# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1815201908:0133 # Permalink to this reading: https://leibnizlegible.com/page/1815201908:0133?run=74 # Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1) # Folio 76, page id 1815201908:0133 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=133 # Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000133.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine # Lines: 48 recognised, mean confidence 0.83 # Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. # Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text. # Wording rule: say "the machine reads it as …", never "Leibniz wrote". # After the first blank line: the recognised lines in reading order, one per line. 1. 1. 1. 1. 11 DR OGR ESSION ES versonem rationis ve A G es ad AF, sic BF ad BFT: _ permurando ve AC ad B F, hoc CA (lCuEOstenaI) M AB du BC, sic AF ad B HI. ConltaCCrSOPEOPOU- tionisvericas. P R ODOSTFIO XL LIV. Intin continua altate sa AB, CB, DB, de incer AB, CB media (IC A EB; inter C B veto _ DB lr media F B; acinde inter L B, C B, ac CB, FB medix sine B, HB: Denigue inter (B, CB, _ CB, FIB Dico rationem AC ad CD, duplicatam esse rationis F C ad CF, quadruplicatam aurem rationis C. C. ad C HI, e octuplicatam rationis IC ad CIE: acque ica in intinicum. sine medix IB, ILB. X Sic deinceps. denapto Vm AB, CB, DB unt concinux proporrionales, exit A C ad CD a ratio ea Lidem cum ratione A B al C B. Icem quia concinuxiunt AB, L. B: C b, Cl ratio AF. ad F C eadem cunt rarione AB ad L B: d quia inter eres concinuas 1bidu AB. C. B. DB media (unt B, EB, Patcec clemens AB, L.B, C6, Fb, 1B omnes elle concinué proporconales: quare rario AB ad C B; id elt veram olccH aI Fa- rio AC ad CD, duplicaca eAt rarionis AB ad B B; id eltreoltendi, LattonIs HL ad F. C. quid aucem concinux proportionales sune AB, EB, CB; LB, ccam ctaI D2. Anins. A F, F C, C F CONFINUA: CFGOVE A F, ad FC; sC R C ad OFs ergoratio AC 2d CD, Cciam duplicata est ractonis B. C ad C F; quod erar primum. Eodem dileur- rendimodo demonstrabimus, rarionem F C ad CF, duplicatam esse racionis GC ad CHI:. adeoque rationem AC ad CD, quadruplicatam esseracionis C C ad C FI denique ostendemus eriam limili rarioeinarione, rationem GC ad CFT, duplica- eam esserationis TC ad CK. Vnde manifestum est rarionem AC ad CD, cius- dem octuplicatam cNC. Dux eranc demonttranda. P R OPOSTTIO ZZXV Acam lineam lecale in quoruis continue propotctates, lecundum constabtde. Mbtrdisoari. dacam racioe. Aca Cc linc. diui denda (CuE PO. Aulac PrOPOM cio, uGdacuor concinuas, secundum racionem dacam C D ad V B. GOKCHECLI coctes Talio CD ad DB, quoc concinuas numero desideras in linca data AB, 10 dent. NempC CD. DP., PF, F. C: cum divide lineam c AB, Sicuc divila cst linea C C: in plultis HL. I. K. Dieo AB, eAc diuilam prour exisic propolicio: patet demonstra, contructione. eOPOSITIO LLLI acarum lincarum alceram ira lecare, veparces linex sectx, cum in se. ta, cincin concinua analoxia. Con u s se s e ete e e u e eta ese s e te t et te u e t e s e s e 1 1e 1 1e u t e si ls