# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0239
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0239?run=74
# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 31, page id 797435492:0239
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=239
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000239.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.93
# 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.

E C X
IV. Patet curram proxolicam esse convexam, aut concavam ad
ealdem partes (conrexam versus parres superiores vel exteriores AI,
concaram introrlum, aut deorlum versus A ZZ) nam hoc iptum,
fore converum aut concarum ad easdem partes, nil ommino delignat
olind, quam a nulla recta linea praeterquam duobus punctis secari;
nec alio recidic, quam inicio libri de Eptaera _ cylindrorradie Ar-
chimedes, linex ad caldemm parres carx definirio. Perspicuum est
r. 8. ut linea M N duobus in punctis M, N curram M NO sccanS ei
rursus occurrat, uc puta in R, debere curram MNO reffecti, ver-
susque partes AY recurrari; id quod modo demonstratum est non
posse concinsere. Ouapropter ipta linea versus caldem partes con-
rexa est, seu COncara.
V. Apertistime constat lineas qualvris rectas (uE BL, CZ) gene
erici A Z parallelas proxositam curram secare (modo contincantur
InETA TerINOS mOTuS Per A Y; quia curra per harum quamvis inde-
tinite promocam deseripra censetur) addo quod harum qua libet cur-
vam in uno tantum punsto secat. 1I Id patet, quia recta genetrix
AZ per unicum duncaxat instans temporis durat in litu quoris uno,
leu B2; simulque pertingit iplam BZ, ac delerit; pexterque
punctum unuMI MI in B M Z reliqua cuncta linex currX puncta sunE
in parallelis ad BZ. Firgo liquidum est ipsam BZ in unotantum apoll. l. 26:
puncto curvam secare. II Hlociplum de parabola, ex hiperbola specia-
tim ostendie Apollonius; de sectionibus conoideon Archimedes.
V I. Don dissimili modo pater ad A Y parallelam quamvis, (qualis
Arch. de Conoid.
E5 Sph. 1b.
PO) unico puncto proxolicam curram attingere. ) Ouod lemel.
Occurret (modo concineatur inera limites descensiis per AZ) Patet,
quia punctum mobile continuo descendens, indetinito prooressu, eam
indetinite procenlam aliquando trajiciet; nec in eo tamen praeterquam
ad unum remporis momentum perdurat. I) Videarur hoc de sectioni- L. 79,
busconicis oltencans Apollonius.
V II. Pater Omnes currx subtensas rectas cum AZ _ ei parallelis,
siprodueantur, concurrere.
Ouod enim subrensa quaeris, ue M N, uni parallelarum alicui, ut
BR, occureic, ibi scilicer ubi ipla curram secat, exinde manifestissimum.
est, quod tora curra per parallelum didx rectae motum describitur..
ErGO, CUM UnI OCCUTFAE, OmnIbUSOCCUETEF; qux enim uni paralle.
larum