Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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in axe capiatur CK = CG; </
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<
s
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xml:space
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<
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ipſius MNPrefractum. </
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<
s
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echoid-s4811
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xml:space
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">Connectantur enim rectæ FG, BG; </
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<
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xml:space
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">& </
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<
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quoniam eſt BZ. </
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<
s
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echoid-s4814
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xml:space
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">CZ:</
s
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<
s
xml:id
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echoid-s4815
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xml:space
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<
s
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echoid-s4816
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xml:space
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">R:</
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<
s
xml:id
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echoid-s4817
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xml:space
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">:) FZ. </
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<
s
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echoid-s4818
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xml:space
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">FC; </
s
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<
s
xml:id
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echoid-s4819
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xml:space
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">erit permutando
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BZ. </
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<
s
xml:id
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echoid-s4820
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xml:space
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">FZ:</
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<
s
xml:id
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echoid-s4821
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xml:space
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">: CZ. </
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<
s
xml:id
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echoid-s4822
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xml:space
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">FC. </
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<
s
xml:id
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echoid-s4823
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xml:space
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">dividendóque BF. </
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<
s
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="
echoid-s4824
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xml:space
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">FZ:</
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<
s
xml:id
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xml:space
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</
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<
s
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<
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left
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xlink:label
="
note-0094-01
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="
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xml:space
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">Fig. 109.</
note
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FC. </
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<
s
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xml:space
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">itaque patet triangula BF G, GFC(latera ſcilicet habentia
<
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circa communem angulum GFCproportionalia) ſimilia fore.
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</
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<
s
xml:id
="
echoid-s4828
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xml:space
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">quamobrem erit BG. </
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<
s
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echoid-s4829
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xml:space
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">GF:</
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<
s
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="
echoid-s4830
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xml:space
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">: GC. </
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<
s
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="
echoid-s4831
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xml:space
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">CF. </
s
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<
s
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="
echoid-s4832
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xml:space
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">ſeu permutatim BG. </
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<
s
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="
echoid-s4833
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xml:space
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:</
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<
s
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echoid-s4834
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xml:space
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">: GF. </
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<
s
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echoid-s4835
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xml:space
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">CF. </
s
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<
s
xml:id
="
echoid-s4836
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xml:space
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">hoc eſt BG. </
s
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<
s
xml:id
="
echoid-s4837
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xml:space
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">GC:</
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<
s
xml:id
="
echoid-s4838
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xml:space
="
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">: FZ. </
s
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<
s
xml:id
="
echoid-s4839
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xml:space
="
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">CF:</
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<
s
xml:id
="
echoid-s4840
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xml:space
="
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">: I. </
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<
s
xml:id
="
echoid-s4841
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xml:space
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">R. </
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<
s
xml:id
="
echoid-s4842
"
xml:space
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">verum in tri-
<
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angulis BC G, NCKeſt BC = CN, & </
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>
<
s
xml:id
="
echoid-s4843
"
xml:space
="
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">CG = CK; </
s
>
<
s
xml:id
="
echoid-s4844
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xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s4845
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xml:space
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">ang. </
s
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<
s
xml:id
="
echoid-s4846
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xml:space
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">
<
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BCG = NCK; </
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<
s
xml:id
="
echoid-s4847
"
xml:space
="
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">adeóque BG. </
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<
s
xml:id
="
echoid-s4848
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xml:space
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">GC:</
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<
s
xml:id
="
echoid-s4849
"
xml:space
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">: NK. </
s
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<
s
xml:id
="
echoid-s4850
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xml:space
="
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">CK. </
s
>
<
s
xml:id
="
echoid-s4851
"
xml:space
="
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">quare erit quo-
<
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que NK. </
s
>
<
s
xml:id
="
echoid-s4852
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xml:space
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">CK:</
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<
s
xml:id
="
echoid-s4853
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xml:space
="
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">: I. </
