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

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            <s xml:id="echoid-s1399" xml:space="preserve">
              <pb o="64" file="0076" n="76" rhead="PROMOTVS"/>
              <note style="it" position="right" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve">I. # II. # III. # IIII.
                <lb/>
              1 {1227/5301}, # 24, # 1 {139/5301}, # 20,</note>
            erit denominator qualitatis auri de qua quæritur quia ille termi-
              <lb/>
            nus indicat partes auri puri in grauitate, qualibus maſſa propoſita
              <lb/>
            constat 24. </s>
            <s xml:id="echoid-s1400" xml:space="preserve">Hoc autem demonstratum eſt prop. </s>
            <s xml:id="echoid-s1401" xml:space="preserve">19, buius.</s>
            <s xml:id="echoid-s1402" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1403" xml:space="preserve">Et quia in propoſito exemplo bæ partes, nempe vnc. </s>
            <s xml:id="echoid-s1404" xml:space="preserve">20, ſunt par-
              <lb/>
            tes vigeſimæ quartæ 24, vnciarum, quæ constituunt grauitatem to-
              <lb/>
            tius maſſæ. </s>
            <s xml:id="echoid-s1405" xml:space="preserve">binc fit quod eædem 20, vnc. </s>
            <s xml:id="echoid-s1406" xml:space="preserve">immediate denominent au-
              <lb/>
            rum propoſitum eße 20, partium. </s>
            <s xml:id="echoid-s1407" xml:space="preserve">Quando vero grauitas totius maſ-
              <lb/>
            ſæ non exprimitur per numerum 24, tunc opus erit inquirere quot
              <lb/>
            partes vigeſimas quartas totius grauitatis efficiat quartus ille pro-
              <lb/>
            portionis terminus vt in ſequenti exemplo clarius apparebit.</s>
            <s xml:id="echoid-s1408" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1409" xml:space="preserve">Sit enim propoſita alia auri maſſa cuius grauitas in aere ſit 5301
              <lb/>
            in aqua vero 4988, ſi igitur bic numerus ſubtrabatur ex numero to
              <lb/>
              <note position="left" xlink:label="note-0076-02" xlink:href="note-0076-02a" xml:space="preserve">5. buius</note>
            tius grauitatis 5301, rcliqaus numerus 313,
              <emph style="sub">*</emph>
            erit grauitas aquæ
              <lb/>
            propoſitæ maſſæ magnitudine æqualis. </s>
            <s xml:id="echoid-s1410" xml:space="preserve">Inueniantur quoq; </s>
            <s xml:id="echoid-s1411" xml:space="preserve">duæ aliæ
              <lb/>
            grauitates aquæ, vnare ſpondentis auro puro magnitudine, altera.
              <lb/>
            </s>
            <s xml:id="echoid-s1412" xml:space="preserve">corpori miſto ex argento & </s>
            <s xml:id="echoid-s1413" xml:space="preserve">ære, ita tamen vt grauitas tum auri pu-
              <lb/>
            ri, tum corporis misti ſit eadem quæ maſſæpropoſitæ, non ſecus ac in
              <lb/>
            præcedenti exemplo factitatum est. </s>
            <s xml:id="echoid-s1414" xml:space="preserve">boc eſt primo fiat vt 19, ad 1, ita
              <lb/>
            5301, ad 279, bic enim numerus erit grauitas aquæ magnitudinem
              <lb/>
            babentis æqualem auro puro, cuius grauitas eſt 5301. </s>
            <s xml:id="echoid-s1415" xml:space="preserve">Deinde fiat
              <lb/>
            vt 279, ad 29, ita rurſum grauitas 5301, ad aliam, bac enim ratione
              <lb/>
            producetur numerus 551, debitus grauitati aquæ, magnitudine,
              <lb/>
            æqualis corpori miſto ex argento & </s>
            <s xml:id="echoid-s1416" xml:space="preserve">ære, grauitatem babenti eandem
              <lb/>
            cum eadem maßa propoſita. </s>
            <s xml:id="echoid-s1417" xml:space="preserve">Atque bæ tres grauitates aquæ ſcriban-
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            tur eo ordine quoſupra; </s>
            <s xml:id="echoid-s1418" xml:space="preserve">inuentiſque differentijs inter primam & </s>
            <s xml:id="echoid-s1419" xml:space="preserve">
              <lb/>
              <note style="it" position="right" xlink:label="note-0076-03" xlink:href="note-0076-03a" xml:space="preserve">Grauitas aqu & magnitu- \\ dine & qualis auro puro. # Grauitas agua & qualis \\ maſlæ propoſita. # Grauitas aquæ æqualis \\ corpori miſto.
                <lb/>
              279 # 313 # 551</note>
            tertiam, nec non inter ſecundam & </s>
            <s xml:id="echoid-s1420" xml:space="preserve">tertiam, quæ ſunt 272, 238; </s>
            <s xml:id="echoid-s1421" xml:space="preserve">sta-
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            tuatur pro primo proportionis termino prior differentia 272, & </s>
            <s xml:id="echoid-s1422" xml:space="preserve">pro
              <lb/>
            tertio posterior 238. </s>
            <s xml:id="echoid-s1423" xml:space="preserve">grauitas vero maſſæ propoſitæ 5301, ponatur
              <lb/>
            pro ſecundo termino, & </s>
            <s xml:id="echoid-s1424" xml:space="preserve">quæratur terminus quartus, qui inpræ-
              <lb/>
              <note style="it" position="right" xlink:label="note-0076-04" xlink:href="note-0076-04a" xml:space="preserve">I. # II. # III. # IIII.
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              272, # 5301, # 238, # 4638 {51/136}.</note>
            ſenti exemplo eſt 4638 {51/136}, is
              <emph style="sub">*</emph>
            enim indicabit grauitatem auri
              <lb/>
              <note position="left" xlink:label="note-0076-05" xlink:href="note-0076-05a" xml:space="preserve">19.
                <lb/>
              buius.</note>
            puriin maſſa propoſita. </s>
            <s xml:id="echoid-s1425" xml:space="preserve">Sed quoniam bæc grauitas non est expreſ-
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            ſa in partibus vigeſimis quartis totius grauitatis, id quod ad </s>
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