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# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 112, page id 1047377675:0128
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=128
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000128.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.89
# 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.

12
adO_ exrarione AB ad BF, ac parallelopipedum super AB
FF cum alticudine AB elt ad parallelopipedu luper cade AB
FE cum alricudine BF ve A B ad BF; e proinde parallelopi-
pedum super A B F F cum alcicudine BF est ad interiorem
truncum eplindrici (uper ITAFFHI VE2O =P ad On quod ac.
OuodsiP Eic maior quam O; sE ve AB ad C C ita BD adC
R DFOEEACEAM VerSUS LK, _ COMPIOAEUT QUAdFAEUM NAEO
ex parte L. R, item ex omnibus punctis R imaginetUF CUrUa
ORII: paret ex constructione racionem BD ad CR eNse mul-
ciplicaram rarionis BD ad BF in ratione P ad 9, e sumendo
excellum ancocedentis supra consequentem ad conseguen-
cem, ratio BF ad C R nempe ratio FiO ad CR es mulciplica
Ca raFiONIS BD ad BF (CU AC 2d AE in raeione D - O2d C; 8
ideo quadraEum NAFO est ad siguram longicudine infni
EAM FTAEOH NE 2O = P ad Q, AEVE ABFF Adt NAEO iFZ F F
SCu AB ad FO seu BF, e id eo rectangulum ABFE eA ad H
BUTam ATAEOIT in eatione COmPOLICA CK ratione 2O -P ad
D_ exrarione AB ad BF. quoniam eAt vE AB ad CC ita BB
ad CH, eric rect angulum AB in C R aequale rect angulo BD
in C C3 de rectangulum AB in C R es communis incerlectio
Cylindricirecti super HIAEOII alcicudinem habencis AB Cu
plane seconce super C R ad basem normali, et rectangulum
BEd in C C est incerlectio eiuldem prioris plani cum erunco
inferiore cxlindrici super HAEFHI; cumque hae incerlectio
Dessemper contingant ese aequales, manifectum est inter
riorem eruncum cylindrici suPex HAEFH aequalem esse cy
lindrico super ITAE OFI alcicudinem habenci AB, 8 id eo pa
rallelopipedum super ABFE cum alcirudine AB cA ad cytin-
dricum super HIAFOTI seu rruncum inferiorem eylindrici sun
DeTHIAEEISUE BBHS ABPE ad baseM HIAEOEI, hOC es in raTIOL
ne compolica ex rarione 29 = P ad d ex ratione AB ad
BF, ac parollelopipedum super ABFE cum aliicudine AB es
ad parallel opipedum super eadem ABFE cum alcieudine BP
ut A B ad BE; e proinde paraILELOPIPEAHM CUPET ABFE CUm
alCi