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<
s
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="
echoid-s4854
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">R. </
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<
s
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echoid-s4855
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xml:space
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">ergò, ſecundum generatim antehac
<
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xml:space
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">_Lect. 3. nu-_
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_mero. 10._</
note
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liquet NK ipſius MN refractum exiſtere.</
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<
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">_Coroll._ </
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<
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">Adnotetur eſſe triangula BFG, GFCſimilia; </
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<
s
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xml:space
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">ac eſſe
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BG. </
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<
s
xml:id
="
echoid-s4860
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xml:space
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">CC:</
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<
s
xml:id
="
echoid-s4861
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xml:space
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">: I. </
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<
s
xml:id
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echoid-s4862
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">R; </
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<
s
xml:id
="
echoid-s4863
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xml:space
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">& </
s
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<
s
xml:id
="
echoid-s4864
"
xml:space
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">ang. </
s
>
<
s
xml:id
="
echoid-s4865
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xml:space
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">BG F = GC F; </
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<
s
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echoid-s4866
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">& </
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<
s
xml:id
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echoid-s4867
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xml:space
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">eſſe BF, FG,
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FC {.</
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<
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">./.</
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<
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<
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</
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<
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<
s
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">III. </
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<
s
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xml:space
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">Ex hoc (ſanè pulchro, perutilíque _Theoremate_) cùm particu-
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laris exoritur methodus hujuſmodi quotcunque refractos expeditiſſimè
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ſeu delineandi, ſeu computandi; </
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<
s
xml:id
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xml:space
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facilimè diſcernuntur ac demonſtrantur. </
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<
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exhibentur _Corollariis._</
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<
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</
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<
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<
s
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<
s
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xml:space
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">Patet hinc punctum Z eſſe limitem ultra quem (reſpectu cen-
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tri) nullus axem interſecat refractus; </
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<
s
xml:id
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xml:space
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">ſeu perpendicularis ipſius AB
<
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(vel ei ſaltem quàm proximè adjacentis radii) refractum ad Z termi-
<
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<
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="
left
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xlink:label
="
note-0094-03
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xlink:href
="
note-0094-03a
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xml:space
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">Fig. 110.</
note
>
nari. </
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<
s
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<
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<
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">CG, vel CR.</
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</
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<
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<
s
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">V. </
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<
s
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">Conſequitur etiam, ſi duorum incidentium MN, QR (quorum
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QR ſit obliquior) refracti conveniant cum axe punctis K, L, fore
<
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CK&</
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>
<
s
xml:id
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">gt; </
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<
s
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">CL. </
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<
s
xml:id
="
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xml:space
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">Etenim ſi rectæ NC, RC ad circulum refractarium
<
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<
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="
left
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xlink:label
="
note-0094-04
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xlink:href
="
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xml:space
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">Fig. 111.</
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>
(itâ circulum EGZmeritò ſubinde nominabimus) producantur, ut
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ipſum ſecent punctis G, H; </
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<
s
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<
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<
s
xml:id
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<
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="
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">adeóque CK
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&</
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<
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xml:id
="
echoid-s4893
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xml:space
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">gt; </
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<
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xml:id
="
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xml:space
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<
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</
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<
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<
s
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">VI. </
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<
s
xml:id
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xml:space
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">Ad eaſdem partes incidentium refracti ſeſe priùs interſecant
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quàm axem; </
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<
s
xml:id
="
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xml:space
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">(veluti puta refracti NK, RL ſeſe decuſſant in X.)</
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<
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</
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<
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<
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">VII. </
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<
s
xml:id
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">Quinetiam, ſi in primo caſu per centrum C dueatur recta
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<
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xlink:label
="
note-0094-05
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xlink:href
="
note-0094-05a
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xml:space
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">Fig. 111.</
note
>
VI ad BZ perpendicularis, dictóque circulo refractario occurrens
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ad I; </
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<
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">& </
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<
s
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">fiat CY = CI, patet punctum Y eſſe limitem </
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