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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 10, page id 1815201908:0067
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.84
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L FN E A R V
Constru otio.
Y. T)AEx reCtX A D CB SnE inter Le Xquales.
eccamratio Lad L, quam CrFI adt FII,
Sc xequalicaris; ad dantur aute, vel decrahaneur in
racione F ad P, LInCX BR; D L, PaTCE VerItaS PrO-
POlicIOnIS.
2. Si fuerie A B maior quam CD; Sc rario
OTIadFTT, maior quoqueratione AB ad C D,
ratio aurem F, _ F aqualicatis; Dico aquales
addinonposte re compolicae linein ratione daca
OTT ad FIT. Cum enim A B ponacue maior qua
CD AaC Y B aegualis ipA C D: addacurque re-
EX AB, quaenis BK; d si ficri polIIE, HE AK
ad LK vC EFFL ad FTI. erit igIEUT FaTIO AK ad
T. K maiorratione AB ad L B, id est ad C. D: e
quia ratio CFIad TIImaior ponitur racione A B
ad F B, eric dividendo, quoque rario GT ad TTI
maior racione AT ad L B: led esEVE EF FT ad FTT
HC A K ad L K ex hypochelis adeoque ve G Fb ad
TTT,SC AL ad LK, igitur se ratiO AL adt L K
maior estracione A T ad F B: Ouod Aerinon po-
cest; ceum IB minor (C ip l2L K. Ouare lincx
Rquales addi nOH POFCFUHE; VE, _C. Demii vero
poterune aquales, vereliquae SinEMIlarione OFI ad FTI: Facta enim L. B aquali ivs
CD; Hac vECTad TTT. SIC AT ad L M, cadet M inter L ex B; (cuim AL ad Y B ostéla
Reminorem habere rationem, quant I ad TII) dein rectae MB, Aac aqualis ND:
Ononiam ipiciir per constructione est ve GI ad IFI, SiC AF ad LM, cric compo
nenido, AM ae L M, Id ett sd C. N per constructionem ve C LL ad FII. Ouod erar de
3.
Si: AB linea rursum fuerie maior rectâ
CD; _ ratiO O FTad FTTminOFPaTIONC AB
ad CD, cacio aucem P ad F aequalicaris, aqua-
les addi pOcerunE ve composiex rationem Ha-
beanc CTIadFII: hac enim I B linca, Xqu2-
lis recta CD; quoniam perhypochelim, racio
AB adT B, id cA CD per construct. maior cst
rarione CrFI ad HII) eric a dividendo, racio AY
adTB, maior racione C:I ad III; Factoisicue
VE GT, 2d TTI, SC AL adLN, PaECE T N ma-
iorem esse linea L B; nam racio GTI ad FTI
tinot ponieur raciorie AB ad IB; id eA
CD, adeoque ec rario G F b 2d LFL,MLCH A L ad L N MinOF CAFaTIONC A L a IL B:
tam CD linex addatur quadam DO ae qualisipli BN: Quoniamigitur cIE AI
aa L. XT, VECIadFII, erie componendo; AN ad T NF, id est C, O, ve CII ad TTI.
LaoactacDiilau.
Tisdem politis, LGuaes deminon porernne, ve relique datam habeane racionem
CFTad HIl: anterantur enim xquales R B, NT D; EE B heri PONIE, (IE VE CEFEadFIICIC
AR act L Rsid elFad C. M. Cumisitue perhypochesim, racio C FI ad FT I mINOE SC PA.
cione AB 2d T B, id est ad C. D, sIC aurem VECSFP a.lTII, SIC A K a dI H, id est ad C. NI,
29. G CxIEraCIO HL R ad L R, Mitsor qlogueratione A B ad L. B, d diuidendo, rario AL ad
b8. Ouinci. L R minorratione AL. 2aI. B. uod herinonb pocest cum P. P linca, maiorlicli-
ea L K. quare hoc calic demi xquales lin CX MON poreruE VEreligUIX, eC.
40 52
monstrandum.
c8. 6)uB1.
po u e is a ti a u pi  ute u i p u e . qut u    e  ti    pt ul .       pgu   em pu g . p   mru