# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0211
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0211?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 154, page id 1815201908:0211
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=211
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000211.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.87
# 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.

1am
PRO GR F SSIO NFS
P R O POSITIO, CLXI
IIdem policis loco rectangulerum incelligacur super normalibus AI,
Dico seriem quadratorum CR, ad seriem F. H, duplicaram haberera-
tionem eius, quateadeeries quadratorum AI, BL, CM, dc. ad (c.
riem quadracorum B L, CM, DN, _C.
Demonsoratio.
ErieS FK est ad seriem a FR vE
quadracum BF. ad quadracum
CF, hoc est in duplicaca racionis
AB ad B C. Smiliter racio heri qua-
dracorum AI, BL, XC. ad seriem
quadracorum BL, CM, Xc. cadem
eAt quae quadraci AI ad quadratum
BL, hoc est duplicaca racionis AF
2d BL: hoc est ex hypochesracio
seriei quadracorum AI, _C. ad sc.
riem quadracorum BL, _cc. eadem
cAt quae AB ad BC. quare cum
ostensum sicracionem seriei R R, 2d
Serrem FR, esc duplicatam rario-
AIS AB ad BB, erir quoque duplicaca rarionis, quam haber seriesrectansulorum
TK, ad seriem rectangulorum L R: Ouod cracdemonstrandum.
PROPOSITIO CLXII.
IIdem polIIS qua supras incer BA, AI, CB, BL, DC, CM, ac. in
Lueniantur medix proportionales AO, BP, C O, _C.
Dico quadrata AO, BP, C ∞, _ec. cubis AI, BL, CM, aC. CAC prO.
portionalia.
Demonstratio.
non suri Voniam B A, A O; AB Cunc concinux proporcionaleS, etic quadrarum AO, re.
ctangulo B AIB eguate: Similicer reliqua quadrata B P, C . dec. Tetgs l.
etangulis CB L, DCM. eC. crunc aequalia quare cum rectangula cdicta lunc conci-
nuc proporcionalia in racione criplicara A L ad B L, quadrara quoque AO, BP,
_c. erunc in dictorum lacerum AI, BL, _c. criplicata rarione COnEInUE PFOBOF
d33. dnac- tionalia. Aequi etiam cubi A I, B L, _c. sunr in lacerum A I, BF, XEC. d eripliCATA
racionc; erpo quadraca AO, BP, XC. cubis AP, B L, e c. sunc proporcionalia. Ouod
erat demonictrandum.
Ibidu
2
ni.
ABL, aC. Construi Peries quadracorum.
  ue i uli is e ur st e pus ue e pue ut e este u  e t pta e e u e  et  t       . te e u    a a