# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0163
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0163?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 106, page id 1815201908:0163
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=163
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000163.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 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.

   ie 1 4 . 1. 1 11
179 touia
PP
GR F SSTONF
Constructio e demonstratio.
ETaEVE A ad B, SICD. C ad F. C. Primoigicur E daca magnieudo C, que primus cermi-
nusproorelsionis cse deber, aqualis (icD E, cric seriesrarionis A ad B haberts pi
106
mum terminum C. aequalis datx magnicudini D G. nam hac D F (id est C ad F F, ve
A ad B. quoniam igirur D C CM ad F C vE A ad B, erie B quoque D F ad F F
ve D C ad F C. ergo prooressioa rationis DE ad B F, (id est progressioracionis A
Secundo si magnirudo C, quu cebetene penuscerminus, maior sic quam
DF, CMeprooressio A B, habehpimum cermmC. maior quam DG. Fiac enim
ips C aeualis LL, vesee  Cu alt B, HC HLL sc ad LR, a progressionis I L al
eo huiu K b rCPCHIAE CCMMuS L. TBIcuFCrIE C VE HII ad D F, SIC HI L cora series pro.
S+.huiuo. Bressionis, HII, IK. ad D C toram Ceriem progressionis D E, P. F. atqus I Lmaior estr
quam DR; erBO _ HIL, maior est quam DC.
Sidenique C, minor sic quam D F. eric quoque progressio rarionis A ad B, habens
primum cerminum C, minor quam D C; quodeodem modo oltendemus, quo pri.
mum. Fecimusigitur quodpeccbacur.
ad B, habens primum cerminum C) constiruer magnicudinem D C.
Y
P R O
ACA SIE prOdrelsioratIOHIS A F ad F G, terminata in B; _ alia ma
onicudo C F: Oporredtinmagnicudine C. C, ica verim que ad C e
F consticuere prosrelsiolterarionis AF ad F G sprogrelsiones, nempe
CHI, HI, aC. U L H, L. L, _C.) ve cundem habeane terminum D, qui
ita diuidat C F, VE AB, C D, D E, Cinc in concinua analogia.
Constructio ex demonstratio.
D Ecta CP ita Mun Per erigelimam sextam huius vE AB, CD, DL. linc
concinue proporrionales. Deinde pernonagelimam huius ita diuide CD, in FI8
L veracio CFY ad TII, eadem sc cum racione A F ad F C, ac simul progressio C II.
TII, cerminetur in D. Idem Facico in P. D. Factumque erir quod perebatur.
PROPOSITIO ZOVII
Iduarum Perierum AM, B N cermini A, B, C, D, E, E, C, _C. alter
Onacim in concinua sint analogia.
DreoMasMcel se eam proportionem habere, quam primi cermini.
Demonstratio.
Voniam A, B, C lunerres continux proportonalesi ergo A est ad C, in duplica
Ledracione A ad B; icerum cum C, D. F Cnceresconcinux, Ceric ad Fi, in du pu
cacaratione C ad D; hoc eAt, repacer ex dacis A ad B: erso cumrationes A ad C, et
a.
  p p   u   ue ie . 1     pie   . u i4  i   . n  u  e at  pa 1    e au u ei