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

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              <pb o="71" file="0083" n="83" rhead="ARCHIMEDES"/>
            pertracto, video grauitates illas, quæ in eius area deſcriptæ ſunt ne-
              <lb/>
            ceſſario eadem differentia procedere, ſicut & </s>
            <s xml:id="echoid-s1617" xml:space="preserve">denominatores quali-
              <lb/>
            tatum eadem differentia procedunt; </s>
            <s xml:id="echoid-s1618" xml:space="preserve">atque adeo differentiam illam
              <lb/>
            eſſe eam, qua grauitas ſemiunciæ auri puri in aqua ſuperat in aqua
              <lb/>
            grauitatĕ ſemiunciæ miſti, quæ quidĕ differentia eſt Gra. </s>
            <s xml:id="echoid-s1619" xml:space="preserve">14 {1374/1767}.
              <lb/>
            </s>
            <s xml:id="echoid-s1620" xml:space="preserve">Conſiderentur enim quæcunque duæ grauitates proximæ in tabula
              <lb/>
            expreßæ, vt exemp. </s>
            <s xml:id="echoid-s1621" xml:space="preserve">gratia, grauitates auri 20, & </s>
            <s xml:id="echoid-s1622" xml:space="preserve">19, partium. </s>
            <s xml:id="echoid-s1623" xml:space="preserve">Quo-
              <lb/>
            niam igitur in auro 20, partium ſunt auri puri 20. </s>
            <s xml:id="echoid-s1624" xml:space="preserve">ſemiuneiæ, misti
              <lb/>
            vero 4, & </s>
            <s xml:id="echoid-s1625" xml:space="preserve">in auro 19, partium ſunt' auri puri 19. </s>
            <s xml:id="echoid-s1626" xml:space="preserve">ſemiunciæ, misti
              <lb/>
            vero 5, erit in auro 20,
              <unsure/>
            partiũ vna ſemiuncia auri puri pluſquam in
              <lb/>
            auro 19, partium, in auro autem 19, partium erit vna ſemiuncia
              <lb/>
            misti plus quam in auro 20, partium; </s>
            <s xml:id="echoid-s1627" xml:space="preserve">quare grauitas auri 20, par-
              <lb/>
            tium in aqua ſuperabit in aqua grauitatem auri 19, partium gra-
              <lb/>
            uitate, qua ſemiuncia auri puri ſuperat ſemiunciam miſti. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">Quod
              <lb/>
            erat demonſtrandum. </s>
            <s xml:id="echoid-s1629" xml:space="preserve">Et eadem est ratio de alijs gr auitatibus, non
              <lb/>
            ſolum quæ in bac tabula deſcribuntur, ſed etiam de illis, quæ deſeri-
              <lb/>
            bentur in alijs, copioſioribus, in quibus videlicet denominatores non
              <lb/>
            eſſent partes integræ, ſed partes partium; </s>
            <s xml:id="echoid-s1630" xml:space="preserve">dummodo etiam illæ partes
              <lb/>
            per vnam eandemque differentiam progrederentur.</s>
            <s xml:id="echoid-s1631" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1632" xml:space="preserve">Quibus in bunc modum præ ostenſis. </s>
            <s xml:id="echoid-s1633" xml:space="preserve">ſi construenda fuerit tabula
              <lb/>
            per continuam additionem eiuſdem numeri, ſic erit progrediendum.
              <lb/>
            </s>
            <s xml:id="echoid-s1634" xml:space="preserve">Primo inuenienda erit grauitas quam babet ſemiuncia auri puri in
              <lb/>
            aqua, quæ inuenietur ſi fiat vt 19, ad 18, it a ſemiuncia ad alium
              <lb/>
            numerum qui ſit vnc. </s>
            <s xml:id="echoid-s1635" xml:space="preserve">{9/19}, is enim dabit grauitatem quæſitam, quæ
              <lb/>
            valet ſcrup. </s>
            <s xml:id="echoid-s1636" xml:space="preserve">11, Gran. </s>
            <s xml:id="echoid-s1637" xml:space="preserve">8 {16/19}.</s>
            <s xml:id="echoid-s1638" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1639" xml:space="preserve">Secundo quærenda est grauitas ſ
              <unsure/>
            emiuncie misti in aqua, quæ ba-
              <lb/>
            bebitur fi fiat vt 279, ad 250, it a ſemiuncia, ad alium numerum, qui
              <lb/>
            ſit vnc. </s>
            <s xml:id="echoid-s1640" xml:space="preserve">{125/279}, is enim dabit grauitatem quæſitam, quæ reducta ad
              <lb/>
            ſcrupula, & </s>
            <s xml:id="echoid-s1641" xml:space="preserve">grana valet ſcrup. </s>
            <s xml:id="echoid-s1642" xml:space="preserve">10, Gran. </s>
            <s xml:id="echoid-s1643" xml:space="preserve">18 {2/3}.</s>
            <s xml:id="echoid-s1644" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1645" xml:space="preserve">Tertio exploranda est differentia inter duas grauitates proximè
              <lb/>
            inuentas, quam per ſubtractionem inuenies Gran. </s>
            <s xml:id="echoid-s1646" xml:space="preserve">14 {458/589}, cuius
              <lb/>
            tamen fractio reducta eſt ad partes 1767, nempe ad {1374/1767}, propter
              <lb/>
            tabellam partis proportionalis.</s>
            <s xml:id="echoid-s1647" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1648" xml:space="preserve">Postremo inuestig anda erit grauitas in aqua vnius libræ misti,
              <lb/>
            quæ inuenietur ſi grauitas ſecundo loco reperta per 24, multiplice-
              <lb/>
            tur, productus enim numerus vnc. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">10, ſcrup. </s>
            <s xml:id="echoid-s1650" xml:space="preserve">18, Gran. </s>
            <s xml:id="echoid-s1651" xml:space="preserve">{969/1767}, da
              <lb/>
            bit quæſitam grauitatem. </s>
            <s xml:id="echoid-s1652" xml:space="preserve">Qua in calce tabulæ deſcripta, compo-
              <lb/>
            nentur reliquæ grauitates omnes per continuam additionem diffe-
              <lb/>
            rentiæ tertio loco inuentæ. </s>
            <s xml:id="echoid-s1653" xml:space="preserve">Si enim addatur ad grauitatem auri
              <lb/>
            partis o, idest ad grauitatem misti vnius libræ in aqua, </s>
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