# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0305
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0305?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 248, page id 1815201908:0305
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=305
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000305.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 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.

a esi B. 1.
ta
1
e 20 2 tt 1t.
daca cllipsi diantectu inuenire.
O
PR O POSITI
Construstio ex demonstratio.
Nera elliptim ducancur varallelx AC, DE, quas bita-
riam leca in punctis Fi, Ci; _ per F ac C, ducaturrecta
BFI.
Dicohanc esse diamerrum.
Demonstrario est manifesta. A enim DEF non est
dIaETEF, SIC L F M, SCCanS DF in R. Duoniam igiEUE
C. Mt ponitur esse diaineter, _ bisecac e parallelis vnam
AC, in F, bilecac 3 alceram quoque DF in R. Quod
heri non porest cum exconstruct. DF. bilecta (IE CY. NOn
isicur P. M aur alia quevis ducta per FCA diameter pra.
cer eam, quae criameran per C hoc est pracer iplam
BFI. In daca igicur ellipli invenimus diametrum. quod
erac Faclendum.
eR ODOSIFIO
Aex ellipleohutum reperire.
Construclio umonstratio.
DErPExCedentem quaere illametrum cllipseos. B H, quam seca bilariam in L. Exde-
finicione cerria pares ellipseoscencrum ele l.
Corollarium.
DACEL ex hac proPOSitiOne Omnem aIRMEETUM EFANAITC PEF CONFruM. EX quo se
converlam tacile deduces, omnes nimirum lineas per cenrrum cranleunres este
diametros.
c24. sexti.
 definit. 3.
R OPO5 1 F
cum, quas propolicioneleta dujus demonstrauimus à diametro se
Cari statu Cetampo.
Dico omneslineas per cenerum ductas in cenero diuidi bitariam.
Demonstratio.
Aca Sicellipsis AD B, cuius diaMeTEF AB, rectaVerO L P, via SITCa-
C 3. htius.
Vaa scenim quaeeunque recta DO, per cencrum
C. Cx D ducantuE D F C Parallela ad L P, GL
parallela ad AB, a LL. CiR Parallelae ad CxD, sive
P. Ouoniam igicut sCi F. HI parallelogrammum cll.
erun OF, B H aequalcs: vnde et quadrara CF, B, F
equalia m. Aceatb be quadrarum CF. est ad, quadez.
cum F HI, ita reclacs um AFi B cM ad rectangulum
AEIB. aequancur isla rectangula AFB, AHIB. et B
ve AF ad AII, sic BI ad BF: ereo dividendo re
AF adF FI, SC B E dd FIF. aequancurigitur AF. BH.
Duare cum cora quoe utameter AB bilecta lic in C.
veparet d ex dehmtoneceneri, reliqua eriam FFI. bi
secta eA in C. Suemah isitur R C ipsiS GD, F HI cM
parallela, recta qubque CF. Bilecacur in R. CA vero cd
DC bisecta i F, MPocCipl L P paxaILela. FrgO CA vt
D
t ets e ury et   tt es tat e t e t s e t. el ptte e pe es Atapute u p   ate s e e  e pe  u  p e e t A   i  e et         e pe   rs e