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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 806933011:0428
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In t
ence between the Ri
L.
ines RN and K n, drann from ehe same Point Le aeseride an Fyperbola, having che Fransverse Dia
in the Curve to boththe Foci, is alvays equal tothe
Transverse Diameter or AXiS I F.
mecer D E, and ihe Loci l and n siven.
From che Point K in the Curre, lex the Ordinat
K Ebe appliec, chen will P Pbe che Abscissa, anc
noced cb. Let C. NPor C n; che Distance From the
Focus torhe Centre, De called m, 25 in (Cor. 2. 0t
Prop. 2.). Then wil IN =- C 1 -] - C N == = 0b
eb. 1 m: And Ln = CL = C n = : 0b. +
eb. m
Square each, and L N Square =  00b B-
cbb -] cc b b -] - 0 b m - 2 c b m- mm
And In Square=
400bb F 0c bb Y ccbb
=ob m. = 2 c b m-  = m m.
Tocach oF wohich Squares, add the Square oF
the Ordinare P. R, Which in ehis Nocarion vill be
Conrid ro BC +cm m - 4c em 
Sec Cor. 3. oE Prop. 3. and chere will arise che
Square oE rhe Hyporhenules, KN = 10 400bb
= 0bm + 2cbm = mm. 1 + em m.
+e e m m
00  and oE K n = = 00 bb = ob m.
2cbm. F mm- p + emm aeemm
Out oF which Onantiries extract the Squari
ROOIS, 25 may casiy be done, and chere will L
toune,
R N = = 0b -] - m -)- 2 em
And
En = : ob = m - 2 e1
Whose Sum is just ob. 2. F. D.
N. B. LAO EHC LalC, L2 n  =0b = p  2 en
be an impossible Equarion, vet ris no matter herc
vecaule alt se Paco, buc: ob. nec to in 1
Addirion.
From N, ac any convenient Distance, a5 N F
Arike an Ark, and keepins cho Compasles ac char
Distance with one Foor in C, mark che Point C ir
the Axis continued; then ich che Lenoth C P
and one Foor in n, Crols He Formex ArK L, 1O IIIAH
vou sind a Point Which is in che Hyperbola; and b
chis Hethod repeated, vou may find anocher Poine
ffurther on, and (0 a5 manr a5 rou pleale.
Th
Realon ot ihich is cridene trom chis PropO-
Etion.
Let the Second Aris or Conjugate Diamerer os the
Tirperbola B A, bc dus i adn i placc at is
Vertex, paranet 10the Granates, ad L. LBet
is from the Centre L, jou dram thro the Points
Oand P, tro RM Lius tunnin on insinuets
And aster this dram a Parallel to this Diameter
Wobidoro oie tesecobtaus ad etrus t sus.
Ic will be plainis demonstrable,
I. Thatthe Parrs of the produced Ordinates, CC
and II R, intercepted between the Curve and the
Asymptotes, will alvars be equal.
Forthe Prianples C E P and C F R beins Simi-
lar, a5 also C F O and CFC:: it must BeaSCF
: P O (OF FP):: C F: F Q OF F R. BuEO F
and P P’are =: WVheretore (L F and F R must bC
equal: From which catins che equal Ordinares
che Remainders: FI R and D C must be equal.
2. F
Il. The Rectansle under C and er l (or l1
and lG) nill ever be equal to the Square of B,
For che Friansles C F. O and C FO, beine
similaE, C F: F O: : C F : F 9: : (OF 25) thC
Square CC: SGlate L.. Hal 15, (b) Cd1. 3
Prop. 3.) 25 the Latus Transversum 10 che Latus
Rectum. Thac is, by che lame Proposition as che
Rectanole DE EiS EO F C Sgnare. And C F Square
EO Square:: C F Square: F O Square. BaE iF
From CF Square, voû tate avay che Rectangle
DF L, chere ill remain C F Square (bY 6.
2 Euclid.) And is FrOm ChC SquAre OF FO, vou
cahie uhe Square ot J C. here wil remain che Rrect
an81
ROP.
C2) or eo a souret part os che Figure.