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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 109, page id 1815201908:0166
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=166
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

S(ICL
deC. eu
2O. e0
R,
ies AC
D, de
ad 
quem
lume
e Perie
Cimu
mnes
uales
olicd.
ionis
MNI
Aen.
ionis
Dea,
Unt.
O.
GFOMEERIC A.
5TFIO
CII
R
acions LL au DC. Comcuuca cerminetur in KE. Daca aurem
E i
l aequalis AB, X quinis numerus (puca 3.) deinde hacracio L. NI,
ad M N muPiCaa LacOS AB ae BC, luaed dacum numerum; (ICG3
cacionis l. M ad MN cerminus O.
Dicoletent AL, da lessent L. O, Calde habere proporcionem, quam
Cocue ce lellai AB, BC. C.D quoc lunc onicares in daco nume
Co, habenc ad primum AB.
Demonstratio.
 exempli eaula, numerus dacusponatur cernatius; crie racio L N ad MIPI
eriplicaca racionis AB ad B C; ostendendum nobis est, A K ellC ad F O, ve
cresprimicermini D A ad primu AB. Cx sCrIC A K (UIE seX CerMINOS A C: IGIEUF LZ2. hNiuS.
Proporrio ADa ad D C, criplicaca est proporcionis A B 3.t B C; aequalisioitur est
rationi LM. ad MN, hoc estbracioni LO ad M O. cum enim O SC terminuS (CrIEK b82. huius.
L. NMN, CrIE L O ad M O, VEL AT ad MN, Dcinde quia R cerminus est Periei AB, c pbid.
BC, CrUIHECErES AK, BR, CR continux proportionales: adeoque omnes eriam le-
QuenLES CTUHECONCINUX: DUAEC _E AK, DR, GFK, inter quas par concinue prOpOE-
cionalium numerus incerijereur, ex elemencis pacec esle concinue proportionales.
Vnde AR, d estaIDK ve AD ad DC, id est (quemadmodum iam ostendi) veL drhuinso
ad M O. Leaque per convertionem rarionis A K est ad AB, VE I. O ad LM, e
permurando AK ad LO, rE AD ad I.M, id es exdaris AB. Quoderas demon.
Arandum.
R O
PO5
 C1I
H 15 F e II. IO
X serie continue proxoltionalium AH, Tumacur quivis cers
Vet
Dicoreriem rationis AB ad B C, habere proporrionem ad leriem ra-
cionis AB ad HII, quam haber HI A comnes nempe terminiiplum H L
Praecedences) ad AB primum terminum.
Haecpropolicio, ve consideranti Focile parebir, eadem est cum praece
denci, led alicer e commodius Forcasse propolica. Ouare eadem erir
veriulque demonstrario.
Corollarium.
iLhoccheoremare licebit pranm acmmere, aisionato quonis termino Hl, in le-
Lete AK, rarionis A B A B C, reperiendi magnicudineim eori leriei racionis AB
ad FTI equalem. Nam si Aac vE HI A adt A B, SIC K A ad aliami L. O; cric I. Oaequ2-
listoci scriciracionis AI 2d HII.
Faccortam en opus non esle ad hancpraxim recurrere; cum vniuertalem mectio.
dum, camque facillimam reperiendi magnieu linem, cori seriei eninleumque FAF:O.
nis equalem, propolicio 80. huius suppedicet.