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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 150, page id 1815201908:0207
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.85
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PR O G R F SSTO NFS
Demonstratio.
exoh. Similium F e KC aquale CriC; CrBOICIICS LOK MH ad PlanUM ANTT, ve seriCSD P, R
ins.
adquadracum A FTI: acqui platum A NI est ad planum AP R, dve quadearum
22. sexri. ATII aa Gdadeatum corius HK. ISIF CX xequalirare series FC K es ad planum
APK, VE TetiCS DFK ad quaetatum AK, _ invercendo planum A P K est ad lc.
Ersz. buins. riem F C L, ve quadeacu A R 3d lCrIC D E R. sed quadratum A K c ad seriem
D P. R. proportionem habec compolicam ex racionibus K A ad B A, e C A ad B A.
ergo _ planum A P K ad seriem F C K, proporrionem haber ex ijidem racionibus
compolitam; quod erat demonstrandum.
Perii
B22. Sexri que planum AF est ad planum A NF quadracum AD ad quadrarum AHI,
130. Bu-
1n5.
que qu
dembalibus AB, BC, etc. construatur quadtatorum series D EK: RaF-
racum AD ad aliud ATII, vE AC. ad AR; quod rocia scrici quadra.
Eorum D E R xquabitur. Super AI verosdc planu AN I simile plano AF. Ica.
hioc es ex constructione re A C ad A R. Duare criam planum ANFI, Cerici planorum
eROPOSITIO CLV
L. S; _C. icem in 9, O, R, _C.
Scoquadratorum series habens bales in directum, de terminum lon-
sgicudinis IE, inscripea CaSa AGKE, iuxca propolicionem 13I.
huius, et completo rectangillo AI, lacera quadrarorum producantur in
ctangulorum MLL, NL, dec. limilium, de continue proporrionalium,
ux progressioni quadrarorum quoque sic ae qualis.
Dico exhaclarerum productiome pespetua, oriri progrelsionem re-
Semonstratio.
Tus. huiu.s Oroniam ex hyporhesi K cerminus est lonsicudinis quadratorum seriei, etiam R
huiue. cerminus Ferir progrestionis balium AB, B C, _ C. ixirur B K B est ad
B ac
 ue i u utos a t t . a     u  que e   p t te e te e e  u pu   e     t    p t     1   e at  i     1.1