Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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xml:space
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">Hujuſmodi plura quædam cogitaram hîc inſerere; </
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<
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xml:space
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iſtimo ſufficere ſubindicando modo, juxta quem, citra _Calculi moleſti-_
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_am, curvarum tangentes_ exquirere licet, unáque conſtructiones de-
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monſtrare. </
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<
s
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xml:space
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">Subjiciam tamen unum aut alterum non aſpernanda, ut vi-
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detur _Theoremata_ perquam generalia.</
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<
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xml:space
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">Sit linea quæpiam ZGE, cujus axis VD; </
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<
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xml:space
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mìs applicatæ perpendiculares (VZ, PG, DE) ab initio VZ con-
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<
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xlink:label
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tinuè utcunque creſcant; </
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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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">rectâ EDF ad VD perpendiculari (quæ _curvas_ ſecet punctis E, F,
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ipſam VD in D) ſit ſemper _rectangulum_ ex DF, & </
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<
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dam R æquale _ſpatio_ reſpectivè _intercepto_ VDEZ; </
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<
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DF:</
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<
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xml:space
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">& </
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<
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">connectatur recta TF; </
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continget.</
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<
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xml:space
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">Sumatur enim in linea VIF punctum quodpiam I (illud primò ſu-
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pra punctum F, verſus initium V) & </
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xml:space
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">per hoc ducantur rectæ IG ad
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VZ, ac KL ad VD parallelæ (quæ lineas expoſitas ſecent, ut vides)
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éſtque tum LF. </
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<
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<
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xml:space
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">adeóque LF x
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R = LK x DE. </
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<
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xml:space
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">Eſt autem (ex præſtituta linearum iſtarum natura)
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LF x R æquale ſpatio PDEG; </
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<
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xml:space
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">ergò LK x DE = PDEG &</
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</
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<
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</
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<
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">Rurſus accipiatur quodvis punctum I, infra punctum F, reliquáq;
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= PDEG &</
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<
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quibus liquidò patet totam rectam TKFK intra (ſeu extra) curvam
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VIFI exiſtere.</
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<
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">Iiſdem quoad cætera poſitis, ſi _ordinatæ_ VZ, PG, DE, &</
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tinuè decreſcant, eadem concluſio ſimili ratiocinio colligetur; </
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cum obvenit _Diſcrimen_, quòd in hoc caſu (contra quàm in priore)
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linea VIF concavas ſu
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as axi VD obvertat.</
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<
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<
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<
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ZGE, VKF ta relatæ, ut ad communem ipſarum axem VD ap-
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<
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plicatâ quâvis rectâ; </
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_plo ſpatio_ VDEZ; </
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<
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<
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<
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attigimus (cujus ſcilicet ad VD applicatæ ſe habeant ut ſpatia VDEZ;
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<
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