# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0149
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0149?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 92, page id 1815201908:0149
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=149
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000149.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.72
# 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.

  . p11. 1. 1
P RIO G RIE IS. SLO, NE.S
∞ O 4 Cs s c
resiiorit csluaoirogonze oril 1OMLEPI
Cerit sisret tBH P e SICISC A _ SBR S.IL
etZB2BBLB SNESE elo ME Si GICN
(1ct lisre
113 (R 11CV1D9NIENOG. rBCIL H CZLEB 
ntA BC.MSLI P 35 S L3.dt
EEADCIS) C 3~BEGDD ALIMLABMIKE i. 71
Si EEhLSHSS etCt S Bd sA et BLeCSOP VC Ci13BBAOMOH 13LCC  9LLD AL
1133
Fodem IDdoS Caa, cum dinersae speciei curuilineis, cres nempe parabol
similes, cum cribus hyperbolis similibus, conferaneur, cadem his quoque demon-
Arandi racio conveniet: cum cam parabola limiles, quam hyperbola sint in duplica-
ca racione subrenlarum. Constac igirur huius cheoremaris rniuerlalis reritaS iil
PROPOSITIO LXZ.
 eiba
Ie DC cridus aamisum rect a linea DB; ducancurq; lIneE D E,
DEEstCSG  baLI AC, _ lateri BC parallele quor libuerie.
Dicoomnes AD, EF, CFI, lK, ireM DE, F C, HII, dec. essc in cadem
concinuata anal0gIa.
 :C3d 6: 3 st 5HP. 1
Demonstratio.
:2
erit
11~IS Bit B 31BFLSSBB DEH CLCB le CDRoducaneur enim linex GF in L.
10203 13 escilis3o2 v3l alliur Pu
ep 13 esleeriit
aEXuim. cit
b 2bia.
2
b
caron
l CD 
A F F in M, GHI in YB CE TEIinP.
sicur cum paralelxe sInE AC, P.M, exir
AD ad DC, VE FI adFM. d com
ponendo AC ad D C, VE FM ad FM
es 3 L CB E te n Ea CA V DC ad F C: Cunc igicur in
Sit crop ceim l.B.
 .  B FE 11
continua ratione AC, DC, L. C, qua-
rCd AD . ad D L, id CAt F F VE AC
est ad DC. Similiter octendam este
COnTINUAS EM, FM, P M: vnderursuS
CAVGPM B ad FML (id CA vE AC ad BC, id CA AD ad RF) BC F. F ad FP, id
CA C TI. continue proporcionales luncigitur AD, LF, CII: eodem modo osten-
dam TK, ee alias quorcumque in eadem seric eAse concinuas. Dein de cum AD ip(
E F, _ D F ipG EC Sicparallela, pacer similia esse criangula AD F, F F C+: CF-
BOVE AD ad EF, ita D P ad P C: Similicer ostendam essC vE F F ad OFI, ica
ti C 2d FTI. quarcerunc etiam D E, FC, IFI, _EC. continux, ex quidem in ca racio.
nC in qua sinE AD, F F, GFI. Ouoderar demonstrandum.
P R OPOSITIO LXZI.
Va linex A L, F L angulum FacienEES, SCCtX LINEIN CONEIHUC PFO-
portionales, quarum cumque rarionum AL, BL, CL, DL, FL,
dec. irem LL, GL, tIL, _c. dein oppolica sectionum puncta lineis AF,
BG, CHI, DI, RC. ConiunganEuT.
Dicorriangula AFL, BCL, C FTL, d carera in infinicum esse in con-
cinua analosia
o lFEsiloyey stao3d2u3
Demon.
 tit ia .  a . e e 1 1   e    pui a  puu  e    et   t    p e      t  i n  ar n n   i