# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0216
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0216?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 159, page id 1815201908:0216
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=216
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000216.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.81
# 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.

i1
e
GEOMETRTCA
AS, B P, _C. CAC in eodem planO. quarE LINCX LKIL, K S Z CTAn(CUNE Per OmMIA AY3L huius.
puncta NV, O, Ac. T,Y, _c. hoc est rangune rocam cuborum leriem. Superest ergo
vedemonstremus lincam RFMI cransire eciam per omnia puncta P, O, ec. quod
sic pexCtabimuS. IF estad HIC, DE TB ad FIB, id CA vE IK ad N R, hoc CA VE
BK ad C. K; Acqui cum serici AB, BC, C D cerminus siCK, b AK, BR, C K linE V 82. huii
continua proporrionalesi ergo BK cAt ad CR, ve AB ad BC: _ IF 2d ITC ve
AB ad BC: quare cum AB, TF aequales sins, etiam BC de incercepea IIC; X-
qualeserunt; erso B Li cransicper verricem anguli C, quadraci SBIIC, cum in:
cercipiae parallelam IIC aequalem laceri dicti quadrari; unde B, C. F sunc in dire-
etum. leaque cum ex clementis conster diamceros aduertas C P, B C+ elle paralle.
las, eciam CP, B F crune parallelX. Ouia isitur linCA BF eA in CplanO BF K, CF. m Endeci
iam CP in eodem d plano BFK cric. Similicer oltendemus lineas D9, CP, eMle dDefin. 34.
Parallelas, et proindecum CP sic in plano B FK, eriam D O esse in plano B F K. Primi.
eodem dilcurlu demonsrabimus omnes BF, CP, DQ, XB, ec. ese in eodem
planO BFR, SinC AMR: deinde BF, C P, _C. cum sinc in oppolicis planis paral.
lelis, Productx nunquam conveniene. quare cum sinc omnes in plano BF C, CrunE
omnesincer se parallelx. Praecerea ex elementis e ex dacis parec diameeros BF, cibid.
CP, exc. eRe laceribus LB, NC, e c. hoc est AB, BC, C. D, _c. proportionales:
Comma
QuAEC EK FM crantic per omnia puncta P, O, B, Xc. Duod aucem eriam balis Z ML adiyc hu-
quadraca (iE, Cc osendo: Z. A es ad X A, VE Z. K ad S R, hoc cA vE AR ad B R, ins.
hoc est re T X ad IK, hoc est denique re L A ad R A: Qui2 ergO X A, R A X-
qualessune, eciam Z. A, I. A SaequaleS CrUHD. PEXFCrCA P M, CA ad IF ve LR ad 514 quinit.
TR, hoc cArE AR ad BK, hoc CAvE AZ ad BS, acqui TI, BS XqualeS (UIME, CF-
i
Soeriamt LM, AZ. xouales crunc. Deindecum L K siC ad LR, VE HMK ad FK, am  Endo-
eric LM parallela ad IF, que cum ad AX Z parallela CIF, etiam L M 2d A X 7
paralleta exir. Duia isieur M Z _ AL. aequales de par2HlelaS LM, AZ conne-
ctune, ipse quoqueiaquales e parallela crunt; est aurem angulus L. AZ rectUS, 2C i 33. primt.
proinde eriam angulus ML A, et conlequemer anguliillis oppoluci suncrecti, balis
sicur L I. eA quadraca: Factum ergo eAt quod pecebarur.
e R OBOSITIO CLXIZ
Lilteo teupscamio cubicapa  Pal A CCL. Opa
Oppramidis includentis, ee inclula differenciam exhibere.
Constructio es demonstratio.
ex quadrato A B in alcicudine linex aequalis sericirationis A B ad DF FaC p2-
allelepipedum, hoc est seriei k cubica aequale eric. Deinde Rac ve Gua aC L B F 105. hi-
ad quadracum AT. C ita prramidis Ci L R alcicudo A K ad aliquam O: denique ius.
super quacaco 1D I MMane lineae; que contineaernam cenantella  hac
valat  aa L LeaeeB et eld.
drato
1
1
1
rat.1