# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1047377675:0099
# Permalink to this reading: https://leibnizlegible.com/page/1047377675:0099?run=74
# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 83, page id 1047377675:0099
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=99
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000099.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
# Lines: 39 recognised, mean confidence 0.86
# 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.

ia
AM
ei laper OB cenerum aequilibeii in bale Cis de porrionis su
perhcieirorundae exea geniea centrum grauitacis FI. mani-
Fectum est puncta C, E, C, esse in eadem recra, icem e C F
eAe ad F. C uc superticies crunci luper OB ad Cuperticiem
crunci (uper A B: eodem modo pacet puncea D, F, TI, ene im
eadem recta, irem DF eNC ad FHI reporeio luperhciei rocun-
dae geniex ex OB ad portionem luperticiei rocundae Beni
ex ex A B; Ccd porriones superticierum rocundarum incer
Pe Tune in directa proportione superficierum truncorum
ur colligitur exhuius 24; Xc idco ve C F ad F. C itaDF ad FFI.
producantur recex C D, F. F, CFI, donccrectam Lh lecene
in puncris L, M, N; cum puncca D, FI, sinc cenera Brauicacis
arcuum circularium in quibus rocaneur puncea C, Cn mani.
Fectum esreCEASC DL, OFIH, ese axi rocationis IK normI.
des de incer se parallellasi _ ideo recta E. F.M cidem IK est
eAnormaliSI CUM AIEVECF ad F Cita DF 2d FHI; e proinde huiusi
AEL D ad L. C vel NIT ad NG ICA MF adM E, (Cd D, FP, sUnE
Cenera grauicatis arcuum circularium limilium in quibusro
Eaneur puncta C, C; se igitur punctum LCM etiam cenerum
Srauicacis limilis arcus circularis in quororatur punctum Lis
quod demonstran dum erae.
Fodem modo demonstratur hoc cheorema quando ra
aliusrocacionis lineas lecac in cribus punctis supponendo
hanc propositionem, sicuchaec supponie huius 40 e sic dein-
ceps (quando secatur line a in pluribus punctis) aMEexIOTeS
demontrationes lemper supponendo.
P R O P. 43. Y H F O R F Mt A.
ldem poticis quae in huiuss; dico solidum rocundum
d
genitum ex rocatione Agura ABSO circa rectam AB
esse ad exlindrum genicum exrocacione rectanguli ABR O
circa eandem AB, re superticies genitA ex rOratiONC CUrVR
Acirca eandem AB ad circulum ex radio AO. ABUrA ABSO
EH proporciomalirer amalosacurrae A C e idCOCCNETA GFa-
la 2
vitatis
huins.