Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
      <text>
        <front>
          <section>
            <pb xlink:href="026/01/021.jpg"/>
            <p id="N10B1B" type="main">
              <s id="N10B1D">4. Tantum eſt ab æqualitate prædicta ceſſionis, & reſiſtentiæ, ad
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              nullam ceſſionem, & notam reſiſtentiam, quantum eſt ad nullam
                <lb/>
                <expan abbr="reſiſtẽtiam">reſiſtentiam</expan>
              , & totam ceſſionem: </s>
              <s id="N10B28">hinc, cùm à tota ceſſione ad æqua­
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              litatem prædictam acquiratur tantùm noua determinato æqualis
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              priori; </s>
              <s id="N10B30">igitur ab eadem æqualitate ad nullam ceſſionem tantun­
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              dem acquiritur; </s>
              <s id="N10B36">igitur dupla prioris, vt iam ſuprà dictum eſt; </s>
              <s id="N10B3A">nulla
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              eſſet reſiſtentia in vacuo; nulla eſt ceſſio, cùm ipſum corpus refle­
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              ctens nullo modo mouetur ab ictu. </s>
            </p>
            <p id="N10B42" type="main">
              <s id="N10B44">5. Determinatio noua per lineam obliquam, eſt ad nouam per
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              lineam perpendicularem, vt ſinus rectus anguli incidentiæ, ad ſi­
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              num totum, in qualibet hypotheſi; </s>
              <s id="N10B4C">quia ſunt hæ, vt ictus, per vtran­
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              que lineam; </s>
              <s id="N10B52">ictus verò vt grauitationes in horizontale planum, &
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              in planum inclinatum, ſub angulo complementi anguli incidentiæ: </s>
              <s id="N10B58">
                <lb/>
              hinc noua determinatio per lineam obliquam, eſt vt dupla ſinus re­
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              cti anguli incidentiæ, ad ſinum totum: </s>
              <s id="N10B5F">hinc ſupra angulum inci­
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              dentiæ 30, noua eſt maior priore, infrà minor; in ipſo angulo 30.
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              æqualis, ſuppoſita hypotheſi plani reflectentis immobilis. </s>
            </p>
            <p id="N10B67" type="main">
              <s id="N10B69">6. Ex hoc poſitiuo principio demonſtratur accuratiſſimè æqua­
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              litas anguli reflexionis, & incidentiæ, quod certè demonſtratum
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              non fuit ab Ariſt. in problematis, ſect. 17. problem. 4. & 13. quibus
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              in locis fusè ſatis explicatur hoc Theorema, ducta comparatione,
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              tùm à grauibus, quæ cadunt, tùm ab orbibus, quæ rotantur, rùm à
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              ſpeculis: ſed minimè demonſtratur ex certis principiis ſine petitio­
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              ne principij. </s>
              <s id="N10B79">In puncto reflexionis, poſita hypotheſi plani immo­
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              bilis reflectentis, nulla datur quies; </s>
              <s id="N10B7F">quia vnum tantùm eſt conta­
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              ctus inſtans; ſed eo inſtanti eſt motus, quo primo acquiritur locus. </s>
            </p>
            <p id="N10B85" type="main">
              <s id="N10B87">7. Omnes lineæ reflexæ per ſe ſunt æqualis longitudinis, & ab
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              eodem puncto contactus, ad communem peripheriam terminan­
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              tur: </s>
              <s id="N10B8F">ſi globus impactus ſit æqualis reflectenti, ſitque linea inciden­
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              tiæ obliqua quælibet terminata ad idem punctum contactus, re­
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              flectitur prædictus globus per lineam tangentem globum refle­
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              ctentem in eodem puncto; </s>
              <s id="N10B99">quia hæc tangens eſt diagonalis com­
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              munis, & determinatio mixta communis omnibus lineis inciden­
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              tiæ: eſt tamen modò longior, modò breuior linea reflexa, éſtque vt
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              vt ſinus complementi anguli incidentiæ, ad ſinum totum, qui ſit
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              determinatio prior, vt facilè demonſtramus. </s>
            </p>
            <p id="N10BA5" type="main">
              <s id="N10BA7">8. Si globus impactus ſit minor corpore reflectente, reflectitur
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              etiam per ipſam perpendicularem, & determinatio noua eſt dupla­
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              prioris, minùs ratione globorum v. g. ſi globus impactus ſit ſubdu-</s>
            </p>
          </section>
        </front>
      </text>
    </archimedes>