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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 982, page id 1815201908:1039
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.88
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NEVL A C FL I
BA.
Constructio e demonstratio.
Noniam P. F O sectio bas ABD, aquidi
acsisicur crectis ererminis linede L. 6, que
elt communis, incerlectio planorum P F C, et
AC D. lineis FI,. P Iin supertcie cxlindrica,
iunetilque punctis P, FI, cricareus IB H x qua
lis arcui F. F C; ducto ivitur plano IFIG, 252-
cur K B linea diuidens bitariam arcum LB F,
secundum quam Aac lectio per axem cxlindri
PTOdUCENS L M, KC, M Fi communes incerle.
ctiones. polcis denique HN, IO, parallelis
rectae BK, iunct aque ON, Aac ve L. 7 2d L. X,
ita I. B ad I V. Cinc rectanguilo BL. X Faca-
quale VF γ, _ per YV FT describacur par2
bola LI V H habensaxem L. V. Dicololidu
habens probasi superticiem incerceptam peri.
pheria circulari IBFI, ec parabolica IV HI al.
cicudinem vero BF, aequari Fructo ongulari
F C GM F. Ouoniam parabola est ITVHI.
idicur ve rectangulum LT. IT ad rectangulum
TR FB, ica est P. V linea ad linean aR F. (Cd
ve est rectangulum IF FI adIR FTrectaDgu-
lum, ita quoque est rectangulum BF. X ad
PR O. hoc estrectangulum VP. v adb rectan-
bgota gulum YR S. Teicur velinea L. V ad R P, ica quoque reccangulu V L. 7 ad Y R 5.
igitur cum ex constructione reccangulu V Ly aequale sic recrangulo BL. X, eriam
reccangulu TR S, aquale eric rectangulo P R O. commiaisicur recrangula T RS,
quantur omnibus recrangulis P R O. ergo per 46. libri de duccibus, planum para-
bolicum IVITLI duccum in planum R S, hoc es in alcicudinem R S, hoc est i
alcicudinem LM sivc B Fi (est enim P. NI ad F. R, veB C aequalis diamerro ad lemi.
diameerum BK) aequacur Colido quod sic ex duccu plani circularis IB FT in planum
Schol. 19. Cixcutare TO) N FI: led ex ductu planorum circularium IBFL _PONET Ac lesmen.
huius.
cum congutare LP B C FI. Igitur solidum habens balim IV HI. L parabolam e 2I.
cirudinem BF, aequale cA parri engulari IF B CTT. ablaco isicur communi cxlin-
drico (eemenco TB F II remanebit Fructum cylindricum F. CONF, Xquale cor-
pori quod balim habet claulam perimetris IBFI, ee PT V II. quod criam aliud se-
nusinvolueri centeri porest parris cxlinderea cui congruic. exhibuimus igicur quod
fuerac requilicum.
PROP OStL1O X al.
TNoulx, quarum alcicudines sune equales diameeris balium cxlin-
droruma quibus decustancur, criplicacam habese racionem earun.
dem diamerrorum.
orrua.
Demor