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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1027, page id 1815201908:1084
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.86
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# After the first blank line: the recognised lines in reading order, one per line.

VN GVLA P AR ADOLFCA.
1027
quadracuI AD CH da quAdEaCUM RO, VE- F B ad BL, HSC CA, VE FT C ad F 9. 2 1. parab.
ergo quadracum FD eA ad quadeacum MNT, vE TIC ad LO. C Ca ED
MN bilecta sinc in FT _ L, erit quadrarum F FT ad quaLACM AI L, ve HIG ad
T G. ergO FM OD parabola est. Ouod crac demonstrandum.
P R O P OSITIO ACI.
Ixlinari recti parabolici balim ABH sccetGuS A C, LccUMOUI
quam de rectam AD Facta lectione ACF, crectaque ex I puncto,
quo dividicur A. C. bitariam diametro IB, Ponatur planum per IB pa-
Fallelum rectae AD, exhibens BF. rectam in Cuperficie crlindri, qua bis-
secta in C, Ponacur per C X AF lincam, planum AGF; de ponantur pla-
NA per ABE; _ CBF. qua exhibeane communes incerlectiones AC,
GF, DE, F F
Dico corpushabens basim ACF, ec hxdris ABG, BCFC, inclusum,
aquale ese corpori quod tc sub basi AD F, claulum planis AG F. D X
CEF: Sivecocum prilma ACFDE B, plano AC F bilecari.
Demonstratio.
Droniam planum TB E parallelum AL
Llecat bitariam A C in T, secabie quoque
DF in E bitariam, gua parallela est rectae
AC e consequenter diuidec bitariam rects
AF in puncto R, Ced ex constructione pla
num AC F dlividic rectam quoque BF bita
riam in C, Parallelogrammumisitur IB G R
xquale est parallelorrammo REF F T. Oua
re cum prramides IBGR A, RGEL F X
quales trabeane bales, ee alticudines irem pa
res linc, quod planum IF. aequidister recti
AD, CF e BiseceEreCtAS AC, D F prrami
des ∞: quales crune. Sed criam eorum prisma
AIT DE B XQUaTUE EOTI ICFLFB. CrgC
e reliquum IBK O F C aequarur reliquo
ROF L D A. quibus ( adda5 aequales illas
prramides, crie solidum AC F G B par (0-
lido ADFC F. Ouod crac demonstrandum.
ic dehuo nus pacadencus iectus Cuus vaus palabora lve,
ducla deinde guamose forcsane LB, atutcls B,
BD. bilccen c m a e a camenatum lint LlI, ,l
ducancur A tl, HIB, Bl, ID, perrectascandem AV, AB, BV, a AII
neas AlE, EIL, BMA, Iti, DB:h Plato autem aMsccclones lactate
ducancur parallela laceri AR plana qua faciane in plano R MO, lccHo-
nes L. S, F. Z, C. V: ducra deniqui diasonali AO Eat lecrio per AO: quae di
vidat
PROPOSITIO XCII.
AIB, Bl, lB. Plaita Penateur caocnua in chMmar LaBence scclasi-
neS S MI, Z L, YN; in planiS verO ADOIE, ABNIK, DBMIO IccciO-
    ot         e   ur t       7 Hueu o   he  Hstrte 1 f gu Be   s  f  ert e   S A