# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1047377675:0041
# Permalink to this reading: https://leibnizlegible.com/page/1047377675:0041?run=74
# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 25, page id 1047377675:0041
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=41
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000041.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 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.

R
e
Ec
m
OrandOut A E 2d B C hOC CRuE P ad O ieA F P AdKM: de-
indeuC. l ad Z M, hoc eH uEP ad O ica FI ad L M, quod 10
proboi racio CIad ZM componitur ex ratione C I adD L. de
DZadZ M, e racio FL ad LM componitur ex ratione F l ad
FIL CeHC Tad DZ _EFTL ad L.MI sCuDZ ad ZM, de proinde
AE FI AdXMICA FI ad P. M, _ permurando uE FI ad FL ItAKM
ad LM; Ced quoniam supponimus EI cadere intra curvam,
AM erie minor quam L. M. S proinde F.I minor erie quam FI,
quod est absurdum: _ ideorectAD MI non CadEF INFTA CUF-
ram verlus verricem: cadar (si heri poMe) incra verlus b8
lem, nempe producta in puncto V. A. L est ad N M uc P ad 
d AO Cs ad R P uc P ad , _ ideo AI est adNM uE AO ad
RT, _ permurando AI CA AA A O UENM ad RT, e ue A Iac
IOItA NM ad ZT, de permurando ut A I adN M sCU VE P ad
Lita 1O ad XT: deinde vE CF adZM CCuP ad Oita IS adX V
(quod probarur licur in priore posicione) de proinde urto
ad XT ita IS ad ZV, dc permutando uE IO ad ISIEAZI adZV;
led (quoniam supponimus V cadere inera curram) critX L
maior quam XV; ec proinde IO maior eric quam lS. quod est
absurdum, non ergo cadic recta DM intra curram versus rhu
balem, e proinde curram ransie in puncto M, quod demon- ius.
atrare oporeuit.
Per hanc proposicionem porest curra, cuiuscunqs superticiei
trunci cxlindrici recti expansae in planum, comparari cum
eiuldem axe velbale opchuius2, limodopollir ducirecta
cangens balem cylindrici in puncto dato.
PROP. 10. THIEORP M A.
 TECUrVA QUECUnquE AD _ recta quEcunque BN: ducan-
2 cur ex duobus currae punstis quibuscunque A, l du
recta parallelae ad rectam BN, nempC AB, DE, _ iunSREUF
LD recta producta in II ducanturque D C, AN rectE cur-
aMst FAMBCAEESir punCtis A, D: dein de compleaneur paralle
10
hu