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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 390, page id 1815201908:0447
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=447
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 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.
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# After the first blank line: the recognised lines in reading order, one per line.

A R ABC
DROPOSIFIO LVII
metrum F C in, C
1stil L
Darabolam A B C cuius diamerex AB, ee ordinacim ad illam nasia
in K _ M: Secer aurem EB linea Mamerrum L. FI in N, X FHI linca dia
parallelogrammu ellad paralleloorammum BL.
Demonstratio.
Acio paralselogrammi FTD ad parallelosrammum
LF B, Composica est ex ratione F FT ad G B, _ FD
ad FC: eA aucem DE FTI ad GB, SCDC ad FFTid
eAt F A ad L A, id est F. L ad F I (CUM A G, AF, AD,
adeoque GB, FHI, DC, id est F A, L A, TA Uncconci-
nue proporcionales) _ VE FD ad F C, SIC= D A ad F A;
id est F A ad G A; id est FTL ad BI: racioigicur pa-
rallelogrammi ID adparallelogrammum FB, com-
Posica est ex rarione R. L ad LI, e exracione L. FI ad
IB; sed ex iiidem quoque compolica es ratio parallelo-
Grammi IIB, ad parallelogrammum B Li iBIEVEVEHTD
Parallelogrammum, ad parallelogrammum FB, SCII F
pacallelogrammum est ad parallelogrammum L. B.
Duod erac demonstrandum.
LOD concingarin Alinea AE, quam in E secet diameter C ti Factilq
AD, AF, AC coneinue proporcionalibus, ducarur ordinarim lincx FHI,
GB: de per B_ FI, diamerri aganeur TK, L. IIOccurrentes F FI, DC lineis
Dico LD patalleloorammum esse ad paralleloscaramum F B, VCHF.
nistonibus
Sco AB C parabolxe diamerer B D, quam in F. secee vecunque recta
de F, Ordinarim linex F. G7, FV.
a 5C
PROPOSITIOL LIX
F C occurrens verim que parabolae in C X F, duCanEuT aurem ex C
Dico BC, BF, BD lincas esse proporrionales.
emonoitalio.
FD ordin
REX CunE ad
iamecrum BD, racil BC dd B apI
cata est eius quam habet GC ad F D, id eltGP.
ad E D; ipicur BC, BF, B D lIHCX SUINEPFOPOE
cionales, posica enim media B F inter BC, BD
erie ve BC, ad BF, ita C F ad F D, _ racio B
ad BB. duplicaca rationis Cs L. ad F. D. 1GIEUF, 8c.
duodtuir demonstrandum.
Corolturton
Tinc sequicuresevE CP ad B F. Uc BF. a B V. na C L. a F, B2
eA ad FD, id cl B L. d BD.
 e pet p e1  es  1ee   e e 1e e e e es se e   e te s e  s u e t  e s s  e e t es es s e e t te  se ue       e te e t   e t e e e  t