# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1047377675:0057
# Permalink to this reading: https://leibnizlegible.com/page/1047377675:0057?run=74
# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 41, page id 1047377675:0057
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=57
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000057.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.87
# 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.

ic
11
iC
C
Secundo, Si heriporest, cadac linea OB exera lineam O A
in puncto D; Suppono curuam OA (quo propius ad A) eomi-
nus distare ab axc C. L; cadar D F perpendicularis in rectam
OInon productam inera curuam DO, de ideoD L cA minor
axC AgurerDOcuolute: lic in cuolura ordinarim applicata F
II equalis recte D I; manifestum cst Aguram OFLII eNc IOD
cuoluram, acque ID Ccu HIE maior cA quam rectAR E, d
idco CLesmaior quam FIE. nempe ld Fmaior quam axis A-
BurEIB OeuolurE, quod eltabsurdum exhuius anceceden.
cc, e proinde Bo non cadic extra AO: eodem modoproba-
tur OB non coincidere cum OA, cadic ergointra, quod den
monstrare oportuit.
Ouod si perpendicularis DF cadat in IO productam, non
Potelt (OB esse figura IO AC. involuta, quoniam lI maior
erie quam vila ordinatim applicaca in figura lOAC.
CONSFOTARIVM.
roniam AgurECAOOR; IBOP, se muruo rangune in
puncto O manifeltum eltrectam, unam ex histiguris
eansencem in puncto o, alceram eriam in eodem puncto can-
Sere; deque hinc cuidens ekmechodus ducendirectam, que
inuolucam in daco puncto eansaI A modo decur methodus
ducendirectam que cuolutam in dato puncto concinsae, de
C contra; recta enim eansens cuolucam eodem inclinat an
Dulo ad ordinarim applicaram, quo tansensinuoluram in-
clinac ad eandem ordinatim applicaram in cenerum involu
cionis cum reliquis concurrentem.
Omnia predicta de ficurarum involutione eodem modo
demonstrantur, quando cuolure curua est conuexa vertus
anem, eriumsi im noAris ABuriS SuOduTS CurUa sE versuS AdC
COREaUA.