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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 53, page id 797435492:0269
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Lo R C F: VI.
=_ GH = y. ergoBF =
i  OF = 8  y; Cr8O
X
C.7g: : b. r; HInC aute xequatio ry = y X = G X. unde DNH
est hyperbola Tupra niox determinata.
Ouod s punctum O sumatur infra DB; Het ae quatio y X - r y -
ex. unde rurlus constat.
ZXI. Ouinetiam, reliquis similiter posiris, recta F X non jam
ipsiD B, sed alteri DII Feratur parallela; ita ut assumpto in B A
puneto habeat semper B P. ad O F rationem altignatam (D B ad m) L18. 54.
erunt intersectiones N icidem ad hyperbolam.
Nam ducatur NVC ad AB Parallela; rocenturque DB = b; HIB
=fa I1O = 8; DC = x; CN = y; eA ergo X. y: : b. - 
a
= BF; X b. f: : x. - = OK; quarEN K (FH) =7.)
_ O F - - y on)
a
 - 5. Est er80. y   - 8:: b. m.
unde resulrat aequatio m y -) - g x - y ∞ =  X x. vel Facto f. b::
et
m. r; est My) - ∞ X - 7 X = X a. COnSEaL iBitE lineam DHB
esle hyperbolam; qualis superius trabetur determinata.
Nocetur, Si compurario ab ipso puncto EI. inicium Cumat, (hoc est
sIE P P. EIF:: DB. m) eranescente cune termino e; erie m y - y x
x; unde quoque supra habetur alia determinatio simpli.
n
ciOr.
ZZII. Estocrianoulum A DB, _ linea DY Y calis, ut duet a uE-
cunque P M ad D B Barallela, SIE PexPCTIIO P Y = a : P M9 -
DB9; erit linea D X P hyperbola; cujusurique Centrum eAt A, se
midiameter AD, (vel asympeotos AB) semiparameter autem P; Faci- F1B. 55.
endo AD. DB:: DB. P.
Sit enim TD == 2 AD. EAqHe AD. P:: (AD9. DB9:: = 6. 2. Ftem.
APG. PMg:: =TPFDP =) ADG. PMg:: TPXDP.
PMg-DBG::) EPFDP. PY9. relFD, 2P; YPxDF.
PYg. unde liquet Propositum.
Corol.