# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1099
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1099?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1042, page id 1815201908:1099
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1099
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001099.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.88
# 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.

E SPH R R OIDP.
1042
Demonstratio.
le lphaeroides AB C cuius axem imimcieum
AC dividae sectio HFL orchogonalicer.
Dicoillam circulum esse. Rac sectio per AC
axem scilicec, eric a haec ellipsis illi similis a qua
spheroides productum elt: sic aucem communis
sectio plani ABCD, _ plani FTF Precta HI,
tandem per punctum I, quoduis in superticie
sphaeroidis assumprum, ec axem A C, planum
AGAEUT AF C occurrens plano HFL, sCcun-
dum lineam RF. eric lectio AF C ellipsis
bamilis ec aequalis ellipsi AB C D. Eequo-
niam exhypocheli axis AR. rectus est plano
HIFL dekn. 3. VAdCCIMI CTUNE RF, KFL nOT-
malesaxi, ac proinde ordinacim police adaxem.
Duoniam igicur ad idem punctum axeos com-
munis elliplium aequalium de similium sincOr-
dinacim ducta RII. K F crunc incer (c aquales.
cAtveto _ TK aequalis KII. CrGORHL, RF,
RI aequales sunc. Sectioigitur HIFP circulus
est. Duod erac demonstrandum.
++O CXIII.
Vnis sectio sphaeroideos ellipsim
Sexhribet si obliqua est ad axem.
Demonstratio.
DEcCcuE Sphaeroides AB C sectiOnE DEF,
quae sic obligua ad axem AC. Dico illam
esse veram elliplm incellisarur Facta sectio
ABC PCFaXCM AC, qua sic recta ad planum
DE F quod heriposse demonstracum est c. De-
inde expuncto Lincersectionis planiperaxem
AC cum plano D F Fcrigacur normalicer IP.
eric ergoTB, linea in plano DF. F; quoniam
ex suppolicione orchogonalicer insistic plano
ABC, per rectam isitur TF. Planum agatur
ETE B, quod sic rectum ad axem A C, attumpro
deinde quouis N puncto in communi incer-
sectione planorum AB C, D F F, CrisATUTN F.
Parallela PF. exic hxc N L. in plano D B F, quod
est ex constructione orchogonum ad planum
AB C. PerNL, deniqueASaCUF PIAnUM KL. M
Parallelum BF FT. Ouoniam CHIEB, RL. M
circulisune, isicur TIIB reccangulum est ad
CiOS. bu. XNM recrangulum, veelC Quadratum PP ad N L. quadrarum. SCd VE C FCCEanSU
Ium AIB AA TCCCANDMT K NYNI, ica est rectangulum D IF ad DNE rectanou-
TMiBItuE ve quadratum TF. ad NL quadracum, ica est D LF recrangulum ad re-
Crangulum D N P, quare vera elliplis est sectio D P. P. P. Ouod Fuic demonstrandum.
1
t
du2 hu:
PRO.