Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
s
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">3. </
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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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echoid-s1282
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xml:space
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">reliquiſque velut anteà præparatis) oſtendetur fore perpetuò NK. </
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<
s
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echoid-s1283
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<
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<
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xlink:label
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note-0047-01
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xml:space
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">Fig. 27.</
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CK :</
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<
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echoid-s1284
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<
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echoid-s1285
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">HK. </
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<
s
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echoid-s1286
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xml:space
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">unde ſi fuerit (ex _Hyperbolæ_ conſtructione) BD.
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</
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<
s
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echoid-s1287
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">HK :</
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<
s
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echoid-s1288
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<
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echoid-s1289
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">R. </
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<
s
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echoid-s1290
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">erit etiam NK. </
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<
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echoid-s1291
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">CK :</
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<
s
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xml:space
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">: I. </
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<
s
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echoid-s1293
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">R. </
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<
s
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echoid-s1294
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xml:space
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">quòd ſi radius MN ad
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CB parallelus refringatur in NK; </
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<
s
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echoid-s1295
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xml:space
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">hoc idem accidet, ut nempe ſit
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NK. </
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<
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">CK :</
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<
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xml:space
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">: I. </
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<
s
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">R. </
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<
s
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echoid-s1299
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xml:space
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">quare radii MN refractus per _Hyperbolæ_ focum
<
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tranſibit.</
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<
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<
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">4. </
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<
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xml:space
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">Quòd verò ab _Ellipſis_ aut _Hyperbolæ_ cujuſvis focorum alterutro
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quilibet curvæ incidens radieus in alterum reflectatur, admodum facilè
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diluceſcit. </
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<
s
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="
echoid-s1303
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xml:space
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">Nam in ellipſe, perpendicularis NC, in _Hyperbolæ_, tan-
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gens. </
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<
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">NT biſecat angulum HNK. </
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<
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xml:space
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">unde patet propoſitum, Hæc
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extra noſtras oleas poſita curſim & </
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<
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">leviſſimè perſtringo; </
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<
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">nec tamen
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ut eò multa putem deſiderari.</
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</
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<
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<
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">Revertamur in orbitani; </
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<
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xml:space
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">& </
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<
s
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xml:space
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">quidem derelictis his generaliſſimis,
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ac abſtractiſſimis, lemmatum vicem obituris, ad particularia deſcenda-
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mus. </
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<
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xml:space
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">Ad planas verò ſuperficies (vel earum loco propter inſinuatam
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antehac cauſam ſubrogatas lineas rectas) inflexis obtingentia radiis pri-
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mò contemplemur. </
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<
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xml:space
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">Etiam quoad has Catoptricis primum, utpote fa-
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cillimis, breviſſimè defungemur.</
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<
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<
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">Parallelorum ſibi radiorum (AB, MN) rectæ (EF) in-
<
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note
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cidentium reflexi (B _α_, Nμ) ſunt etiam ſibi paralleli.</
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<
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">Nam quoniam AB, MN ex hypotheſi ſunt pàralleli, erunt anguli
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ABE, MNE pares. </
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<
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</
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<
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">Quare rectæ _α_ B, μ N ſunt parallelæ.</
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<
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">Sit recta ABZ rectæ reflectenti EF perpendicularis; </
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<
s
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hacverò promanantis ab A cujuſvis radii AN reflexus _α_ N. </
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<
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in Z; </
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<
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<
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<
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">_α_ NF =
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ZNB. </
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<
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">quare liquet triangula BNA, BNZ ſibi mutuò æquilatera
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fore; </
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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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">Hinc, omnes ab uno puncto, divergentium tanquam ab altero
<
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<
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xlink:label
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note-0047-03
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quodam uno prodeuntes.</
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<
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">Quoad punctum longè diſſitum (ſuo parallelos ad ſenſum radios eja-
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@ulante) patet è penultima. </
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<
s
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xml:space
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">Quòad punctum è ſenſibiliter finita di-
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ſtantia radians, ex ultima patet, quòd omnium ab A divergentium ra-
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diorum reflexi protracti concurrunt in Z; </
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<
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promanare.</
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