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# Title: Optica Promota, Seu Abdita radiorum reflexorum & refractorum Mysteria, Geometrice Enucleata (shelfmark Leibn. Marg. 94)
# Folio 89, page id 727094130:0101
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=727094130&page=101
# Source image: https://digitale-sammlungen.gwlb.de/content/727094130/jpgs/default/00000101.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
# Lines: 32 recognised, mean confidence 0.90
# 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.

89
EOrUMI, datuSS CnEq; dati anouli TL HI, TL M, e LT, dictanrio
oculi ab imagine prima; in criangulo igitur rectangulo L. IW, da-
tis, angelo IL. N; e lacere IL, dacur _ lacus IN; eodemque mO-
doreperitur TM: daca igicur vilibilis imagine, M N; OpC quoF-
cunque lencium, vel speculorum, projecta: e daris, lenrium, vel
speculorum, ec imaginum, a Ce invicem, diltanciis; inventatur, vi-
libilis angulus vilorius, ex vercice suae incidentixe per Prop. 53 hu-
jus: Quod erat Faciendum.
Expediriuscamen; ue YD ad IL, ita cangens anguli M L. I, ad
cangencem ansuli M DI, Peu BD V: Cmilicer quoque reperieUE
VDB; dacisicaq:e lenrium, vel speculorum, ec imoginum à Pe in-
vicem distantiis, e anculo visorioimasinis, ex verrice sux inci-
dencix, AD B; eodem modo procedendum uc in solutione Prop.
53 hujutor
5. Ltoolema.
Datis; specie ellipseos, uno foco, es positione axeos; dataqe linea axem,
positione datum, secante: ellipsim invexire, cujus circumferentia,
perpendicularis sit livea data.
CTCrecta AB, urrinq; producta; secans axem polcione datum
Fa, in puncto A. Cuque invenienda cllip(IS, Cujus FOcuSF, e
axis in linea FA; racio distantiX FOCOruMI, ad axem ellip(eOS, UF R
adS; ita, ue BA recta, incidens in circumferentiam ellipleos; in
puncto E, Screcta, FM ellipsim tangenci, in puncto C, perpendi-
cularis. Sic uE R ad S, Ita FA, 2d FF3 SICG; anguIUS AFL, aequalis
anoulo FFa; e jungacur recta FL. DicoF, L, puncta, eAe FO-
c05, _ FF, FL, Timul, esse aequales axi ellipseos quaesicae. Delcri-
Praenim cali ellipli, recta BAF dividens angulum L. F P bitariaim,
cric perpendicularis ad concinsencem in puncto F, nempe M F 5
e quoniam anguli L. F. A, A F F sunc xquales; CrIE UT F F, ad FA,
ica F L, 2d L. A; igicurut F F. ad F A, hoc est S ad R, IFA FF, F. L
Cimul