# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0173
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0173?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 116, page id 1815201908:0173
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=173
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000173.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.84
# 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.

  e   BI Iu GuIB II
126
PRO GR F SSIONFS
i
Temma primum.
eta in C, InTEF A _ T. 1.
Dicobilectionem partis C B, cadere incet Ld L M D; d bilectionem partis D A,
cadere inter Le C in L; rurlum oilectionem parris L B, concingere incer Da R,
in F; ipsius aurem P A bilectionem, inter P. d I in G: aeque ica in infinicum.
Acasiemagnicudo AB sectain EeS partes equales, in FNt R: ex rursum aliter se-
bobnslatto.
Lquam AI. ergobilectio iphus CB, Cadic vlera B, vertus B. lcerum C B plus
est quam dupla RB, adeoque ipsius C B dimidia, maior quam BR; quare bilectio
CB, cacMera R, verlu  adeoque cadicincer Y et K in D. Deinde cum CB
plus sicquam ala cerTIX, ipuS AB, erie CD eius dimidia, plus quam rna cerria
iplius AB; lIC aucem AC ex dacisminor, quam vna cerria; ergo CD maior est
AC. E bilectio ipsius D A, cadec vlera C vertus B. Similicer cum A L cciam maior
sic quam DI, cadec bilectio ipsius D A vlera Y ver(uS A, adeoque intex C d P, in
Fi non alicer octendemus reliqua, quae in asserrione propoluimus. Constacisieur ve-
riras lemmatis.
Lemma sect.
Voniam CBmaior est, quam FB dupIa A T; CHIC IPHAS C B MIMIOIA, IIAIOP
cadere inter C, e Li, in L; bilectionem aurem parcis F B, Cadere inTeE R e D in
Fs Parris vero F A, bisectionem concingere inter F _ I in C; acque ica in infinieu.
Demonstracio eadem prope qua lemmarispraecedenris.
P R O POSIFIO CXIV
X maonicudine A B lect a MIIctes parres aequales in LX K, Cuma-
Scur A C minor vel maior tcsla parre rorius AB, ex bitariam divida-
cuF C B In D, _ D A bIcaltam in E, _ F. B in F, e F A in C. RUF-
Cum G B bitariant I FI, _ HI A in L. acque hoc semper Aac.
Dico huius progressionis alcernae terminos diuidere magnicudinem
AB in cres parces a quales.
INEeEIQR, in C.
DACA rUrTUM RE AB secta in trespartes equales, in T et R; d rursum alitex sect a
Dicobilectionem parcis CB cadere incer R X B in D; de bilectionem partis D A,
Demonstratio.
219. Duin.
Vm CB dupla sc DB, _ F B dupla FB, eric CB ad DB, ve EB ad FB.
ergO C F adDF, a VE F B adFB. Guare cum P. B dupidHL FB, Cca CF,
iplius D F. dupla erir. Deinde cum D  du  batse L A capra ipiu
Et A, erie
 i i  .        e        mm nm