# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0381
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0381?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 135, page id 797435492:0381
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=381
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000381.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.92
# 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.

lo E C X. RIII.
Alicer (_ Forre commodius; pro singulo trium serierum gradu ran-
cum unam adhibendo lincam) explicantur iltae praecedanea aequatio-
Des, hoc pacto:
Sit A Il recta indefinite prorensa, ex huic perpendicularis AD, in Fig. 209.
qua Tumatur AB =n, e ducatur BR ad a II parallela, cum sine
liInCA L XI, MXM, N XN cales, ut Cumpro in AHI quocunque
puncto C, _x dust a G R ad AD parallela, sit in proportione AC ad
GR (vel A B) provortione tertia C L, quarta GM, quinta GN; lx
linex propoliarum aeguationum naturx explicande inserviene.
Nam CumPEa A F == b (lumatur autem A F ob primam seriem
ad parces I, ob secundam e cerriam ad partes H) et hac an-
gulus F F II semirectus (ilte quidem pro prima e secunda le
rie inclinans versus H, pro certia reclinans ab H, ur Schema laris
monstrat) tum rectae L. P cum exposiris lineis incerlectiones respectirx
radices a determinabunt; nempe li per has ductx concipiantur ad A II
perpendiculares (L. C, M C, N C) erunt interceprae A C radicibus a
aquales respectiro.
2100
Fxhrinc constat, quod
Not.
2. In hac explicatione coefficiens b indererminata Baberur. ut in PEx
cedentibus ipsan.
2. In prima ex secunda serie semper una policira radix habetur, e
unica.
3. In secunda Perie minima radix ipst A B,. vel n XequatuT.
4. Communis omnium linearum nodus est punctum Z, ubi B X
(vel a) =n.
5. In terria serie subinde dux habentur radices posicirx (guando
Scilicet F: F curras bis (ecaT) nonnunquam una cancum (cum F F ip.
sarum aliquam contingat; id quod accidir in secundo sradu cum
a = =; in terrio cum a = = b; in quarto cum a = = b) aliquando
nulla, cum P F intra rarigentes cadie, e adeo nusquam curris occur-
rit.
6. Sccundi gradus curra est hyperbola, reliqua Byperboliformes,
quarum communes asymptoti sunt recta A II, AD.
Seriei