Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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quæ circa radiorum inflectionem primitùs obveniunt) exiſtimo peten-
<
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dam, quod lucis radius non mera ſit linea, verùm dimenſionibus om-
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nimodis præditum corpus; </
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<
s
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echoid-s467
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xml:space
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">utpote (juxta quæ præmonuimus) cylin-
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dricum aut priſmaticum, pro figura corpuſculi, a quo oritur. </
s
>
<
s
xml:id
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echoid-s468
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xml:space
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">Sup-
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ponatur, aliquatenus illuſtrandi propoſiti ergò, Parallelepipedum
<
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<
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xlink:label
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note-0029-01
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xlink:href
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note-0029-01a
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xml:space
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">Fig. 3.</
note
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ABCDEFGH lucis radium obliquè ſpeculo incurrentem repræ-
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ſentare; </
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<
s
xml:id
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echoid-s469
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xml:space
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">cujus latus B F applicetur ſpeculo, dum interea reliquum
<
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ejus ſupra ſpeculi planum elevatur. </
s
>
<
s
xml:id
="
echoid-s470
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xml:space
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">Impedietur ergò Parallelogramum
<
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ABFE, nè recta procedat; </
s
>
<
s
xml:id
="
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xml:space
="
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">indè continget rectam BF aliquò ſupra
<
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dictum planum reſilire. </
s
>
<
s
xml:id
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xml:space
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">Verùm in allas ſaltem partes fiet hæc refle-
<
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ctio, ſecundum quas rectus radii progreſſus, quoad ejus fieri poteſt,
<
lb
/>
quàm minimè pervertetur. </
s
>
<
s
xml:id
="
echoid-s473
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xml:space
="
preserve
">Cùm enim is rectiſſimum curſum affectet,
<
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/>
eum (ex indole certa, perpetuáque lege naturæ) ſi perfectè nequit,
<
lb
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at tamen ut proximè conſequetur. </
s
>
<
s
xml:id
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xml:space
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">Itaque cùm inter plana latera
<
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ABDC, EFHG ſibimet oppoſita curſus ejus anteà dirigeretur, & </
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>
<
s
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="
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<
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objecta ſuperficies nihil jam obſtet, quo minùs inter eadem plana, ta-
<
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/>
metſi ſurſum excuſſus, progrediatur, admodum liquet etiamnum inter
<
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/>
illa ſemitam ejus contineri; </
s
>
<
s
xml:id
="
echoid-s476
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xml:space
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">locumque ſeu plagam reflexionis eatenus
<
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haud perperam determinari. </
s
>
<
s
xml:id
="
echoid-s477
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xml:space
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">Cæterùm eſt planum ABDC, eíque
<
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oppoſitum EFGH ſpeculi plano rectum; </
s
>
<
s
xml:id
="
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xml:space
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">quia Parallelepipedum
<
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rectum ponitur, & </
s
>
<
s
xml:id
="
echoid-s479
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xml:space
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preserve
">ideò lateralisrecta B F in ſpeculi plano exiſtens,
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planis ABDC, EFHG recta. </
s
>
<
s
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xml:space
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">Quocircà ſitotum hoc Paralleledipedum
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ob exilitatem ſuam, aut Mathematicæ computationis gratiâ, pro recta
<
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quaſi linea cenſeatur, erit pariter & </
s
>
<
s
xml:id
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xml:space
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">reflexus radius etiam linea recta;
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</
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<
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xml:space
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">nec non uterque continebitur in ſuperficie ad ſpeculi planum recta. </
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<
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Non diſſimili ratiocinio, ſi radius cylindri recti figura præditus admit-
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tatur (qualis nimirum à corpore procurrente, vel impulſo producetur,
<
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id ſi Sphæricum fuerit) etiam radius in ſuperficie plano ſpeculi recta
<
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reflectionem oſtendetur ſubire. </
s
>
<
s
xml:id
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xml:space
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">Speculi quippe plano rectus incidat
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cylindrus ABDC; </
s
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<
s
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xml:space
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">cujus baſes AMCN, BODP, axis XZ; </
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<
s
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xml:space
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<
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<
note
position
="
right
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xlink:label
="
note-0029-02
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xlink:href
="
note-0029-02a
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xml:space
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">Fig. 4.</
note
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ità ſcilicet, ut baſis BODP ſpeculi planum contingat in B; </
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<
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xml:space
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">reli-
<
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quum ejus corpus (prout in figura depictum exhibetur) obliquè ſur-
<
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gens ſupra planum emineat. </
s
>
<
s
xml:id
="
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xml:space
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preserve
">Baſis autem diametri B D, P O ſeſe nor-
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maliter ſecent; </
s
>
<
s
xml:id
="
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xml:space
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">ac per ipſam P O, & </
s
>
<
s
xml:id
="
echoid-s490
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xml:space
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">axem ductum planum efficiat in
<
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cylindro Parallelogrammum P O M N. </
s
>
<
s
xml:id
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xml:space
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">Si jam per hujuſce latera
<
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MO, NP ducta concipiantur duo plana axi parallela, cylindrúmque
<
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contingentia, liquebit (ex antedictis cauſis pariter applicatis) totius
<
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cylindri ductum inter hæc duo plana comprehendi, radiique reflecti-
<
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onem inter ipſa definiri. </
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>
<
s
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xml:space
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">Sunt autem hæc plana ſpeculi plano recta.
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</
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<
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">Sit enim recta G B H communis ſectio circnli B O D P, </
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