# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1815201908:1074 # Permalink to this reading: https://leibnizlegible.com/page/1815201908:1074?run=74 # Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1) # Folio 1017, page id 1815201908:1074 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1074 # Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001074.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine # Lines: 46 recognised, mean confidence 0.88 # 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. YNCVLA CLLLADKFOA. 1027 Demonstratio. Vod IFatium parallels circulis AEC, ODO comprehentum aequale sic cit- Erculo cujus radius meciam proporcionem hiabeac incet lincas. A O _ OT, AF Simul sumpeas,non incendo demonstrare, cum id ab Archim ede libro primo de (phxe. ra e cylindro propolicione decima lexra sic demonstrarum. Superest igicur hocip- sum demonstremus de Agura MR S N, quod illa scilicec regualis sic quadraro medie proporrionalis incer lincaS MI R, e aggregacum ex duabUS M K, R V. hoc aurem AC Ostettab. Duoniam extyportieh exlindrus ex quo delumitur rngula, rectus est; erie lacus cxlindri rectum ad Basim OFTL, adeoque per definic. 3. vndec. angiilus NNTL rC etus est. Ouia aurem parallela plana ex hypoctieli NM R, S R V sccac planum NML, crunc communes lectiones NVM, S Ra ParallelX. cum igitur anguluS NM K a1S. Vudéc. rectus lic, criam S R V rectus etic; crapezium isitur MNS R rectangulum est ad balim suam MR. hac igicur in X secabitariam, ductaque Y Z. Parallela ad M N, NS, Cric rectangulum MR, YZ aequale crapezio MN SR, quodcacim pasec, si pet Z. ducacur parallela ad M R occurrens rectis MNI, R S. recta quoque Y Z crie dimidia summe rectarum MIV, RS, quod eddem constructione facta nullo eriam negocioliquer. lam vero quia LFI alcicudo ongula ponieur aqualis diametro ( L, crie hec dupla semidiameeris adeoque _c NM dupla b ipsUS M K. CumigiEUEN N, B Exde SR sincparallelaes eriam S R dupla eAt R V. Ergo Z Z dimidia summa rectarum monstr. 41. NVNI, SR, aequatui rectis MK, R V. Ergo rectangulum (Ub MR AE MKR V, hoc huius. est ouadracum medixe proporcionalis inter MI R _E MR, RV, aequatur rectangulo M RE, YZ, hoc est reance octendi, plano MNS R. Guod erac demonstrandum. Priu(quam hic manum collo decabula, ve sphaera acque rnsulae admira: bilis similicudo clarius incelligatur, communes veriusque proprietates praecivuas rnum Cub aspectum Lectori dabo. Symbolizationes oncula cylindrica cum sphara, primocirea Colidorum rationem. P R Y N A. Vemadmodum ingula a vngulam in criplicara est rarione lace um homolos otutu, lea quoque lphaera ad sphaeram. Seomenta ongularia ex sphxricaram ea guxe planis ad diamerrum rectis abscinduntur, quam ea qua ad cenera consistune eandem incer sehabene tatiotem. semihexagonilincas plana tanc axi xequidistantia, idem quoque preste- curin lemicireulo maximo (phaerx, ex hixec figura circulo inseripea in or- bemagatur producens conicas superlcies; in cadem rarione (ecte erune e vngula e (ptiera: Duemadmocum pracetomococcaara ae luam parcem inscri pram habecrationem octoad lex: ira quo que sphiara ad siguram in seripea habet proporcionem octo ad sex. Ouod sibali rngulari Semihexasonum inscribatur, et secundum huius Sieur e ss. A. A . e e . B H. 1 et ets. st 1 s . et u 1a e 11 . ur1