Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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hoc eſt AX x CB = 2 AC x CZ; </
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<
s
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xml:space
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">vel 2 AX x CE = 2 AC
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x CZ; </
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<
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xml:space
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<
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<
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xml:space
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<
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<
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xml:space
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<
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<
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</
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<
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">CE. </
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<
s
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">quapropter eſt XH = CZ : </
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<
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<
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xml:space
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<
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<
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<
s
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xml:space
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">Quoad radiationem ad partes concavas, planè ſimilis eſt diſcurſus.
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</
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<
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<
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<
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<
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xml:space
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">Fig. 193,
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194, 195.</
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nes punctorum F limites, ſeu foci (quales Z) ad ellipſin exiſtunt;
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</
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<
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<
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">cujus _axis_ TV è præmiſſis, non uno modo, deter-
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minatur. </
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<
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xml:space
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">item ſi CA = CE, limites Z ad parabolam conſiſtent
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cujus _focus_ C, _axis_ CT = {1/2} CE, _vertex_ T. </
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<
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puncta Z ad _h@perbolas eſſe conſtat_, quarum itidem _focus_ C; </
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xml:space
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xml:space
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TV facilè de modò (vel alibi) dictis reperitur; </
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<
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onum _Parameter_ ipſi CB æquatur.</
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<
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xml:space
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">Hinc in ſingulis reſpectivè caſibus, ejuſmodi _ſectiones co-_
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_nicæ_ ſunt rectarum F α G abſolutæ imagines; </
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<
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ſunt imagines ad oculum relatæ in ſpeculi centro conſtitutum; </
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<
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flectione ſcilicet ad concavas ſpeculi partes effectæ quæ ſolæ oculo
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ſic poſito conſpicuæ ſunt.</
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<
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">Patet autem ſirecta F α G infinitè diſtet, quòd _ellipſis_ in _cir-_
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_culum_ abit. </
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">utì quoque ſi F α G per centrum tranſeat, quòd _hyperbolæ_
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iſtæ in rectam lineam degenerant.</
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<
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">Subnotetur etiam in caſu quum _imago fit hyperbolica_, quod
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_hyperbolæ_ YTY pars YEEY, neque non tota ζ V ζ ad circuli partes
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MBN pertinent; </
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">(nempe ſi centro C per E deſcriptus circulus ipſam
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FG interſecet punctis K, tota hyperbola ζ V ζ rectam interceptam KK
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referet; </
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">hyperbolicæ lineæ alterius pars ſuperior YEEY quod
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reliquum eſt repræ ſentabit hinc indè protenſæ rectæ FG) pars autem
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ETE ad partem concavam MDN ſpectat. </
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monitum.</
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<
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bus commodius de relatis judicum fiet. </
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ad quem (convexis è partibus) ab F, & </
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ON L; </
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rectæ FAG imago; </
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<
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