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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 543, page id 1815201908:0600
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DB
cC.
re-
U2-
id
eatis
A6
ergo
IR:
LI
TL Y P ER B O, L A.
Demonstratio.
C em heri POTCA Byperbol in punctis O’e R. et Hac quadeace
C aequale rectangulum OFR. eric itaque punctum T, in ipla sectiono
CiFFi, adeoque ee inrecta AO. Idemisicur est punctum O e Y cum virumque
duarum lineatum OP, AO, communis sic incersectio: quod est coneri constru-
ctionem, qua O Y R, rectangulum equale tr quadraco AC: codemmodoosten-
decur punctum R communenon cMe recx CR, ee sectiohi: igicur F C M hyper-
bola rectis AC, C B, nusquam occurrir. Quod vero semper maxis ac masis adhy-
verbolam accedane, sic octendo: cum D F F rectangula per hypochesim aequalia
sinc quadrato A C adeoque d inter sC, vED F ad D F, siC F F. 2d F F, recipro-
Cc: sed FL. qux tetmorior est a vercice C maior es, F F viciniore, igicux _ LD,
rect_ AC vicinior, maior eA FD, remoriore ab AC. similicer octendetur re-
etasM F eo magis decrelcere quo remoriores sune a verrice C: rectae isitur A C
CB maxis sempeemagisque ad lectionem accedune; ee hu(quam OECUrruHE. aCym.
proci suncisicut, hsperbole C F. V. Quoderac demonstrandum.
Oler 
1
Coro gh: iY X olneim ai
Corourta  MolenaBO :t R _ 3aWBC. IL et
inc sequitur xectas, incet alimproros de hyperbolaminter cepeas aequales estes
Lostenta sunc enim in propol. 14. huius recrx DF, NP. xequales. undecum
Per Y5. huiuS punCE D e F. ad alymprocos tine, patee vericas Corollaris.
PROPOSITIO XVI
ila pera pS POnerE. 
Motrctib.
et 2) estio A.s C i
 2AIICCI. B A3 F.t
Con.
 ies   sie