# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1025
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1025?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 968, page id 1815201908:1025
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1025
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001025.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.91
# 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.

Onantur AB, B C aequales linee obcendentes arcus AHB, BGC, de
ccCcu t  a  B, BC, quae axi linc parallela.
Dicolesmentui rngula AR BF. O A
ad legmentum rngula BSCDF, cam
obcinere rationem quam haber linca
FII ad lincam OIE, quae normalicer
ducuncur ad diameerum AL. diuiden-
res arcus AB, B C bitariam.
Demonstratio.
IEprimo BC paraIIela diRMCErO AL, &t
planum ponatur Per R cencrum baseOS
quod bisecet arcum AB in FI, ec rectam
HIO producar in cylindri superticie; in pla-
no aucem cMliprico ADL, rectam RO, de-
nique in plano AB F rectam R MI: ex cuius
cermino M polica MNV, quae aquidistceR FI
sectio hacper lineam NM parallela AB, e
planum candem duCaTF YOV PCFKO, d
rectam VT parallelam ad AB, ostensum
est scomencum vngulx AVOTB equari
sCsmEntO AOEB; octensum quoque cA
AVNOTB, scomencum ad legmencum
BCD C cam racionem habere quam habee
TTO linca ad lineam C D: est aurem HT ad
GK. ve (TO ad GD, cum (B, _ K D sinc in eodem plano: sinci; criangula LH O.
ROD Cmilia Lsicur manifectum est segmencum AOE B ongulare ad ongulare
seomentum BCD C eam habere rationem quam linea HI ad CK. Ouod Fuie
demonstrandum. Ouod A B C non sic parallela A P. Hac parallela quedam quae RC
aequalis AB e concinuata constructione praecedenci comparetur verumque legme-
cum AOFB, _ BE D F C cum seomenco illo quod haber rectam aequalem ipsi
AB parallelae diamerro, acque ita veriusque rationem invenier ad illud segmentum
cognicam, ac proinde eriam inter le.
PROPOSITIO LLL.
VEmiceu, Gurbalis estongula, inscribacur dimidium hexagOn
regularis per cuius latera AB, BC, C D plana pONANEUF, quae Xqui-
distenc axi cx lindri, Formancia segmenca vngularia AIB M, B HI HENC,
C NGD.
Dicolesea risaale abrenta pranoe eti ene ad rengua uo
lesmenta limul sumpra, verecta F HI, que exmedio arcus C B puncto C,
ducitur AD diamerro normalis, est ad duas limul lineas HII, GO, qua
exmediisarcuum B A, C. D punctis lunenormales eidem diametro AD.
TNGVLA CXLINDRICA.
PROPOSITIO XVIII.
a26. 1t 1 102
Demon-