# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0484
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0484?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 427, page id 1815201908:0484
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=484
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000484.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.89
# 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.

trea TB eAt in diametro a BD. RurUM CrIGAEUT CX A dIAMCFCF A P OCCUEreNS A Ex endem
F. D F parabola in B: de IC rectae in R. duCAEUFGUCPeF F, ex Y, linca PF, OcCUF.
rens parabolX E D F in F, _ iungantur puncta CF. Ouoniam A B, K D, rectR D2.
raHela luNC, ve AT ad DP, SIC FL cAt ad KI: Sed ve AF ad DF, Sic B AD est ad
DC(quia TA, ID, LC proportionales (UNC) _ ve BI ad RI, lic F K est ad R F, quia
E. L, KE, FI provortionales TunE; igieUE VE AD est ad D C, SICFK cA ad XF, 2.
deoque FC linca aequidictar RD: vIcerIUIS per C _ HI, policis diamCtrIS IM,
NYO, producatur CFI linea doncC F C OECUTEAE in O. CFIE IGIEUE DE ADC rC
De pro-
pressionibus.
ctangulum ad rectangulum ANC, c hc BD linea ad lineam HN: scd vc AD C. C47 huino.
rectangulum ad rectangulum AN C, (hoC CAVE F K F rectangulum ad rectanou-
Ium F.OF,) SIC KD linca quoque est ad lineam HIO; igicur ve BD ad FTHY, sC
KD est ad OFI; e permucando inverrendo ve BD ad BD, Sic OTI cA ad HIVY,
hoc estF 9 ad OC, hoc cA M C ad GL, hoc eA P R ad R P.
Componendoigitur, inveneo axe D B ParabolX B D F, cum dara sine punet a D
e B, acta pet B contingence BI, agaCUE per D quoque contingens parabolam
EDF in puncto D, secans AB C, in A et C: convenictilla cum BI (veostendi)
in puncto quouis I: dacaisitur lune puncta I, A, C. Criganeur ergO ex A de C, dia-
meeri AF, CF occurrences parabola ED B, in punctis P. & F: ductaque ex Iper
R linca occurret iIla recrE C F in P, (veostensum est)  BD linca in R. vnde ec
K puncrum quoque datum est. HaC IGItUEVE R D ad BD, SC F R ad R A, vel FO
ad OC, ducacurque recca LR vel IO. Patet per resolurionem, in illd esse punera
incerlectionum B e C. isicur exhibuimus, _C. Ouod eracfaciendum.
PR OPOSITIO CLI.
Sco AB C patabolX aAIs BD, de oedinacim ad illum POSITA AC, per
si veto delcribatur palabola AP. F cuius vercex (IC A, X A C linea
ContingenS; OCCUITaF quoque A F F parabola, parabola AB C In F, 0.
POrret E punctum incerlectionis exhibere.
Constructio ex demonstratio.
Accum sic quod petitur: exectaque ex C diamerer
CFT OCCUTTAE paTabOIX AF F in F; duCaTurque
F R, OcCurrenS B D linex in MI: dein peF P ECCEX PO
NANEUE AR HI, IE R; _ AF quidem OECUEEAE FC
in FI, TK vero aequidister axI B D. CFIEIgIEUEVE ADC
rectangulum ad recrangulum AR C, sic BD linca ad
lincam E R: sed vE AD C. rectangulum adreccansu-
Ium AKC, hOC CADE AM F rectangulum adrectan-
sulum ATF, EC MC linca ad lincam L P: igituE VEBD
ad FK, SiC M G est ad IF; _ permutando ve BL
ad MIG, sIC F K Cst ad TF, hoc cst CHI cA ad FFI.
lsicur per compositionem cum AC, BD lincxe et