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# Title: Optica Promota, Seu Abdita radiorum reflexorum & refractorum Mysteria, Geometrice Enucleata (shelfmark Leibn. Marg. 94)
# Folio 15, page id 727094130:0027
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5
punctum I, linca PT, cangens Lsyperbolam PL. X in puncto I, &
a puncto I ducatur linex I T pervendicularis, TM, ericq; F I M an-
oulus incidenta, cur hiac aequalis ex. foco ellipleos D, anoulus
ODF, _ ducta recta B C, axi A C aequili; ex praecedente cOr-
rolario evidens est, angulum C BD esse aequalem angulo retracti-
onis IZ, comperencem angulo incidentia C:D L, seu F IM:
Aac icaq; IO aequalis rectae lH, _ jungatur OHI; cricque FO
aequalis axi, hyperbola NP, _ I Y dividens angulum IIIO bita-
riam, est perpendicularis ad OHI; led e perpendicularis est ad
TM; isicur IM, OH, Cune parallela, _ angulus P. I M ae qualis
angulo LOH: sed FIM, est aequalis anguloCi D F, igicur e lO
H eidem CD F est aequalis. In criangulis igitur F OHI, BDO
duo lacera HF, FO sune provorrionalia, duobus lareribus GB,
BD, ec ariculus HIOE, aequalis angulo CDB, ergo _ angulus
GBD, eAt aequalis angulo EI F O, hoc est angulus OTL, aequalis 6. 6.
anouloO FH, Parallelaigicur lune IZ, ec F H, quod erat demon.
Arandum.
Scholium.
Pocerat eriam de hyperbola densicaris per experientiam primo
inveniri, d ellipis demonstrarione Geometrica ex en deduci;
NNos aucem, hixec scriplimus eadem Mechodo, qua a nobis reperta
TunE.
Aeque hisce de suxerticiebus, quae Resractiones meciuncur per
analogiam claristine Monstratis, per experiencias Armirer proba-
eis, e per demonstrationem Geomerricam solide contirmatis;
Reltac nine uc Machinss Opticas, ance per approximationem,
nunc Geomerrice demonstremus. Ouoniam vero, hactenus de
Superticiebus retractionum cancum, loquuri sumus; opOrcOL ue
Eliquoe Lemmaca praemitcamus, quorum ope a superticiebus ad
Tolida, (qualia nimirum sunc omnia MactiinumenCa oprica) liCeaE
Progredi.
AP. 3.5T.
AP. 3. 48.