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

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            <s xml:id="echoid-s1050" xml:space="preserve">
              <pb o="55" file="0067" n="67" rhead="ARCHIMEDES."/>
            dictum eſt in propoſitionis octauæ exemplo, non enim neceſſe eſt ha-
              <lb/>
            bere duo corpora ex auro & </s>
            <s xml:id="echoid-s1051" xml:space="preserve">argento, grauitatem habentia eandem
              <lb/>
            quam & </s>
            <s xml:id="echoid-s1052" xml:space="preserve">corona, & </s>
            <s xml:id="echoid-s1053" xml:space="preserve">hac de cauſa diximus ſupra intelligãtur duo cor-
              <lb/>
            pora, non autem accipiantur. </s>
            <s xml:id="echoid-s1054" xml:space="preserve">ſit igitur primi corporis aquei æqualis
              <lb/>
            aureo A, inuenta grauitas G, ſecundi vero æqualis coronæ B, graui-
              <lb/>
            tas F, & </s>
            <s xml:id="echoid-s1055" xml:space="preserve">tertij æqualis corpori argenteo D, grauitas H, & </s>
            <s xml:id="echoid-s1056" xml:space="preserve">fiat vt dif-
              <lb/>
            ferentia inter G, & </s>
            <s xml:id="echoid-s1057" xml:space="preserve">H, ad EK, ita differentia inter G, & </s>
            <s xml:id="echoid-s1058" xml:space="preserve">F, ad aliam-,
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            grauitatem, quæ ſit K. </s>
            <s xml:id="echoid-s1059" xml:space="preserve">Dico K, grauitatem eſſe portionis argenti,
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            quod eſt in corona, E vero grauitatem auri.</s>
            <s xml:id="echoid-s1060" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1061" xml:space="preserve">Vel ſi pro tertio proportionis termino ſumatur differentia inter F,
              <lb/>
            & </s>
            <s xml:id="echoid-s1062" xml:space="preserve">H, & </s>
            <s xml:id="echoid-s1063" xml:space="preserve">quartus terminus ſit E, Dico E, grauitatem eſſe portionis au-
              <lb/>
            ri, K vero argenti.</s>
            <s xml:id="echoid-s1064" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1065" xml:space="preserve">Quartus autem vtriuſque proportionis terminus * minor eſt ſe-
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">14. 5.
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              Elem.</note>
            cundo EK, quod & </s>
            <s xml:id="echoid-s1066" xml:space="preserve">tertius minor eſt primo, primus enim terminus
              <lb/>
            eſt differentia inter G, & </s>
            <s xml:id="echoid-s1067" xml:space="preserve">H, tertius vero, vel eſt differentia inter G, & </s>
            <s xml:id="echoid-s1068" xml:space="preserve">
              <lb/>
            F, vel differentia inter F, & </s>
            <s xml:id="echoid-s1069" xml:space="preserve">H, vter que minor primo. </s>
            <s xml:id="echoid-s1070" xml:space="preserve">Exemplis autem
              <lb/>
            res fiet illuſtrior.</s>
            <s xml:id="echoid-s1071" xml:space="preserve"/>
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          <head xml:id="echoid-head43" xml:space="preserve">Exemplum. I.</head>
          <p style="it">
            <s xml:id="echoid-s1072" xml:space="preserve">Sit coronæ grauitas 95, lib. </s>
            <s xml:id="echoid-s1073" xml:space="preserve">& </s>
            <s xml:id="echoid-s1074" xml:space="preserve">oporteat facere quod imperatum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s1075" xml:space="preserve">Intellig antur duo corpora, vnum aureum, alterum argenteum, æque
              <lb/>
            grauia atque corona, deinde trium corporum ex aqua, magnitudine
              <lb/>
            æqualium, aureo ſcilicet corpori vnum, alterum coronæ, tertium cor-
              <lb/>
            pori argenteo, inueniantur grauitates, vt in exemplo prop. </s>
            <s xml:id="echoid-s1076" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1077" xml:space="preserve">dictum
              <lb/>
            est, quæ ſint primi nimirum corporis aquei @, ſecundi vero 6, & </s>
            <s xml:id="echoid-s1078" xml:space="preserve">terty
              <lb/>
            9 {8/31}, & </s>
            <s xml:id="echoid-s1079" xml:space="preserve">fiat vt differentia inter 5, & </s>
            <s xml:id="echoid-s1080" xml:space="preserve">9 {6/31}, boc eſt vt 4 {6/31}, ad 95,
              <lb/>
            grauitatem videlicet coronæ, ita differentia inter 5, & </s>
            <s xml:id="echoid-s1081" xml:space="preserve">6, boc est 1, ad
              <lb/>
            22 {17/26}, ergo 22 {17/26}, erit grauitas portionis argenti quod est in coro-
              <lb/>
            na, qua detracta ex totali grauitate coronæ, reliquum 72 {9/26}, erit
              <lb/>
            grauitas portionis auri.</s>
            <s xml:id="echoid-s1082" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1083" xml:space="preserve">Vel ſi pro tertio proportionis termino ſumatur differentia inter 6,
              <lb/>
            & </s>
            <s xml:id="echoid-s1084" xml:space="preserve">9 {6/31}, quæ eſt 3 {6/31}, quartus terminus 72 {9/26}, erit grauitas por-
              <lb/>
            tionis auri, quæ ſi dematur ex totali grauitate coronæ, remanebit
              <lb/>
            22 {17/26}, pro grauitate portionis argenti.</s>
            <s xml:id="echoid-s1085" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div72" type="section" level="1" n="41">
          <head xml:id="echoid-head44" xml:space="preserve">Exemplum. II.</head>
          <p style="it">
            <s xml:id="echoid-s1086" xml:space="preserve">Sit aliquod corpus mistum ex auro. </s>
            <s xml:id="echoid-s1087" xml:space="preserve">& </s>
            <s xml:id="echoid-s1088" xml:space="preserve">ære, & </s>
            <s xml:id="echoid-s1089" xml:space="preserve">babeat grauitatem
              <lb/>
            171. </s>
            <s xml:id="echoid-s1090" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1091" xml:space="preserve">& </s>
            <s xml:id="echoid-s1092" xml:space="preserve">oporteat inuenire quanta erit portio æris in ipſo </s>
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