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

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            <s xml:id="echoid-s1425" xml:space="preserve">
              <pb o="65" file="0077" n="77" rhead="ARCHIMEDES."/>
            manam qualitatis auri pronunciationem requiritur, vt ſupra mul-
              <lb/>
            tis oſtendimus, reuocanda erit ad partes vigeſimas quartas boc est
              <lb/>
            ad partes, qualium tota propoſita maſſa est 24, quod factu non est
              <lb/>
            difficile. </s>
            <s xml:id="echoid-s1426" xml:space="preserve">N am ſi fiat vt tota grauit as maſſæ propoſitæ 5301, algra-
              <lb/>
            uitatem auri puri 4638 {45/136}, vel vt 272, ad 238, cum vtrobique
              <lb/>
            eadem ſit ratio ita 24, ad a lium numerum. </s>
            <s xml:id="echoid-s1427" xml:space="preserve">proculdubio quartus nu-
              <lb/>
            merus proportionalis, erit ille qui quæritur. </s>
            <s xml:id="echoid-s1428" xml:space="preserve">Est autem bic quar-
              <lb/>
            tus numerus 21. </s>
            <s xml:id="echoid-s1429" xml:space="preserve">Quare aurum maſſæ propoſitæ appellabitur par-
              <lb/>
            tium 21.</s>
            <s xml:id="echoid-s1430" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1431" xml:space="preserve">Ex his igitur patet in inuenienda auri qualitate primum pro-
              <lb/>
            portionis terminum 272, & </s>
            <s xml:id="echoid-s1432" xml:space="preserve">ſecundum 5301, perpetuo manere eoſ-
              <lb/>
            dem, quia primus terminus est differentia inter grauitates primæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s1433" xml:space="preserve">tertiæ aquæ, quæ nunquam mutantur, nam illæ aquæ magnitu-
              <lb/>
            dine ſunt æquales altera auro puro, reliqua miſto ex argento & </s>
            <s xml:id="echoid-s1434" xml:space="preserve">ære,
              <lb/>
            quæ corpora aureum ſcilicet & </s>
            <s xml:id="echoid-s1435" xml:space="preserve">mistum ſemper ponuntur eiuſdem
              <lb/>
            grauitatis nempe 5301, Secundus vero terminus 5301, eſt grauit as
              <lb/>
            maſſæ propoſitæ, quæ ſi maior fuerit, vel minor, ad eam facile reuo-
              <lb/>
            cabitur. </s>
            <s xml:id="echoid-s1436" xml:space="preserve">V nde in posterum ſolum opus erit inuenire tertium pro-
              <lb/>
            portionis terminum, boc est differentiam inter grauitates ſecundæ
              <lb/>
            & </s>
            <s xml:id="echoid-s1437" xml:space="preserve">tertiæ aquæ.</s>
            <s xml:id="echoid-s1438" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1439" xml:space="preserve">Sed vt boc etiam exemplo illustretur, proponatur aliqua maſſa
              <lb/>
            auri, cuius inue ſtigãda ſit qualitas, & </s>
            <s xml:id="echoid-s1440" xml:space="preserve">ſit ipſius maſſæ grauitas qui-
              <lb/>
            dem in aere 837, in aqua vero 784, ergo * grauitas aquæ magnitu-
              <lb/>
              <note position="right" xlink:label="note-0077-01" xlink:href="note-0077-01a" xml:space="preserve">5. huins</note>
            dinem babentis æqualem propoſitæ maſſæ erit 53, differentia enim
              <lb/>
            inter primam, & </s>
            <s xml:id="echoid-s1441" xml:space="preserve">ſecundam grauitatem est 53.</s>
            <s xml:id="echoid-s1442" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1443" xml:space="preserve">Ad inueniendum igitur tertium proportionis terminum manen-
              <lb/>
            tibus primis duobus 272, 5301, bæc erit ratio. </s>
            <s xml:id="echoid-s1444" xml:space="preserve">Reuocetur primum
              <lb/>
            ptopoſitæ maſſæ grauitas 837, ad grauitatem 5301, boc est intelli-
              <lb/>
            gatur ipſa maſſa grauit atem babere 5301. </s>
            <s xml:id="echoid-s1445" xml:space="preserve">deinde fiat vt 837, ad 53,
              <lb/>
            grauitatem videlicet aquæ ipſi maſſæ æqualis, ita 5301, ad 335 {2/3},
              <lb/>
            ergo 335 {2/3}, erit grauitas aquæ magnitudinem babentis æqualem
              <lb/>
            aureæ maßæ, cuius grauitas 837, reuocata est ad grauitatem 5301;
              <lb/>
            </s>
            <s xml:id="echoid-s1446" xml:space="preserve">quare grauitas ſecundæ aquæ erit 335 {2/3}, & </s>
            <s xml:id="echoid-s1447" xml:space="preserve">conſequenter differen-
              <lb/>
              <note style="it" position="right" xlink:label="note-0077-02" xlink:href="note-0077-02a" xml:space="preserve">Grauitas primæ aquæ. # Grauitas ſecundæ aquæ. # Grauitas tertiæ aquæ.
                <lb/>
              279, # 335 {2/3}, # 551.</note>
            tia inter ipſam grauitatem ſecundæ aquæ & </s>
            <s xml:id="echoid-s1448" xml:space="preserve">grauitatem tertiæ 551,
              <lb/>
            erit 215 {1/3}, ſed ipſa differentia ponitur pro tertio proportionis ter-
              <lb/>
            mino; </s>
            <s xml:id="echoid-s1449" xml:space="preserve">ergo 215 {1/2}, erit quæſitus terminus, nempe proportionis </s>
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