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

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            <s xml:id="echoid-s1542" xml:space="preserve">
              <pb o="69" file="0081" n="81" rhead="ARCHIMEDES."/>
            mas eadem eſt differentia, propterea quod omnes grauitates in tabu-
              <lb/>
            la procedunt per æqualem exceſſum, vel defectum, vt inferius de-
              <lb/>
            monſtrabitur. </s>
            <s xml:id="echoid-s1543" xml:space="preserve">Inueniatur quoque differentia inter eandem gra-
              <lb/>
            uitatem proxime minorem & </s>
            <s xml:id="echoid-s1544" xml:space="preserve">inter grauitatem auri propoſiti quam
              <lb/>
            babet in aqua, quæ quidĕ eſt Gran. </s>
            <s xml:id="echoid-s1545" xml:space="preserve">7 {627/1767}, & </s>
            <s xml:id="echoid-s1546" xml:space="preserve">fiat vt 14 {1374/1767},
              <lb/>
            ad 1, ita 7 {637/1767}, ad alium numerum & </s>
            <s xml:id="echoid-s1547" xml:space="preserve">inuenietur bæc fractio
              <lb/>
            {1/2}, eademque adijcienda erit ad denominatorem 20, partium, vt
              <lb/>
            componatur totus denominator auripropoſiti partium 20 {1/2}, & </s>
            <s xml:id="echoid-s1548" xml:space="preserve">eo-
              <lb/>
            dem modo inueniendus erit denominator cuiuſcunq; </s>
            <s xml:id="echoid-s1549" xml:space="preserve">alterius auri,
              <lb/>
            cuius grauitas in aqua, in tabula non reperitur.</s>
            <s xml:id="echoid-s1550" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1551" xml:space="preserve">Ceterum qui volet contentus eſſe partibus vigeſimis quartis de-
              <lb/>
            nominatorum auri, is multo breuius aſſequetur quod quæritur, per
              <lb/>
            tabellam partis proportionalis. </s>
            <s xml:id="echoid-s1552" xml:space="preserve">illic enim vnico ingreſſu offendet
              <lb/>
            partem proportionalem, quam quærit, vt in eodem exemplo apparet,
              <lb/>
            in quo differentia grauitatum auri erat Gran. </s>
            <s xml:id="echoid-s1553" xml:space="preserve">7 {687/1767}, quæ in
              <lb/>
            tabella partis proportionalis babetur præcisè è regione particularum
              <lb/>
            12. </s>
            <s xml:id="echoid-s1554" xml:space="preserve">V nde concluditur, denominatorem auri propoſiti eſſe partium
              <lb/>
            20 {12/24}, vel quod idem es
              <unsure/>
            t partium 20 {1/2}, vt prius. </s>
            <s xml:id="echoid-s1555" xml:space="preserve">Quando vero
              <lb/>
            differentia grauitatum in tabella partis proportionalis non babetur
              <lb/>
            præcisè. </s>
            <s xml:id="echoid-s1556" xml:space="preserve">accipiatur alia ipſi propinquior & </s>
            <s xml:id="echoid-s1557" xml:space="preserve">particula illi in latere
              <unsure/>
              <lb/>
            reſpondens addatur denominatori auri ex primaria tabula extr a-
              <lb/>
            cti. </s>
            <s xml:id="echoid-s1558" xml:space="preserve">ſic enim ſaltem non errabitur in vna particula vigeſimaquarta
              <lb/>
            vnius partis denominatoris auri.</s>
            <s xml:id="echoid-s1559" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1560" xml:space="preserve">Denique ſi proponatur aurum non vnius libræ ſed vel plurium,
              <lb/>
            vel ſolum aliquot vnciarum. </s>
            <s xml:id="echoid-s1561" xml:space="preserve">R educenda erit eius grauitas quam
              <lb/>
            babet in aqua, ad grauitatem quam haberet ſi eßet vnius libræ, id
              <lb/>
            quod abſoluetur per proportionis ratiocinationem, ſi pro termino
              <lb/>
            primo ponatur vera grauitas auri propoſiti, pro ſecundo, e iuſdem
              <lb/>
            grauitas in aqua, & </s>
            <s xml:id="echoid-s1562" xml:space="preserve">pro tertio lib. </s>
            <s xml:id="echoid-s1563" xml:space="preserve">1, quartus enim terminus indic a-
              <lb/>
            bit grauitatem in aqua reſpondentem vni libræ auri propoſiti. </s>
            <s xml:id="echoid-s1564" xml:space="preserve">& </s>
            <s xml:id="echoid-s1565" xml:space="preserve">
              <lb/>
            bac inuenta reliqua expedientur vt prius.</s>
            <s xml:id="echoid-s1566" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1567" xml:space="preserve">Exemplum buius caſus bic non affero, quod per ſe res ſit clara.
              <lb/>
            </s>
            <s xml:id="echoid-s1568" xml:space="preserve">Sed illud tantum obiter aduertere placet, quod videtur pertinere. </s>
            <s xml:id="echoid-s1569" xml:space="preserve">
              <lb/>
            ad commodiorem vſum tabulæ, videlicet vt ijs in caſibus in quibus
              <lb/>
            neceßarius est calculus, fractiones granorum ommittantur quando
              <lb/>
            minus valent quam {1/2}, & </s>
            <s xml:id="echoid-s1570" xml:space="preserve">quando valent plus, eorum loco, addatur
              <lb/>
            vnum granum reliquis granis, & </s>
            <s xml:id="echoid-s1571" xml:space="preserve">ſi quando accidat binc procreari
              <lb/>
            grana 24. </s>
            <s xml:id="echoid-s1572" xml:space="preserve">tunc etiam grana ommittantur addita prius vnitate ad
              <lb/>
            ſcrupula in tabula inuenta. </s>
            <s xml:id="echoid-s1573" xml:space="preserve">bac enim ratione calculus erit expedi-
              <lb/>
            tior & </s>
            <s xml:id="echoid-s1574" xml:space="preserve">error qui binc oborietur erit inſenſibilis.</s>
            <s xml:id="echoid-s1575" xml:space="preserve"/>
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