# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1026
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1026?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 969, page id 1815201908:1026
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1026
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001026.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 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.

VNGVLA CFLTADRICA.
Demonstratio.
seomencum B ALVL, VEF FT ad F. P. Smilicet
per praecollencem lESthencum C B MK N est ad
Scomencu NC VL, Ve FFI ad C9, hoc est.
(quia GO, E. P XGUanEUF) VE FHI ad F P, hoc
est re idem rurlus leomencum CBMRN ad IC
EmenCUM B AIM; Segmenca isitur B A TM,
NCDOL aequalia sunc. Quoniam igieur se
emencum C BMRN es ad singula segMenFA X
qualia B AIM, NC P L, ve recta F FI est ad
angulas aequales lincas PP, G9, crir scomen-
cum CBMKN ad duo aequalia Cegmenca
BATM, NCDOT Cmol Cumpca, verecta FFI,
ad duas aequales rectas P. P, C+O) CimuI sumPCaS.
Duod oporrui demonArare.
Scholion.
969
DEFPEXCCdeNEEM SESMENEHIC BRMN est ad
samus per semicirculum in se
mus qualis sit ea cylliait pats.
quae circulo in se ducto aqualis
ne ratione ad partes cylindricat
reducantur. Sit itaque semicir-
Cemicirculo, qui ita constiruan-
Ossensum est propositio.
ne 26. libri de ductit
plani in planum, qutu cat
ductum ex simul demonstrani-
mus solidum inde productum
esse veram cylindri partem.
rerum postulat huius loci ratio
sequentium proposiionum
clarior explicatie, vt ostenda-
sit, e quae ejusdem partes qua
culus ABC aequalis ADC
tur inter se, ut ad rectos an-
sulos eorum plana insistant
habentes communem dia-
metrum RC. ex sccundum
explicatum n se invicem du
cantur, ita ot pidauantfn-
dricas supersicies, scilicet FC
es CLL sitg C planum el
lipricum. quodnoc corpus aiui-
modum in lioro ac aultibus
dic. quonam omns inea lF
aequales sunt rects LII: produ-
cext linea, IF, dC ductae in
lineas L H. quadrara infinita LF C F quorum diamerri erune in plano elliprico LC, ila-
erit FC sinc d lted uort abet dasti et s udse a
Sa
que solidum AB F. D C Carpitco plano LChanas aguaus patuseutsum, quarum vna
aaeeeoo a   o