# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/727094130:0031
# Permalink to this reading: https://leibnizlegible.com/page/727094130:0031?run=74
# Title: Optica Promota, Seu Abdita radiorum reflexorum & refractorum Mysteria, Geometrice Enucleata (shelfmark Leibn. Marg. 94)
# Folio 19, page id 727094130:0031
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=727094130&page=31
# Source image: https://digitale-sammlungen.gwlb.de/content/727094130/jpgs/default/00000031.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.88
# 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.

_ lineam inci-
denrixM L, du-
CatUE Planum B
AFLHIC; erie
illud ad planum
FFFIC Perpen-
diculare, _ FraH-
sibic per punctu
l ideoque erit
Superticies rese.
ctionis, vel re-
Fractionis lines
incidencix M L5
est aucem sectio
conica, ex qua de-
scribitur Conois, vel Spharois: quod erac demonstrandum.
9. 11)IIS.
: FIU JIS.
lrOP. Tr. Theorema.
Si parabolam recta linea raneat, es a tactu dueatur una recta intra
parabolam axi parallela, alia vero ad easdemt partes, faciens an
culum cum contingente, equalem prioris anculo cum contincente;
dicohans lineam (ecundam. (ecare axem parabolae intra parabolam,
itant linea inter verticem es intersectionem, semper aequalis sit qua-
dranti lateris Recti.. Dicitur autem intersectionis punctum, focus
Parabola.
anc Pulcherrimam conolutionem, primus quod sciam in-
venic Vicellio, sed quoniam jucundum omitie Corollari
um, Hos aliter, ec Torlan Facisius, hanc iplam demonstrabiimus.
Sic Parabola B A C F, cujus axis L A M, canontque eam linea
L.CNI, in puncto C, a quo ducarur 2Xi varalela C D, Racque, u
eulo DCHI, aequilis L. C F, dico A L elle aequilem quadrani lace
ris recti R. Sinc ordinacim applicatae CC, M F, perpendicularis
ad contingentem CI, eruncque na linex proxortionsles Rs
GC:: OC: CA = = AL, _ HO: BC:: GC: CL ergo OL: GA: :R.
HIO; Sed CL. est dupla linex C a, ergo R est dupls linea 1H C:
de