Ghetaldi, Marino, Marini Ghetaldi Promotvs Archimedis sev de varijs corporum generibus grauitate & magnitudine comparatis

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              <pb o="56" file="0068" n="68" rhead="PROMOTVS"/>
            & </s>
            <s xml:id="echoid-s1093" xml:space="preserve">quanta auri. </s>
            <s xml:id="echoid-s1094" xml:space="preserve">Intellig antur duo corpora, vnum ex auro puro, al-
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            terum ex are, æque grauia atque corpus mistum, & </s>
            <s xml:id="echoid-s1095" xml:space="preserve">trium corporum
              <lb/>
            ex aqua, quorum vnum ſit æquale corpori aureo magnitudine, alte-
              <lb/>
            rum misto, tertium æreo, inueniantur grauitates, vt in exemplo pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s1096" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1097" xml:space="preserve">dictum est, quæ ſint 9, 11, & </s>
            <s xml:id="echoid-s1098" xml:space="preserve">19, & </s>
            <s xml:id="echoid-s1099" xml:space="preserve">fiat vt differentia inter 9, & </s>
            <s xml:id="echoid-s1100" xml:space="preserve">
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            19, ad 171, grauitatem videlicet corporis misti, ita differentia inter
              <lb/>
            9, & </s>
            <s xml:id="echoid-s1101" xml:space="preserve">11, ad 34 {1/5}, portio igitur corporis miſti ærea grauitatem babebit
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            34 {1/5}, quæ ſi auferatur ex totali corporis misti grauitate, remanebit
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            136 {4/5}, pro grauitate portionis auri.</s>
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            <s xml:id="echoid-s1103" xml:space="preserve">Vel ſi pro tertio proportionis termino ſumatur differentia inter 11,
              <lb/>
            & </s>
            <s xml:id="echoid-s1104" xml:space="preserve">19, quartus terminus 136 {4/6}, erit grauitas portionis auri, qua ab-
              <lb/>
            lata ex totali corporis miſti grauitate, reliquum 34 {1/5}, dabit grauita-
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            tem portionis æreæ.</s>
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          <p>
            <s xml:id="echoid-s1106" xml:space="preserve">At vero huiuſmodi ratio cinationem ad diſcernendum ar-
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            gentum ab auro, vel aliud metallum ab altero metallo, recte
              <lb/>
            eſſe inſtitutam, ſequenti Theoremate demonſtrabitur.</s>
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          <head xml:id="echoid-head45" xml:space="preserve">THEOREMA X. PROPOS. XIX.</head>
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            <s xml:id="echoid-s1108" xml:space="preserve">SI trium corporum æque grauium primum & </s>
            <s xml:id="echoid-s1109" xml:space="preserve">ter-
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            tium fuerint generis diuerſi, ſecundi autem portio
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            fuerit eiuſdem generis cum corpore primo, reliqua ve-
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            ro eiuſdem generis cum corpore tertio, fuerint etiam
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            tres quantitates aquæ prædictis corporibus æquales, pri-
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            ma videlicet corpori primo, ſecunda ſecundo, & </s>
            <s xml:id="echoid-s1110" xml:space="preserve">tertia
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            tertio. </s>
            <s xml:id="echoid-s1111" xml:space="preserve">erit vt differentia grauitatum primæ & </s>
            <s xml:id="echoid-s1112" xml:space="preserve">tertiæ
              <lb/>
            quantitatis aquæ, ad grauitatem corporis ſecundi, ita
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            differentia grauitatum primæ & </s>
            <s xml:id="echoid-s1113" xml:space="preserve">ſecundæ quantitatis
              <lb/>
            aquæ, ad grauitatem portionis corporis ſecundi, quæ eſt
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            eiuſdem generis cum corpore tertio.</s>
            <s xml:id="echoid-s1114" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s1115" xml:space="preserve">Et ita differentia grauitatum ſecundæ & </s>
            <s xml:id="echoid-s1116" xml:space="preserve">tertiæ quan
              <lb/>
            titatis aquæ, ad grauitatem portionis eiuſdem generis
              <lb/>
            cum corpore primo.</s>
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