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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 120, page id 1815201908:0177
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.85
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

OHL
212. guinei. 2d F FL, icem DE ET ad FTO. CFGOAVE A F viid ancecedentium, ad C F vnamconse-
quencium, ica omnes ancecedences, id est linca LL, ad omnes consequences, nempe
lincam CO. Acqui ex constructione re AF. ad C,  C AR al CB, ErSOAI
cst ad CO ve AK ad C. D, quod esse absue paet ex elementis. non est igitur
racio AB ad C B, maiorracione AP ad C F: Patec ergo propolitionis rericas.
odudrium.
quancicas alcerius dupla.
Duabus quancitacibus AB, C D, aUFErrI pOsSinEA F, C F, Xqualta; de nonmino
ra dimidio iplarum AB, C D; ec a reliduis F B, F D rurlum auferri polsintF. C,
CrunE quancitates AB, CD. Pater ex demonstratione proposicionis.
F FI, aqualia ex non minora dimidio rehduorum: Si hoc temper heripolsic, xquales
alcerius quadrupla. Requeicam intincum per proporciones quadruplam, quintu-
plam, etc. licebic procedere.
Duamquam Facear hoc Fhicorema aliud non continere, quam parcicularem ca-
Cum proposicionis prioris: tamen quia in libris sequentibus non lemel vlui veniet
vilus mihilum operae precium lacca acilitalis Caaephelee apponerem.
Similicer hoc quoque Theorema ciuldem proposicionis vnivertalis calus erie: A
Fuerinc dux quancirares, a quidus auterri semper possint non minora dimidio, liC de
ablaca lingula rnius, dupla perpecuo sinc lingulorum ex alcera ablacorum, criema
Duodhablacarnius, semper eripla Fuerincablacorum alcerius, crie vna quancitas,
PRO1
NOPE
ACx Sinc eres magnitudines, aut plures AB, CD, E F ex a Cingulis
auterri polli nonminus dumene, la Habiaca t, LL, Le mu
in concinua analogia Oad R. Beinde a eluus auretus porsieneu tiou
minuisdimidio, ira ve ablaca I, RL, N O sinccontinue proportiona-
lia inrarione eadem O al H: & hoc semperheri polF.
Dicopropolitas maslucudines AB, C D, F. F esse in continua analoslat
Demonstratio.
bi6. tu
Voniam AC est ad C K, ex hypochesi ve 9 ad R; e OH ad R F, e HY 2t
L M, VE O ad R crunc partes ablacX AC, CR, CFP, RC; II L, L MI, acque ica
in finicum invicem proporrictates. uac Cum cxnspocnencctau ngura ucnon
b minores dimidiis suorum inescora ee ABadC B. be AadC L HoCCC
dacisve O ad R. Similicer Menaam C D eitc aa bL, ve CR ad L. N, hoc cle
cacis ve . Clum  B. C B.FC. Colcina Blopocoates a
nes. Ouoderat demonstrandum.
o