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# Title: Optica Promota, Seu Abdita radiorum reflexorum & refractorum Mysteria, Geometrice Enucleata (shelfmark Leibn. Marg. 94)
# Folio 55, page id 727094130:0067
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=727094130&page=67
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 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.
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# After the first blank line: the recognised lines in reading order, one per line.

cuiperpendicularis siC axis PC: per alEerUM FOCuM M, dUCaEUF
aliud planum priori parallelum, I. M Y N. Dico apices penicillo-
rum, Cingulorum superticici ractiancis punctorum, cadere quam prox-
me in planum L. M TN. Sic enim unius penicilli axis F R, per-
pendicularicer incidens in speculum, in puncto R; per quem, e
axem speculi, ducacur planum, Faciens communem sectionem cum
Speculo, elliplem AC RB, ex qua generatur speculum; cum pla-
nisvero, rectas lincas FPK, L. M TN; _ per punctum R, du-
eatur recta DRO, tangens elliplem, ex occurrens axi in O; et ad
idem punctum R, ducatur a Foco P, recta PR, quae ideo reflecte-
cur in alcerum focum M, Peu apicem penicilli radiorum, ex FOCOP 22. FI jus.
divergentium3. ducacurqs ad verricem speculi, ex puncto F, recta
FC, quae reflecterur in H, apicem penicilli, radiorum ex puncto F
divergencium. Sinc icaquo anguli C F R, C PR, aequales; (P2. COr. 22.
rum enim differune uc demonstravimus) erunrq; igicur anguli Hujus.
incidentiae PR F, P C F aequales: _ ideo anguli reAleri G RM,
GC. II, aequales crunc; quare criangula G R M, C C HI Cun similia.
LCUE
OR: GM:: G C: GH,
et ob limilicudinem crianoulorum C RO, OMT, UE
eroDUE
OR: G Mt :: 6O: OT3
SC: 6O:: GH: GT; Si vero punctum
R, non recedar mulcum a verrice ellipseos C: (de quibus peni-
cillis nos cantum loquimur) CC Ferme aequalis erie rectae 603.
eric ergo _CII, quam proxime aequalis iph G P; Incidicigitue
apex penicilli racliorum, ex F divergentium, nempeH, in superfi
Ciem plana, L. M T Nfere: quod demonstrandum erac.
s
aMCOIemIa.
Si supersicies plana, foco speculi hypesbolici convexi (eni normalis
sit axis speculi) mucat radios in speculum; erunt apices conorum
radiosorum reftenm, sineulorum superficiei punctorum, in uno
quans prox plano.
t olu Conden AC b; CujuoanislL
, Toct, M. Illes in toco P, superticies plina racians LP H.