# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0188
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0188?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 131, page id 1815201908:0188
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=188
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000188.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 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.

si
ret
dt
E OMF TR IG A.
emonstratio.
Dex propositionem cencelmam vigelimam sextam huius, Fora series quadracorum
MIK, elt ad primum quadracum AM, vE ST ad AB; acqui rectangulum super
ST in alcicudine AB, est ad quadraruM AMI, ve2S Y ad AB; ergo series qua-
dTAEOTUM MK est ad quadraTuM AM, ve rectangulum S F AB ad quadratum = 2. senm.
AM: aequalia Cune ixitur rectatigulum, es coraleries. Ouod erar demonstrandum.
Corollarium.
Ine sequitur quadratum SY, cocam seriem NTK, ex quadrarum AM in conci-
lnua esse analogias nam quadracum S T ad rectangulum super SY _ AB, est
vc SY linea ad AB lineam: Se d rectangulum idem, hoc est rocu leries M K, eAt ad
AM quadracum in eadem rationCI eTGO, e C.
ina
eROPOSTFIO CXXIX
IIdem potiris ve AB ad BC, sIC HAE A X ad ZK.
Dicorectangulum Z AB, rori quadratorum scricixquale esse.
Demonstratio.
VIa AL CH +d XR, ve AB ad BC, cririnnerrendo ac componendo, R A ad
LX A, VE C A ad B A: Acqui eciam R A b est ad seriem lincarum AB, CD, ve b1O3. hu-
CA 2d BA; CrgO R A candem haberrationem ad X A, ex ad seriem AB, CD, ins
aequales suncigicur series AB, CD ec linea Z A. unde per praecedenrem rectan-
sulum X AB, coriquadrarorum serieiest aequale. Quod erac deMonarandum.
Corollarium.
Lduabus proposicionibus colligere modum licet, quo quadratorum darx seriei
reperiri possie quadracum rnum aequale. nimirum s incer AB & SY, vel inCOF
AB, REC. AX, media hac proportionalis; crit haec lacus guadrari aequalis, coci seriei:
repacer ex duobus iam demonstraris cheorematibus: Verum luculencius et vniver.
aliushoc Theorema sequenri propolirione construemus.
PR OPOSTETO CKK
Aca Cicleries planorum quorumcum que balibus in directum AB,
BC, CD, _cC. policis, ac terminum habens lonsicudinis punctum H.
Clicurplanis serici rniver (a planum ae quale ac simile extriberi.
Ca