Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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111 - 120
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131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
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tardiùs in medio contumaciore delatum minorem arcum B β delineet;
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<
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<
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xml:space
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">Cùm verò jam punctum
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D denſius quoque medium interet ad δ; </
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<
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retardetur; </
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<
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xml:space
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">motus iſti circulares protinus extinguantur oportet (nec
<
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enim jam punctum D velociùs feretur quàm B; </
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<
s
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xml:space
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">nec ideò majorem ut
<
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priùs ſimul arcum deſcribet.) </
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<
s
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xml:space
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">Itaque prius iter, quàm poterunt proxi-
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mè, deſerentia tendent utrumque per horum arcuum tangentes δ κ,
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β α; </
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>
<
s
xml:id
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xml:space
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">radiúſque totus ABCD hoc modo detortus, & </
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>
<
s
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="
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xml:space
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">ſitum α β δ κ
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nactus per hanc poſteà ſemitam rectà decnrret Adnotandum eſt au-
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tem quæcunque ſit rectæ AB ad rectam EF inclinatio arcus D δ, B β
<
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/>
(vel ſemidiametros ZD, ZB) eandem ſemper habere proportionem
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inter ſe; </
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<
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xml:space
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">talem nempe, qualem in denſitate, ſeu reſiſtentia peculiare
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diſcrimen exigit. </
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<
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">Etenim ſupponatur in quovis ſuperficiei pellucidæ
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">Fig. 7.</
note
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loco poſitum nobile punctum B; </
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<
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">cùm medium hoc ex hypotheſi ſit
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homogeneum (hoc eſt ubique pariter obſiſtens) nulla poteſt, opinor
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aſſignari ratio cur hoc mobile non in quaſvis partes æ quâ velocitate de-
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ferri poſſit; </
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<
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xml:space
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">nimirum æquè celeriter ad Q tendet, (impetum modò
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ceperit iſthàc dirigentem) per rectam OBQ, ac in N per rectam
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ABN. </
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<
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">Adeóque radii lucidi AB, OB utcunque differenter inclinati
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<
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">Fig. 8.</
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parem omnino reſiſtentiam invenient; </
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<
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xml:space
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">punctum, inquam, B, ſeu verſus
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Q, ſeu verſus N nitatur, æqualiter, eodémque modo retardabitur.
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</
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<
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">Quinetiam cùm punctum D in primo medio ſemper eâdem, quæcunque
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fuerit ejus poſitio, celeritate promoveatur, ſatis apparet motus iſtos,
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aut motuum ſemitas eodem tempore decurſas, arcus nempe circulares
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D δ, B β ſemper eandem inter ſe proportionem ſervare; </
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<
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lam, quam habent ſemidiametri ZD, ZB, vel Z δ, ZB; </
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<
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co proportio, principaliter ac primariò, radiorum refractiones, ad
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eadem duo media factas, determinat atque metitur. </
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<
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dem eſſe patet cum illa, quam habent recti ſinus angulorum ipſis Zδ,
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ZB in triangulo Z δ B oppoſitorum, ipſorum ſcilicet ZB δ (vel
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ZBE) & </
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">Eſt autem angulus ZBE complementum anguli
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ABE, (hoc eſt angulus inclinationis rectæ AB ad EF) & </
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Z δ B eſt complementum anguli F δ κ, vel inclinatio rectæ δ κ ad ean-
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dem EF. </
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">Patet vero, quod in hoc
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caſu, angulus EBZ major eſt angulo B δ Z; </
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<
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">vel, ductis BM, δ N
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ad EF perpendicularibus, quòd angulus MBG major eſt angulo
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N δ κ; </
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unt. </
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ipſi magis obſiſtens, ſen denſiùs. </
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">At ſi medio incurrit faciliorem tran-
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ſitum præbenti, ſeu rariori, planè ſimili modo, ſed inverſè ſe res habet.</
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