Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="063/01/015.jpg"/>
              hypomochlium. </s>
              <s>Differre enim à ſe conſtat ex eo, quòd hæc
                <lb/>
              augeri poteſt infinitè, nihilo auctâ illâ. </s>
              <s>
                <expan abbr="Neq;">Neque</expan>
              enim velociùs de­
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              ſcendit vectis ob remotionem ponderis à lineâ hypomochlij:
                <lb/>
                <expan abbr="neq;">neque</expan>
              ſi alià trutinâ explores in quouis ſitu, magis ponderabit. </s>
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              <s>Propterea quòd hic impulſus hypomochlium, non verò mun­
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              di centrum reſpicit, quantumuis ab eadem grauitate oriatur.
                <lb/>
                <expan abbr="Atq;">Atque</expan>
              hunc impulſum augeri in eà ratione, quam vectis obtinet,
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              demonſtrat Archimedes in lib. de æquiponderantibus. </s>
              <s>Alio
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              modo Grauitas, ſeu impulſus in ordine ad motum expenditur
                <lb/>
              abſolutè,
                <expan abbr="abſq;">abſque</expan>
              ullo reſpectu ad hypomochlium: & tum
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              rationem quadrati habere dicimus; cuius latera ſint duratio
                <lb/>
              motûs. </s>
              <s>Nam cùm in aliquo tempore produci ſit neceſſe,
                <expan abbr="atq;">atque</expan>
                <lb/>
              eo modo augeatur, quo triangulum ſibi ſimile manens, per po­
                <lb/>
              ſit. quintam; habebit impulſus hic ad illum, rationem eius,
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              quam habent tempora, duplicatam. per propoſ. 12. </s>
            </p>
            <p type="main">
              <s>Aduerte ſecundo, duobus modis fieri contactum mobi­
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              lis & plani: vno modo, cùm incidit plano: alio modo, cùm la­
                <lb/>
              bitur per ipſum. </s>
              <s>
                <expan abbr="Neq;">Neque</expan>
              eadem ratio
                <expan abbr="utrobiq;">utrobique</expan>
              . </s>
              <s>Nam cùm labi­
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              tur, & labendo tangit planum, eodem modo videtur ſe habe­
                <lb/>
              re ad hypomochlium,
                <expan abbr="eandémq;">eandémque</expan>
              diſtantiam obtinere centrum
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              grauitatis: Manet ergo ratio partis motæ ad quieſcentem,
                <expan abbr="quã">quam</expan>
                <lb/>
              linea hypomochlii à principio induxit. </s>
              <s>At verò cùm incidit
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              eidem plano, plagam infert, & recipit: vnde reflecti contin­
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              git. </s>
              <s>Oſtenſum verò prop: 37-Plagam in aliquo tempore
                <lb/>
              fieri: à Plaga verò impulſum exſolui. quam ergo rationem
                <lb/>
              habet mora plagæ iam perfectæ ad aliam moram plagæ nec­
                <lb/>
              dum perfectæ, candem habet impulſus totus ad illum duplica.
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              tum. </s>
              <s>Igitur in caſu verticali, quia hypomochlium occurrit
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              centro,
                <expan abbr="neq;">neque</expan>
              percuſſioni cedit, plagam inducit
                <expan abbr="perfectã">perfectam</expan>
              ,
                <expan abbr="totũq">totunq</expan>
              ,
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              impulſum exſoluit. & cùm æqualem à percuſſo recipiat plaga,
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              eadem, quâ incidit, viâ retro agitur. </s>
              <s>In occurſu autem plani </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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