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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 641, page id 1815201908:0698
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ra1.
AC.
Atat.
Oque
P rC.
lEC.
Qud.
Culus
HB
con
COn.
BLV
M. d
qu2.
ODem
veem
in
1C.
lont
IBH
aB1
atune
eBA
ad12
dHy.
DOn
1IIII
TTY P E R BO L 1.
P R O POSITIO CCLX.
rculo AB C POnantuF ConCenEricI D F F. COHMMCAL GuOM AC
scircellum AB C occurrens reliquis circulis in GO. Fiancauremre.
cis A C x quales F l, Orthogonaliter crectx ex P. P. punctis.
Dico BII esse hyperbolam cuius
diameret crahluerta eAt BHI.
Demonstratio.
Vadraris AC equalia sunc rectangula
LCD A, hoc es HEB. isitur ctiam
quadracis R Laequalsa sunc rectangula HIF B.
quare rectangulum HIEB ad HIEB cA, VE
quadracum L I 2. l FL quadeacum; PAFCE
igicur FTB elle lacus cransuersum hyperbo-
Ia BII. Ouodtuir demonstrandum.
PR O POSITIO C
Andem hyperbolam producere in infinicum eadem praxi.
Constructioes demonstratio.
Filac rectanisulO AB, AC, sive quadratO
LAD aeguale rectangulum F A F cuius
lacuS. A F minus sIc lacere AB. deinde de-
Scribatur. circulus cuius diamerer (IC F F, _
ducta SINE R MN, crunc rectangula M R W
aequalia rectagulis PR 9. ductisicaq; CFIK
Parallelis AV, tane rectangulis TIOR X-
qualia quadrata +C. Dico CTesead can-
dem hyperbolam IOD. nam ance octensum
est ese II ad hrperbolam. In super ex con-
Aruct. sunc rectangula MI R N aequalia re-
ctangulis PR O, isicureriam quadrata R O
equalia sunc rectangulis M R N, sed perpre.
cedentem quadraca R O, CTlunc ad can-
demhyperbolam, ex eo quod quadrata R O, L
OT sint aqualia rectangulis MI R W, HICR:
isicur produximus hyperbolam DOO, quod
requilicum Fuerar. quod si vlcerius candem
hrperbolam excedere quisincendac. candem
praxim excendac ad circulum maiorem cir-
culo P HF, ita tamen ve oblerverur eadem
condicio, quam haec propolirio requiric.
PROPOSTFIO CCXI
IIrculum AB C cuius diameter BD secet quaevis A C orthosona ad
AB D, _ pONANEUF E F gux xquidistenEB D, OCCUrreNteS A C in pun-
Ais CC, cum peE Cenerum K _ puncta C, aganTuEK, PFI, rectis aurem
K, CFI, hanexquales CI.
Dico BIC esse ad hyperbolam.
MMLITM 3
Demon-
es si  ete ap  si t e ite tis   ea et pue ta  ite t  t  t e e e ut ti sta it i   e ee t e ti   ea A  t e     t t  a