Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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CN Π, angulo CNP æquari. </
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<
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xml:space
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<
s
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xml:space
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">Accepto quovis in NM puncto
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(puta M) centro C per M deſcribatur circulus MQH; </
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<
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xml:space
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<
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">Fig. 63.</
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N per M deſcribatur circulus MRH, qui priorem MQH ſecet
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in H; </
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<
s
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echoid-s2645
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xml:space
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">erit HN Π reflexus ipſius MN P. </
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<
s
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echoid-s2646
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">Etenim connexis CM,
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CH; </
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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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">NM, NH, ex conſtructione liquet triangula CMN, CHN,
<
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invicem æquilatera fore; </
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<
s
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echoid-s2649
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xml:space
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">proindéque angulos CNM, CNH (& </
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<
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indè relìquos MNR, HNR) æquari 3. </
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<
s
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xml:space
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">protenſà CNR, à quovis
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in MN puncto, puta M ducatur MG ad CR perpendicularis, & </
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<
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in hac producta ſumatur GH = GM; </
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<
s
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xml:space
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">erit conjuncta HN Π iterum
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reflexus. </
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<
s
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xml:space
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">Nam connexis NH, NM patet angulos GNM, GNH
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æquari. </
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<
s
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xml:space
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">verum hi modi ſufficiunt huic conficiendo perfacili negotio.</
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<
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</
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<
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xml:space
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">IV. </
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<
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xml:space
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">Nocetur ſi fuerit HN P reflexus ipſius MN P fore N Π =
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N P.</
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</
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<
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<
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xml:space
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">V. </
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<
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">Diſpiciamus jam primò quid ex hujuſmodi reflectione contingat
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puncto ab infinitâ quo ad ſenſum diſtantiâ radianti, ſeu parallelos
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projicienti radios. </
s
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<
s
xml:id
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xml:space
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">quorſum, per circuli reflectentis centrum C
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protendatur indefinitè recta ABC (hoc autem in ſequentibus evitandæ
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repetitioni perpetuò factum intelligatur; </
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<
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xml:space
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">quin ejuſmodi recta nomi-
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netur axis; </
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<
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xml:space
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">hîc _Speculi,_ poſteà _Diapbani_) biſecetur autem Semidiame-
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ter CB in Z; </
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<
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">& </
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<
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">per Z tranſeat recta ZY ad CB perpendicularis,
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indeſinitéque protenſa ; </
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<
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xml:space
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">tum quilibet incidat axi parallelus radius
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MN P ad N; </
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<
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xml:space
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">(convexo circuli nil refert, an cavo; </
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<
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">nam in utroque
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caſu reflexus quoad directionem idem erit; </
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<
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xml:space
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">vel ejus qui in hoc, iſte qui
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in illo productus erit) connexáque CN ipſam ZY interſecet in V;
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</
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<
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">ſiátque CK = CV; </
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<
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">ducatúrque NK; </
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<
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">erit NK ipſius MN reflex-
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us (vel reflexi productus) Nam ducatur NQ ad CB perpendicu-
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laris, & </
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<
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<
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CQ. </
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<
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PN. </
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<
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">CN. </
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<
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">item angulus KCN æquatur alterno CNP. </
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<
s
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">ergò tri-
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angula CKN, NCP ſimilia ſunt; </
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<
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">adeoque KN = KC. </
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<
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">igitur è
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ſuprà generatim oſtenſis patet fore KN, ipſius MN reflexum.</
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<
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">VI. </
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">Hinc particularis emergit methodus hujuſmodi quotcunque
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reflexos quàm expeditiſſime deſignandi; </
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<
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<
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tiones ac reſpectus; </
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<
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diluceſcunt; </
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<
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<
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