Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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compoſitam è rationibus applicatarum ab iſtis punctis ad rectam AZ
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(ipſi ſcilicet AY parallelarum) & </
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<
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puncta ac dictis applicatis (vel, rationem velocitatum æquari rationi
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applicatarum ex interceptarum ratione ſubductæ.)</
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<
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<
s
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">Nempe ſi duæ rectæ MT, NX curvam tangent ad puncta M, N;
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</
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<
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<
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xml:space
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<
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xml:space
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">applicentur NP, NQ ad
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YA parallelæ, velocitatum ad puncta, M, N proportio componetur
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è proportione ipſius TP ad PM, & </
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<
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<
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velocitas in M ad velocitatem uniformem per AY ſe habet ut TP ad
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PM; </
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<
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<
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">velocitas iſta uniformis ſe habet ad velocitatem in N, ut
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QN ad QX. </
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<
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">Ergo velocitas in M ad velocitatem in N ex his
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duabus rationibus PP ad PM, & </
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concurſu tangentium ductâ FE ad AY parallelâ; </
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<
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= TP. </
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_Problematis iſtius ſolutionem_, quam tanti fecit, & </
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impendit G_alilæus_, quámque _Torricellius_ pronunciat eum quàm optimè
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& </
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<
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">ingenioſiſſimè reperiſſe. </
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<
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">Rem ità proponit _Torricellius_ (nam ipſe
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_Galilæus_ ad manum non eſt) propoſitâ quâvis _parabolâ_, cujus
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_vertex_ A oportet punctum aliquod ſublime reperire; </
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<
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cadat uſque ad A, & </
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liter convertatur, ipſa _propoſitam parabolam_ deſcribat (notetur, quod
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motus deſcenſivus parabolam deſcribens non è puncto ſublimi, ſed ab
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ipſo puncto A cenſetur inchoare.) </
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<
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xml:space
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">Huc recidit _Problema, @ alilæi_ ſup-
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poſitis inſiſtendo, ut determinentur particulares velocitates motuum,
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uniformis horizontalis, ſeu tranſverſi, & </
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<
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ſivi quorum è compoſitione deſcripta concipitur exhibita parabola.
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<
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">Nos illud, quæcunque ſit creſcentis deſcenſivi motûs ratio, quicunque
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modus, generaliter exequemur; </
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exemplum ſubjuncturi.</
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<
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">‖ Reperiatur in recta AZ (quæ ſanè curvæ
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diameter eſt) punctum aliquod, ut P, à quo ſi ordinatim applicetur
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PM, & </
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<
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">ducatur tangens MT, rectæ AZ occurrens in T, ſit in-
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tercepta TP æqualis ipſi PM; </
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AS = AP. </
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<
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">Nam quoniam SA = AP, concipiet mobile deſcendens ab S in
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A tantum impetum, quantum ab A ad P curvam deſcribendo (ponitur
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enim increſcentis velocitatis motus utrobique prorſus idem) iſte verò
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impetus æquatur impetui, quo mobile à T deſcendens uniformi motu
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percurret rectam TP, eodem tempore quo recta AZ </
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