Fabri, Honoré, Tractatus physicus de motu locali, 1646

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            <pb pagenum="257" xlink:href="026/01/291.jpg"/>
            <p id="N205C9" type="main">
              <s id="N205CB">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              65.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N205D7" type="main">
              <s id="N205D9">
                <emph type="italics"/>
              Si globus minor in maiorem impingatur per lineam obliquam incidentiæ,
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              ſemper reflectitur
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              ; </s>
              <s id="N205E4">quippè ſit determinatio mixta ex priore, & noua, quæ
                <lb/>
              determinari poteſt, ſi aliquid à nouæ figuræ deſcribatur; </s>
              <s id="N205EA">ſit circulus
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              FQCD; </s>
              <s id="N205F0">ſint diametri QD, FC; </s>
              <s id="N205F4">ſit AI dupla AF, ſitque determi­
                <lb/>
              natio prior vt FA, ſi ſecunda ſit vt AI, erit dupla prioris; </s>
              <s id="N205FA">igitur corpus
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              reflectens erit immobile; </s>
              <s id="N20600">igitur ſi linea incidentiæ ſit EA, reflexa erit
                <lb/>
              AT, ita vt anguli TAF, EAF ſint æquales; </s>
              <s id="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="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; </s>
              <s id="N2061A">de­
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              ſcribatur circulus KMNR, ſit linea quælibet incidentiæ obliqua EA; </s>
              <s id="N20620">
                <lb/>
              producatur in B; </s>
              <s id="N20625">ducantur OX BT parallelæ AH; </s>
              <s id="N20629">aſſumatur AG æqua­
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              lis OX, & GS æqualis AB; </s>
              <s id="N2062F">certè BS erit æqualis OX vel AG; </s>
              <s id="N20633">duca­
                <lb/>
              tur AS, hæc erit reflexa quæſita: </s>
              <s id="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. </s>
            </p>
            <p id="N20641" type="main">
              <s id="N20643">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              66.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2064F" type="main">
              <s id="N20651">
                <emph type="italics"/>
              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.
                <emph.end type="italics"/>
              132. lib.1. in qua verò proportione retardetur
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              motus non ita facilè dictu eſt; dici tamen poteſt & explicari in fig. </s>
              <s id="N20660">Th.
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              63. ſi enim globi ſunt æquales, ceſſio æqualis eſt impulſioni; </s>
              <s id="N20667">ſi globus
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              impactus ſit maior, ceſſio eſt maior impulſione, vt conſtat; </s>
              <s id="N2066D">igitur, ſi globus
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              eſt ad globum vt FB ad FB; </s>
              <s id="N20673">determinatio noua erit ad priorem vt FB
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              ad FB; </s>
              <s id="N20679">igitur quieſcet globus impactus per Th. 62. ſi verò globus impa­
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              ctus ſit ad alium vt EB ad ER; </s>
              <s id="N2067F">determinatio noua erit ad priorem, vt
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              BG ad BF; </s>
              <s id="N20685">igitur motus retardatus globi impacti eſt ad non retardatum
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              vt FG ad FB; </s>
              <s id="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; </s>
              <s id="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
                <lb/>
              globus reſiſtens; neque res aliter eſſe poteſt. </s>
            </p>
            <p id="N20699" type="main">
              <s id="N2069B">Hinc vides duos terminos oppoſitos, qui ſunt, nulla reſiſtentia, & infi­
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              nita reſiſtentia; </s>
              <s id="N206A1">nulla eſt reſiſtentia, cum globus impactus in nullum in­
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              cidit, ſed eſt veluti infinita ceſſio; </s>
              <s id="N206A7">cum verò globus in corpus immobile
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              impingitur, eſt veluti infinita reſiſtentia ratione huius motus; </s>
              <s id="N206AD">cum verò
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              globus in alium globum, quem mouet, impingitur, ſi vterque æqualis eſt; </s>
              <s id="N206B3">
                <lb/>
              eſt etiam æqualis ceſſio reſiſtentiæ; </s>
              <s id="N206B8">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; </s>
              <s id="N206C0">media eſt æqualis ceſſio; </s>
              <s id="N206C4">& inter nul­
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              lam reſiſtentiam & infinitam reſiſtentiam media eſt æqualis reſiſtentia; </s>
              <s id="N206CA"/>
            </p>
          </chap>
        </body>
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    </archimedes>
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