Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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361 - 390
391 - 420
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451 - 480
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026/01/291.jpg
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Theorema
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65.
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Si globus minor in maiorem impingatur per lineam obliquam incidentiæ,
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ſemper reflectitur
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; </
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<
s
id
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">quippè ſit determinatio mixta ex priore, & noua, quæ
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determinari poteſt, ſi aliquid à nouæ figuræ deſcribatur; </
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<
s
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">ſit circulus
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FQCD; </
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<
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">ſint diametri QD, FC; </
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<
s
id
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">ſit AI dupla AF, ſitque determi
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natio prior vt FA, ſi ſecunda ſit vt AI, erit dupla prioris; </
s
>
<
s
id
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">igitur corpus
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reflectens erit immobile; </
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>
<
s
id
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">igitur ſi linea incidentiæ ſit EA, reflexa erit
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AT, ita vt anguli TAF, EAF ſint æquales; </
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>
<
s
id
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N20606
">ſi autem determinatio no
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ua ſit ad priorem vt AH ad AF, id eſt, v.g. vt 3. ad 2. poſitâ ſcilicet li
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neâ incidentiæ perpendiculari FA in planum reflectens QD, quod certè
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mouebitur per Th. 64. aliter procedendum eſt vt inueniatur linea re
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flexa reſpondens lineæ incidentiæ obliquæ; </
s
>
<
s
id
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N20614
">diuidatur FAMK ita vt
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KN ſit ad AF vt 3.ad 2. ac proinde AH ſit diuiſa bifariam in K; </
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>
<
s
id
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N2061A
">de
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ſcribatur circulus KMNR, ſit linea quælibet incidentiæ obliqua EA; </
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>
<
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N20620
">
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producatur in B; </
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>
<
s
id
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N20625
">ducantur OX BT parallelæ AH; </
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<
s
id
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N20629
">aſſumatur AG æqua
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lis OX, & GS æqualis AB; </
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>
<
s
id
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N2062F
">certè BS erit æqualis OX vel AG; </
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>
<
s
id
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N20633
">duca
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tur AS, hæc erit reflexa quæſita: </
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>
<
s
id
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N20639
">idem dico de omnibus aliis lineis in
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cidentiæ; demonſtratur eodem modo quo ſuprà in Th. 30. 31. 32. quæ
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conſule, ne hic repetere cogar. </
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<
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"/>
Theorema
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emph.end
type
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"/>
66.
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type
="
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>
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<
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">
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"/>
Si globus maior impingatur in minorem, per lineam incidentiæ connecten
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tem centra nullo modo reflectitur ſed per eandem lineam primum motum pro
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pagat licèt tardiùs per Th.
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132. lib.1. in qua verò proportione retardetur
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motus non ita facilè dictu eſt; dici tamen poteſt & explicari in fig. </
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<
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">Th.
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63. ſi enim globi ſunt æquales, ceſſio æqualis eſt impulſioni; </
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<
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id
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">ſi globus
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impactus ſit maior, ceſſio eſt maior impulſione, vt conſtat; </
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>
<
s
id
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N2066D
">igitur, ſi globus
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eſt ad globum vt FB ad FB; </
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>
<
s
id
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">determinatio noua erit ad priorem vt FB
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ad FB; </
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>
<
s
id
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N20679
">igitur quieſcet globus impactus per Th. 62. ſi verò globus impa
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ctus ſit ad alium vt EB ad ER; </
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<
s
id
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N2067F
">determinatio noua erit ad priorem, vt
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BG ad BF; </
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>
<
s
id
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">igitur motus retardatus globi impacti eſt ad non retardatum
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vt FG ad FB; </
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<
s
id
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N2068B
">quod ſi globus impactus eſt ad alium vt DB ad DS, deter
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minatio noua eſt ad priorem vt BH ad BF; </
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>
<
s
id
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N20691
">ſi ſit vt TV, ad VB, deter
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minatio noua erit ad priorem vt BX ad BF, donec tandem nullus ſit
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globus reſiſtens; neque res aliter eſſe poteſt. </
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<
s
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">Hinc vides duos terminos oppoſitos, qui ſunt, nulla reſiſtentia, & infi
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nita reſiſtentia; </
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<
s
id
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">nulla eſt reſiſtentia, cum globus impactus in nullum in
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cidit, ſed eſt veluti infinita ceſſio; </
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<
s
id
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">cum verò globus in corpus immobile
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impingitur, eſt veluti infinita reſiſtentia ratione huius motus; </
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<
s
id
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">cum verò
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globus in alium globum, quem mouet, impingitur, ſi vterque æqualis eſt; </
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<
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eſt etiam æqualis ceſſio reſiſtentiæ; </
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<
s
id
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">igitur globus impactus quieſcit, &
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hoc eſt iuſtum medium extremorum prædictorum, id eſt, inter nullam
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ceſſionem, & infinitam ceſſionem; </
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>
<
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id
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">media eſt æqualis ceſſio; </
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>
<
s
id
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N206C4
">& inter nul
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lam reſiſtentiam & infinitam reſiſtentiam media eſt æqualis reſiſtentia; </
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