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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 623, page id 1815201908:0680
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# Lines: 82 recognised, mean confidence 0.83
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ram
it
ticure
b
bere
ABU
B6
cinuet
eries
CC. IIC
vonine
DEOp
E0 A
neint
3n
inic
YB2
1
EIXPFR BC
Demonstratio.
ABCANE ABC, ADF hyPCtO
communem diameerum ExAMIUCPLam
dinacim ponancur IDB,  L. C, CCbLD.
CF proportionales ese LB, 6C: cum
enim quadeacum ID sic ad Guaoratum
EG VE FI A rectansulum ad rectansu.
lum FCA; candemque leruent propot-
cionem quadeaca BI, CC: Patoc LB, L. C quadraca proporcionalia elle quaurals
IB, C. C, 2deo que de lineas, lineis proporrionales, quod eracprimum.
Sinc iam ID, CF linea proporcionales rectis IB, C. C; dicohypetooras ABC.
A F, ad quam ex ijldem punctis T, G Or.
ADE Communein habere eransuerlam dia neerum F A. sic enim F A diamecerhy
perbole AB C. cricigitur ve quadratum IB ad quadracum CG, AC FI A rectan-
sulum ad rectansitum FC A, sed ve IB quadracum ad quadratum CG, sCID
dracum eAt ve FIR, reca claz LE A: quare LA quoque dia
Guadracum ad quadrarum F C ex luppoo, Gdadracum isicur ID ad F C, qua-
merer eMhyperbolae AVI. Quodecuc demonttrandum.
Scholion.
que adeo vacam esse e indeterminatam, di palet omusabiquus proprietates in quibu
periatur: es vii circulus A BC
cum quauis ellipsi comparari potest,
secundum ordinatim positas, scilicet
secundum rationem P F ad F F,
vel CF, (dummodo proposita quae-
vis ellipsis ad unam sibi similem quae
axem AC habeat aequalem reduca-
rur) ita quoque omnibus hyperbolis
id commune est: quod quo melius
assequi valeamus, comparabimus hy-
perbolam ABC. cuius asymptoti
rectum continent anculum circulo
AB C: in circulo quadrata B F or-
dinarim applicatarum ad diametru
C, aequalia sunt rectaculis AF C:
ita quoque in hyperbola cuius asym-
peoti se ad rectos secat anculos qua-
draca F; B ordinatim pesicarum ad C
diaetrum F, equalia existunt
s
Lit A sit s.3C B F.lectE3e L Y  2 60.s
00239 MMSIEECIL SYSMMESTCIC CINI
recfanentis DF, A i F. ip seen Vere d rpEimih :. T F 3 syaril sgiseni 10 rcll BB. B L. C
EFVEL CF guadrata rectarum
quae ordinatim ponuntur ad axem
C patem obtinent inter serario
nem quae inter quadrata BL repe
ritur. eodem prorsus renore in hy-
pe dolis contincit, nam quadrata
FF, vel C F, candem inter sesor-
Derit LAC
1V cit
Len 101t
ins
Ocus hic exigere videtur, ve paulo fusius explicemus in quibus similitudo hyperbolarum si
omilium consistat, ut melius discrimen quo differre videntur inter se hyperbolicae sectiones
dignosci queat. Enimuero plurimi persuasum sibi habent, differentiam inter sectiones illas, Vs
omnes hrverbolae conveniunt, quales sunt diamerri coniucatae asymptori, laterarecta, ordinatim
positae, es his similia, nulla possit formari scientia, qua alia ab aliis dignoscatur. Sed prorsit
falluntur: nam inter Ellipses non est mains discrimen, ac circulum, quam inter hyperbolas re-
R KKK 2
tiuntur
e eo ere s ao es o eheae eales aero