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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 152, page id 1815201908:0209
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.84
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mmuumm
PR OER F SSIONF 3
diro isicur communi PO. aequabitur rectangulum a 9. hoc est rectangulum sub
AB e VY, rectangulo P Y: Aequi rectangulum P Y, a duplum est progressionis
eriangulorum C P M, AI LL NB _C. ergo et rectangulum lub AB _ V Y, progressio-
nis criangulorum est duplum: quare cum pragrelsiorectangulorum PO, IIO, etc.
etiam Reprogressionis criangulorum dupla, rectangulum (ub A B _ V Z, e pFO.
srellio rectangulorum xqualia erune: uod postremum fuic corum, qux erant de
monstranca.
LlOeIO EVII
Aca lic quadracorum series, Datous indirectum policis, de rerminum
hrabens longicudinis IL. MPares aurem quadratorum bales AB,
Dico, primum quadracum AMI esse ad secundum BH, ve AB ad C D.
139. 1l.
CD, E F, _C. norenturnumteris imparibus L. 3. 5. 7. dc.
_ ad quarTUM D P, ve A B ad  FI. Acgueira in inAinicum, baleS HOTaEE
imparibus numeris, Cuie pmo quadraco cum lubsequentibus compa-
e rurtum primum quadracum  enc ac ceum CO. ne AB ad LI3
raco, proporrionales.
Demonstratio.
Opalemus exempli graria quadrarum AM, cum cerrio CO; Quoniam qua-
deaEa OmAIA ANI, BN, C O. Qc. in concinua tu aoaC a Bales Con-
tinue proporrionales; ex aequalicare igitur etiam AB, C D, F F, crunt continuae; (cu
cetcet tcad astatiue Pitca Mllco lio vit caccalula
AM est ad quadrarum CO, vE AB ad P F; (cum raciones tam quadrati ad quadra-
cum, quamlinex AB ad lincam F F, sincrationis AB ad CD duplicala) Cacen
ralebic demonstracio, si quadrarum AM cum quovis alio comparetur. Constac ereo
propolcionis conclutio.
eR OPOSITIO CLZIX.
Adem polica ligura, cala  platoru u etes n i laveis
bdleshomolosas  directum, de terminum longicudinisR.
Dicoletset i ad nullam lui parcem, verbi oratta sa lchem HI
aucleriem OK, vel seriem PH, Xc. eam habere rarionem, quam incer le
habenc dux quacumque in hac balium scric, recta linea, inter quaspar
lincarum numerus incercedic.
Demonstratio.
minuni, vel par incer ce dat planorum numerus, vel impar; compareneur primose-
riCS MK. _ OK, incer quarum inicia, impar cerminorum numetus incer cedie; quia
SiCuX
Fries enim data MR, cum cx sui parre comparatur, ve incer veriulque primum cer-
i a ui u u u ei  te te ae t u pt e t  e se  p   t p . 1 1. e e    et o p ti     ua  a quet pa  . HII