# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/727094130:0069
# Permalink to this reading: https://leibnizlegible.com/page/727094130:0069?run=74
# Title: Optica Promota, Seu Abdita radiorum reflexorum & refractorum Mysteria, Geometrice Enucleata (shelfmark Leibn. Marg. 94)
# Folio 57, page id 727094130:0069
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=727094130&page=69
# Source image: https://digitale-sammlungen.gwlb.de/content/727094130/jpgs/default/00000069.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.91
# 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.

157
n perpendicularis AC axis P C; per alterum FOCUM M, ducatUE
aliud planum, priori parallelum L. M TN. Dicoapices conOrum
radiolorum reffexorum, singulorum superficiei eadiancis puncto-
rum, non procul abesse a superticie plana, LM TNI. Sic enim uni-
us Cori radio axis L. R perpendicularicer incidens in speculi su-
pertciem in puncto R, per quem, d arem speculi, ducatur planum
Faciens communem sectionem cum speculo, hyperbolam AC R
B, ex qu2 generatuE, cum Dlanis vero rectas IE P F, L MN; &
per punctum R, ducatur recta RO, tangens Hyperbolum, e
axi Occurrens in O; ducacurq: a FocoP, ad idem puinctum R, Fe-
eta PR, quae ideoresectetur a foco M, Peu opice coniradiorum 24. Hujns.
puncti P reflexorum: ducatur deinde ad verricem speculi ex puncto
t, recta F C, quae refectetur ab II, apice coniractiorum reAexo- cor. 24.
rum puncti F. Sincicaq; anguli C FR, C P R aequales; (qui Pa- Hujusi
rum admodum difterune uc demonstravimus) cruncqs ioicur angu
li incidencix PR F, P C I aquales; et ideo anguliretlexi FRV.
PCS, seu illis ad verricem M R G, HC. C, aequales erunE: quare
triangula C RM, CC H, Cunc Cimilia; Q uE
OR: OM:: GC: OH;
Ec ob Cmilicudinem criangulorum C RO, OMT, ut
ergout
GR: OM: : 6O: CT
CC: 6O:: OHI: OT; Si vero punctum R
non recedar mulrum a verrice Hyperbolae, (de quibus conis radions
nos cancum loquimur) recta C C, Ferme aequalis erit rectae (,05
etic ereo _ C HI, quam proxime aequalis rectae GT3. apexereo
comirudiorum resexorum puncti F, nempe HI, non procul diltac 2:
plaro L. M F N; quod demonstrandum etat.
Scholium.
In. Corollariis ad problemaca nostra caroperica, e cioperica,
diximus eadem problemata, (qux geomerrice rantum resolvuntur
per Focos sectionum conicarum) quo ad sentum etiam resolvi, per
alia quaedam puneta, a focis pautulum diltancia. Fx hrs aurem The.
orematibus, nuper demonstraris, parer omnia illa puncta ese in
uno quam proxime plano, cui perpendicularis eit axis lenris, vet
sxeculio.