# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0198
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0198?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 141, page id 1815201908:0198
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=198
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000198.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.83
# 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.

eriam
Maa
ei
Peree
qu
Quod
onin
A6
naC
R
ian
ecta
A
C F OMELLLC
Demonstratio.
Blinearum AF, BC. CHI aequidistantiam, angulus F AB, angulo GBC,
XCF A, angulo HIGB, e BCF, ansulo CHIC, e ABC, angulo BCFB
usclaceoe   decei ltle cle ccllla etcan l
eD dl BC, a e BC adCD, DE AR ad BK. Cum igicul enam A (IC 24 = l haus
CB, HEAk ad BR, CrIC L A ad CB, ve AB ad B C, e permurando L A ad A B,
De CiB ad BC: limilicer cum AB scad BC bVE AK ad BK, hoc es extiypochC- bIbi.
IL, DEBK ad CR, hoc eA ve B C ad HC, CM PCTMIMCAHCO ALB au BO, VE BC
ad CTI: non alicer eriam ostendemus B C essc ad GF, ve CHl ad H, L F
2d F A, VE FIC ad CFB. quare cum trapeziorum F B, CC ec anguli omnes sInC X
quales, ee latera circa aequales angulos proportionalia, Prapezia c F B, C C d omnia cD,f. 1. Sox-
reliqua, erunc similia. Ouoderar demonstrandum.
PROPOSITIO
Ata sic quadratorum series, Habens BalES IAITCCFIMI, d TermInuM
longicudinis IE, inscripta criangulo AGIE; ac primi quadrari la-
cerc L. MI bilecto in F, per F ducatur recta FK, occurrens ipsi A C in I.
Dicorriangulum AIK seriei quadratorum; criansulum vero LOK,
Ccricicriangulorum L. G M, TM N, Xc. Xquale esse.
sF, _ S. NI, LL Cx ly.
Pocheli sinc parallela, Pacet
criangula IF L, SFM a
qualiaese, ac proinde ad-
dito communi ALF SB,
crapezium AISB quadra-
20 AM aequale. Doinde cu
Percorollarium propolicio.
nis12s huius, proorestionis A
basium AB, BC cerminus
AIE R, CEUINEd AR, BK, _C.
continux: quare cum etiam AI, BS, CZ, Qc. Sinc parallele, crunc per lemma, era-
Peria IB, SC, X D, Xc. similia incer sc. vnde _c erapezia IB, SC, XD, _C. Tunc c20. Soxst.
in duplicata racione lacerum homologorum AB, BC, CD, _c. acqui ee quadrata
AM, BN, C O, ec. sune in dictorum lacerum duplicacaratione, ergo trapezia sunc
quadratis proporcionalia, ee reprimum Ecrapexium TB, ad primum quadearum, ita FI2. sexri.
coca crapeziorum series, ad quadracorum seriem. Acqui primum crapezium, oltendi-
musprimo quadrato aqualceste, erso craperiorum eriam e quadratorum leries
equalessunc. Deinde Seriestrapeziorum s G B, M C, ND, consticuic criangulum 5138. hu-
GK, ergo e series crapeziorum IB, SC, criangulo ATK aequalis crit; GuarC
ansulum AIK, quadracorum serieix quabicur: Quod erac primum; ex quo eriam
Daceclecundum. qua erant demonstranda.
LCdstati
Vm L M bucca M
PROPOSITIO CZLII
etum, ee cerminum lonsirudinispunctum l; licque leriei racionis
D Plua. aelertiam C. D, ae qualis linca V I. linea vero Y Ccricirarionis
AB Pa, da CF Guucam sic xqualisi
Aca Cic planorum limilium series savens vales Homorosas iume
82. hroins.
Dico