Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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arc {NR & </
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<
s
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<
s
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xml:space
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">: πσ/2} = NX; </
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<
s
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echoid-s5339
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xml:space
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<
s
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s
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<
s
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xml:space
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">: Z π/2} = GZ. </
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<
s
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xml:space
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">eri@ ergòarc
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<
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xml:space
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">Fig. 124.</
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NR. </
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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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<
s
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xml:space
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">GZ. </
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<
s
xml:id
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echoid-s5346
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xml:space
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">quapropter erit (juxta præcedentem)
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NZ. </
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<
s
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echoid-s5347
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xml:space
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">GZ = NG. </
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<
s
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<
s
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xml:space
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">CG.</
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<
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<
s
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<
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xml:space
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">Porrò liquet punctum Z eſſe locum imaginis, quem expe-
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timus, oculo conſpicuæ in recta N π conſtituto; </
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<
s
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xml:space
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">utpote circa quod
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viciniorum ipſi NP radiorum refracti ipſam N π interſecant; </
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<
s
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xml:space
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">qua de
<
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re multoties egimus, ut pigeat eò plura βαττλγ{εĩ}ν.</
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<
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<
s
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xml:space
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">IX. </
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<
s
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xml:space
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">Facilè verò, Secundum _Theorema pramiſſum_, deſignatur
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punctum Z. </
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<
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xml:space
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">Ducatur nempe CG ad refractum NK perpendicula-
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ris; </
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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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">ad connexam CN ducatur perpendicularis GV; </
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<
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xml:space
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">& </
s
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<
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xml:space
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">per V
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ducatur VZ ad CK parallela, ſecans ipſam NK in Z. </
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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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">Nam, connexâ GE, liquet angulos GEC, GNC(circumducti
<
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<
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">Fig. 125.</
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nempe per N, E, G, C circuli ſubtenfæ GE inſiſtentes ambos) æqua-
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ri; </
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<
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xml:space
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">hoc eſt angulos GEC, VGCæquari. </
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<
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xml:space
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">quapropter (utrique
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rectum adjiciendo) toti NEG, ZGVæquantur. </
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<
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xml:space
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GNE, VZGæquantur. </
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<
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xml:space
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">ergò triangula GN E, VZGſimilia ſunt,
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unde NG. </
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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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">itaque. </
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xml:space
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">NE =
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CE. </
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<
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<
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:</
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<
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">hoc eſt NZ. </
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<
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<
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<
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<
s
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CE. </
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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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<
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<
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<
s
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obtinet, imaginis loco congruentem, è mox oſtenſis. </
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<
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propoſitum.</
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<
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<
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NZ. </
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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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<
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<
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<
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<
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<
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<
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CB perpendicularis circumferentiæ occurrat ad N; </
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<
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ad CB paralleli refractus ſit NK, circuli peripheriæ denuò occur-
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<
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position
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xlink:label
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">Fig. 126.</
note
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rens in Z; </
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<
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">dico punctum Z eſſe imaginem, qualem mox definivimus,
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oculo conſpicuam in ipſa NK ſito.</
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</
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<
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<
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ac junctâ CN) ob 3 Rq. </
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<
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<
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<
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<
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3 CGq. </
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<
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<
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<
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<
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