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# Title: Optica Promota, Seu Abdita radiorum reflexorum & refractorum Mysteria, Geometrice Enucleata (shelfmark Leibn. Marg. 94)
# Folio 53, page id 727094130:0065
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=727094130&page=65
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# Lines: 38 recognised, mean confidence 0.87
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D
d. 41. Jet
lo
Si exuno hyperbolae foco ducarur rectula, axi perpendicularis; et ab
aliquo rectelae puncto ducantur duae rectae, una. ad hyperbola verticem,
alcera illius circumferentiae perpendicularis; es a foco hyperbolae
praedicto, ducatur alia recta, occurrens perpendiculari in circumfe-
remtia: erit anculus comprehensus a duabus primis rectis, ferme
aequalis aneulo comprehenso, a terria, e axc hyperbola.
IE hyperbola A C R ex cujus LOCOM, diicatur rectL M Y, adi
M C. perxendicularis; e apuncto T, ad hyperbola verricem
C ducatur una recta TC;. _ ab eodem puncto Y, ducatur altera
ad punctum contactus R, cangenti OR O perpendicularis, I R;
e a fOCOM, ad punctum R, duCATUTMB. Dic angulOS CMR,
CYRfere aequales esse. PrOduICALUT FNGenS Q R O, UE COnCUT
FAL CuM axC inO5:
_ dIaCETO TO,
cucatur circulus,
qui cransibie per
Puncta R, E BI,
quoniam anguli
TMO, TRO.
TUNE reCtI: CrUHI-
que angeti OM
R, OYR, in Ca-
dem circuli por.
tione, inter le a-
Quales 5: aBgulus
aurem RETC, nOD
diftere uIEuM,
ab anguloRTO;
quoniam ER punctum, cadat prove verricem C; (quod semper
evenic proprer brevitacem Linex M P) TaNgenS QRO, COnCUT-
reccum axe, Ferme in verrice C: et probrevicacerectae C, dimi-
nuicur aneulus O. TC, differentia Incer angulOS R M C, R F C:
Ouare (M T fueric breviuscula; crunt anguli R TC, RM C, tere
requales; quod demonstrandum erat.
PrOP