# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0311
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0311?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 254, page id 1815201908:0311
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=311
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000311.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.86
# 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.

1 112 11 1 1 1 1 11 1
a + huins
E LL IP. S
d
Demonstratio.
DOnatur HL R ParaIlela FC, quae producta OCCUErAE
L.C in l; cric ieaque HIK aequalis RI. Ergo, cum
rectangulum BKD ad BF D, a cam habeac racionem,
quam IIR quadracum ad quadracum A F, crit quogne
BKD rectangulum ad rectanoulum BF D, ve IK qua-
dracum adquadracum F. C: unde punctum I est 2d el-
liplim, ee FIT linca perimetrum BIC, _ F. C rectam
in eodem puncto inter (ecar. Ouod tuic demonstrandum.
PROPOSITIO XVIII.
Adem manente Houra, sine A BC ellipleos
saxeS AC, BD, _ HIF diameter quaecunque.
OPOTTCE Ex E vertus C diatellum educere, x qualem ipsi HF.
Constructio ex demonstratio.
Gtat angulo BP F aequalis anguluS BFF, dico rectam F. P Patisfacere pecirioni,
productx enim linex HIC, L. L, Sccurrane actae per B concingenci in F _ C.
Tungantur puncta FF, I. quomam auvli B F FT BF F POnuneuE aqualeS, lunE LU-
cem _E F B F, F B C anguli rect a BF linca communis, PATCE FBF. G BR
criangula, adeoque de lacera FB, B C incer se esse aequalia; unde _ HTD equidi-
b parry. Aac FC, CAqUC DE FF ad L, SC FTF 2d TF, quare HTF, TF linex aequalesi
PROPOStTIO XIX.
Inex in ellips coniungentes extrema quarumcunq: diamerrorum
incer se sui a guates a Parallela.
Demonstratio.
ECenE AB C elliplm diamecri dux quaevis A C, BD.
dicoiunctas AB, C D, icem AD, BC, CNTCINCCFCC X-
quales _ parallelas: cum DB, AC bilecta SnE in F,
CFIE DE DF ad EB, sC CF ad AF, e permutando
DEDF ad CF, AIC BF. ad AF. sunc vero ec anguliad
F Xquales, similia igitur Cunceriangula DF. C, AF B;
ergo ve DF ad F B, sic D C ad AB; quarE CUMDF,
F. B aequencur, etiam AB, DC xquales crune. similicee
octendemus AD, BC Equales eAse. Ouod exax demon.
Arandum.
LADPOSTTIO XX.
Inec que da extrenmates diametri, inera sectionem equidistantes
ohacu, equales quoque cruncincerle.
hurus. ixitur ex F. diametrum cduximus, et c. Quod erac Faciendum.
7. hviuio
Demon.
es  u u  ei . ue  u. e a rt ti te 1 e u pt   eta p  t t ste   e   t    1t.   1 1   sa    s  1