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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 83, page id 834940469:0167
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=167
# Source image: https://digitale-sammlungen.gwlb.de/content/834940469/jpgs/default/00000167.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 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.

Ei super OB cenerum aequilibrii in base C de porrionis luo
perticieirocundx ex ea genica cenerum gravicacis II. mani-
Fectum eA puncta C, F, C, esse in eadem recta, item e C. F
ense ad E: C ne superticies crunci luper OB ad superticiem
erunci luper A B: eodem modo pacet puncca D, L. FI, Cnc im
eadem recea, item DF eNsC ad FFI re porcio superticiei rocun.
dae geniex ex OB ad porcionem lupertciei rocundae geni
ex ex A B; Ced poreiones superhicierum rocundarum incer
se sune in directa proportione superticierum cruncorum
ut collisitur exhuius 24; de ideo ve CF ad F: C ita DF ad FFI.
DTOdUCRNEUF RECEK C D, F. F, CrII, donccreccam IK secenE
in punccis L, MI, N; cum puncta D, HI, sine cenera grauicacis
aecuum circularium in quibus rOEaneuE puncea C Cn mani-
FelUm eARECEASCDL, GFTN, ele axi rocacionis TE normI.
les de inter (e parallellaS; e idCOrecra F: F M eidem IK cAt
CAnormaliSd CUM (IE VE CE ad F. G ita DF ad F. FI; ee proinde nuivs
vEL Dad L. C vel NHI ad NI C ita MF adM Es (ed D, IP, Cune
centra srauicaris arcuum circularium similium in quibusio.
EaNEUT PunCTA C, C; de isicur punctum L. es eriam centrum
Gravicaris similis orcus circularis in GuOrOEATUE PUNCEUM Lis
quod demonserandum erac.
Podem modo demonstraeur hoc cheorema quando ra.
diusrocacionis lineas lecac in cribus punctis supponendo
hanc propolicionem, scurhaec supponie huius 40 ee sic dein-
ceps (quando secacur linea in pluribus punctis) anteriores
demonctrationes semper supponendo.
P RO P. 43. Z H F O R E M A.
IEdem politis quae in huius6; dico solidum rocundum
genitum exrocatione Agura ABSO circa rectam A B
elle ad erlindrum genicum ex rocacione rectanguli A. BR O
circa eandem A B, Ve luperticies genita ex rocatione currae
AOcircs eandem AB ad circulum ex radio AO. AGura ABSO
EA
2
Proportionaliter analosa curra A Oe ideo cenera sca. huiun
ViEaCIS