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

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            <p type="main">
              <s>
                <pb xlink:href="063/01/059.jpg"/>
              Had ABCD. </s>
              <s>Hoc eſt permutando ut AF ad H, ita FE ad
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              ABCD. </s>
              <s>Quòd ſi
                <expan abbr="itaq;">itaque</expan>
              fiat ut FE ad AF, ita ABCD ad aliud
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              quadratum: inventum erit circulo H æquale quadratum. </s>
            </p>
            <p type="main">
              <s>Quòd ſi ex illâ plagâ moveatur E per lineam parallelam GK:
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              erit per Lemma 2. minor proportio AF ad H, quàm FE ad
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              ABCD:
                <expan abbr="Atq;">Atque</expan>
              huius motus velocior motu circuli. eandem er
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              gò plagam recipit quadratum ABCD, quam infert circulo:
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              ac proinde illius impulſus à percuſſione erit æqualis AE: com
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              poſitus nimirum ex plagâ reciprocâ AF & impulſu reſiduo FE. </s>
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              <s>Supponamus verò AE ad AF eſſe ut 6 ad 2, hoc eſt in ratione
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              triplâ: ſpatium verò decurſum ab E ad ſpatium decurſum ab H
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              ut 3 ad 2. </s>
              <s>Quòd ſi
                <expan abbr="itaq;">itaque</expan>
              circulus H accipiat impulſum ut 3. hoc
                <lb/>
              eſt additâ ſemiſſe, movebitur ad idem intervallum cumquadra­
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              to ABCD. </s>
              <s>Et ſi fiat ut 6 ad 3, ita ABCD ad aliud, inventum
                <lb/>
              erit quadratum circulo H æquale. </s>
            </p>
            <p type="main">
              <s>Demum ſi motus quadrati E à percuſſione fiat parallelus li
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              neæ mediæ inter tangentem GB, & perpen dicularem GH; erit
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              per Lemma 3 maior proportio AF ad H, quàm FE ad ABCD:
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              & motus H velocior motu ABCD. </s>
              <s>Ponamus
                <expan abbr="itaq;">itaque</expan>
              interval­
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              lum motûs Had interuallum motûs ABCD in ſeſqui alterâ
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              ratione, hoc eſt ut 3 ad 2: FE autem ad AF ut 4 ad 2. </s>
              <s>Quòdſi
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                <expan abbr="itaq;">itaque</expan>
              quadratum ABCD accipiat impulſum ut 6; movebitur
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              eadem velocitate, & ad idem intervallum cum circulo H per
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              poſit. 5. propterea quòd impulſus eandem rationem habeat ad
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              ſuum mobile, per corollarium 2. 1 Axiomatis. </s>
              <s>Et ſi fiat ut 6
                <lb/>
              ad 2, ita quadratum ABCD ad aliud quadratum, inventum
                <lb/>
              erit circulo H æquale quadratum. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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