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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 190, page id 175906937X:0214
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=214
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# Lines: 37 recognised, mean confidence 0.90
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 L F ML. C U R Y A R U N
Y H E O R E M a VI.
Proposirio 6.
Recta per quodlibec IIrperbola punctum ad ueram-
que Asymptocon ducta, qua in eodem puncto bita-
riam diriditur, curvam ibidem contingit; de Contra,
concinsens ad utram que Alymptocon producta in pun-
eto contactus bitariam divila elt.
Sit per punctum C in FIyperbola BCD, cujus ACympeotiAF,
AF, ducta recta GCII, utrinque ACympeoris terminata, qux
in eodem puncto C bitariam diridatur. Dico rectam OFICur-
ram contingere in C. Secetenim, lihieri potest, recta OFIIIy-
per 2C0r. perbolam in C _ I: eritque = III rectae C C, ideoque e ipsi
C HI aequalis. quod est ablurdum. Non secat ergo C FI FIyper-
bolam, sea eandem continoit. Dico porro conversim, (iC TI in
puncto C. Hyperbolam contingat, candem quoque in C bitariam
diridi. Hloc enim linon Cic, Cumatur in C HI majori parte ip(a FTI
aequalis C C. Ilinc cum punctum C sic in FIyperbola, crit quo-
per 4Cor. Gdc: punctum I in IIyperbola, totaque CI3 intra curram ca-
dec, ideogne ip(aCFI Fsyperbolam non continget, led eandem
Thujus. In punctis C X I lecabie, contra id quod ponebatur. NTon ergo
OC ipsi C HIinaqualis est. Ideoque casu vtroque constat pro-
policum.
Corollarium T.
Manifectum itaque est ex ancedictis, lingula rectangula, quae
comprehenduntur sub parcibus cujuslibet rectae contingenti pa-
rallelae, inter IIyperbolam ee ACymptotos interceptis, esse x-
qualia dimidixe cangentis quadrato. TIE, ( tangenti CC HI aequi-
distans urcunque ducta (IEB D, A(ympEOtiS OCCUETenS in F _ F.
ver 2C0r. Ct. Crectangulum E B F Sire + BFD, UE_E FD F SIVCDF B aqua-
shujus. le rectant, Id eA, ipsius C HI ret C6, dimidie
Carcbo sllachal.
S bujus.
Shujus.
3 per 3 Cor.
per S Bu-
fus.