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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 600, page id 1815201908:0657
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e
e
ciizan ZsilicesE
Constructio e demonstratio.
Neer AB, AC media ponacur A P,
hancque concinua, AP, AC, A C7, dico
E terminum esse quaesicum. Fiane AFI
AB, asymproci hyperbolx LR L, _ eri.
Bantur BL, C. K, DF, _C. parallela aCym-
Proco: Duoniam AB, AC, AD, AF ra.
cionem concinuane proporcionis criplica.
tX, rectae quoque LB, R CL D, M FEn _C,
proportionem concinuant racionis cripli-
Cata. Vndeb planum TC, eriplum elt pla-
ni KD: de illud rursum eriplum plani L. P,
_ lic inicaereris procedendo habecur progressio planorum in racione eripla: quia ve
roi AB, AP, AC proporcionales lunt, ec ipsis A P, A C, cercia proporcionalis est ad.
iecta A C ConcinuabanC A B, AP, AC, A C rationem candem: _ S ex P crisatue
parallela asymptoco, BLPO, CR. OG, CrunE ipAS AB, AP, AC, AG proPOr.
tionales, ac proinde in racione concinua. Ergo rario IB adOC, est lelquialcerara
tionis FB, ad K C, 00lenlu quoin definitione r0. e rr libris. elem proporciones di-
cuntur duplicara, criplicata, ecc. Ergo planum IC selquialcerum est plani TC, Sed
toca prooressio planorum TC, RD, L F, _c. sese muruo in proportione eripla exce
c86. depro deneium sesquialcera c est primiplani TC. erpo planum IG aguacuF cocI prOOTCMO-
pressionibus. ni planorum LB, RD, L. F, _c. ac proinde linca OC cerminae prosrectionem pla-
norum. Aequi progressionem planorum perpecuo comitarur progeellio racionis eri
plicaca, AB ad AC, AC ad AD, Xc. ergo haec quoque cerminatur in C. Extri.
buimus ergo, dc. Ouod erar faciendum.
102aS is
PROPOSITIO CZXRV.L anii
eiab
A 5G) E. LLWB  :B EsBSINCUL S. ∞.
DOnacurrario AB, adt R C, quadruplicata rarionis AC, ad AD; ratio
rurem, AC 3d, AD, quadruplicaca rationis AD ad A F. X SIC COn
lequenter, huius vero progectsionis tinis siuc cerminus sic punctum F.
ationem AB, adL C tore criplicaram eius, quam habet A C, ed
C
e b  Demonstratio.
9 399511 91C)
13 ce111.
i
11C L.lquii
15tee1S.leE.
2 c
I1
13
112 CC. HE3. 3id
iRecta ad A F normali AO, incec
yipeocos AF, AO. brperbola
deseribatur CHK,  ex B, C, D, F
_C, duCanCuE BC, CK, DF, etc. 2
quidittancesalymproco A O. ve AB ad
AC, hCKC, 2d C B; _ L. D ad RC BE
C al AD, quadruplicaca cs iBiclE
H Z D E R BOL A.
eROPOSITIO CXKXLMMIS
Oporccathuius progrestioniscerminum assienare.
VTEratio AB ad AC, criplicata rarionis A C ad A D, ee rario AC
ad AD criplicararationis AD ad A F, 8Ec. 15.
rectatri AF
A1.  32 (5 133CS C Cit  B. C)
ESFIIL IILB MMEMLEMM SE A CDIES ad L COr.
1n
3Z XF. Rficorna2
l 1C   7 . et c
Vnde, _ CC planum quadrupium est Pr  D. Mmmicer ostendicue planum
Eo
1
111F. 2C. CIV
racio CB al HC, TatOMIS RC du
L D quadruplum cMleplani L. L. de lic de cxetetidi Proereto ivicur suc est planrorum