# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1047377675:0017
# Permalink to this reading: https://leibnizlegible.com/page/1047377675:0017?run=74
# Title: [Geometriae Pars Universalis, Inserviens Quantitatum Curvarum transmutationi & mensurae] Geometriæ Pars Vniversalis, Inserviens Quantitatum Curvarum transmutationi & mensuræ (shelfmark Ms IV, 377a)
# Folio 1, page id 1047377675:0017
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1047377675&page=17
# Source image: https://digitale-sammlungen.gwlb.de/content/1047377675/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
# Lines: 29 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.

L La
surandi quantitates curvas
tra
PROD. I THEOREMA.
Ic curra quae cunque KB Simplex d non l.
nuola, hoc est a K ad B, rectam quandam
politione datam M P semper appropinquas
vel lemperab illa recedens. Sic (in prima
sigura) punctum in curraRB recteMP ma-
xime propinquu, KL. ex duobus quibus.
cunque punctis curre HB, nempc C, B, de-
mictaltur perpencularis CO BP, in rectam M P, e a pun-
etocurra repore puncoR proximiore ducatur recta C A
curram tangens in C, et PB producte occurrens in A. dico
rectam CA majorem ene curra C B. curram tangens in B, e
reCtECA OCCUTreNS in R, d OC producte in D, dUCAEUF FC.
Eta BRB. quoniam in prooreltu a AE ad B, curra IEB Tempet
ndeiselongatur arecta PM, igitur recta BD currum can-
Bens in puncto B, de vergens versus R C contra rendic ac
concurlum cum recta PM, d idco angulus ABR eAt obcusus,
Luperans nempe rectum MPB illo an guto; in quo cum PM
producta concurrie, ckisitur angulus ABR major ansulo
RAB, e lacus AR maius lacere BR, et commune addendo,
recta AC maior eA rectis BRRC. sed BR, RC, curram FaM-
sences in punctis B, C, luncmaiores arcu BC; _ ideo AC TC
eta eodem arcu C B est mulro maior, quod demonstrare op.
DOrEHIE
ransmutanas ex
3e