional Malto cu Latus
Roctum Couptc, L F.
COROLLARY N.
Flence may as many Points as rou please, Be
Found e0 dram an EllipsiS, Whose Latus Rectum and
Transversum are siven, by sindins Ordinares, and
applrins chem co che Axis chus.
Take any Abscissa, a5 F. I, and then make 25
DE, FL:: S0 DI: IS. Then And a mean
Proporrional bermeen this Fourth, IS and E I
erhich ill be PK, che Ordinare Coughe; Whose
P R O P. HI
In the Ellipsis the Square of the Ordinatos R I, GF.
are as the Roctanelos D IP. and DFP, made by
the Lines lying bermeen the Ordinates, and the
Verrices of ihe Lacus Frarlrerlum.
LeF E E De here Called ib, 25 F. L a25 Belore
called e B, rhen ir wrill be plain From whac hach
been Caid in che precedene Propolicion, That che
Square CF, che Ordinace will be in eliis Noration
= ei c d. AISO che Rectanele D F F. Wwii
by mulciplyins D F (= 0b = ib) by FE (= i b)
betound eobeoi bb = : i b b.
Non since by Prop. T. the Square KI = 0CC d
ece d, and here ve hare tound the Square ( F.
0i c8= cicd. H mte necdo be chac ihe
quare