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

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            <s xml:id="echoid-s1118" xml:space="preserve">SINT tria corpora æque grauia A, BC, D, quorum A, primum,
              <lb/>
            & </s>
            <s xml:id="echoid-s1119" xml:space="preserve">tertium D. </s>
            <s xml:id="echoid-s1120" xml:space="preserve">ſint generis diuerſi, portio vero ſecundi B, ſit eiuſdem
              <lb/>
            generis cum corpore A. </s>
            <s xml:id="echoid-s1121" xml:space="preserve">& </s>
            <s xml:id="echoid-s1122" xml:space="preserve">portio C, eiuſdem generis cum corpore
              <lb/>
              <figure xlink:label="fig-0069-01" xlink:href="fig-0069-01a" number="22">
                <image file="0069-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0069-01"/>
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            D, ſint etiam alia tria
              <lb/>
            corpora aquea P, OL,
              <lb/>
            & </s>
            <s xml:id="echoid-s1123" xml:space="preserve">Q, quorũ P, ſit æqua-
              <lb/>
            le corpori A, magnitu-
              <lb/>
            dine, ipſum vero OL,
              <lb/>
            æquale corpori BC, & </s>
            <s xml:id="echoid-s1124" xml:space="preserve">
              <lb/>
            ipſum Q, æquale cor-
              <lb/>
            pori D, & </s>
            <s xml:id="echoid-s1125" xml:space="preserve">ſint earum
              <lb/>
            grauitates, G, ipſius P,
              <lb/>
            & </s>
            <s xml:id="echoid-s1126" xml:space="preserve">FV, ipſius OL, & </s>
            <s xml:id="echoid-s1127" xml:space="preserve">H,
              <lb/>
            ipſius Q. </s>
            <s xml:id="echoid-s1128" xml:space="preserve">Dico vt diffe-
              <lb/>
            rentia grauitatum G,
              <lb/>
            H, ad grauitatem cor-
              <lb/>
            poris BC, ita eſſe diffe-
              <lb/>
            rentiam grauitatum
              <lb/>
            G, FV, ad grauitatem
              <lb/>
            portionis C; </s>
            <s xml:id="echoid-s1129" xml:space="preserve">& </s>
            <s xml:id="echoid-s1130" xml:space="preserve">ita differentiam grauitatum FV, H, ad portionis B,
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            grauitatem. </s>
            <s xml:id="echoid-s1131" xml:space="preserve">Sit enim portionis B, grauitas E, & </s>
            <s xml:id="echoid-s1132" xml:space="preserve">portionis C, gra-
              <lb/>
            uitas K; </s>
            <s xml:id="echoid-s1133" xml:space="preserve">ergo totius corporis BC, grauitas erit EK, ſitq; </s>
            <s xml:id="echoid-s1134" xml:space="preserve">portionis O,
              <lb/>
            quæ ſit æqualis portioni B, grauitas F, ergo reliquæ portionis L,
              <lb/>
            æqualis portioni C, grauitas erit V, Quoniam igitur eſt, vt A, ad P,
              <lb/>
            ita B, ad O, æquale videlicet ad æquale, erit permutando, vt A, ad B,
              <lb/>
            ita p. </s>
            <s xml:id="echoid-s1135" xml:space="preserve">ad O, & </s>
            <s xml:id="echoid-s1136" xml:space="preserve">quoniam ſunt eiuſdem generis A, B, ſimiliter & </s>
            <s xml:id="echoid-s1137" xml:space="preserve">P, O,
              <lb/>
            * erit vt grauitas corporis A, hoc eſt vt EK, (ponuntur enim cor-
              <lb/>
              <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">4. huius</note>
            pora A, BC, D, æque grauia,) ad E, ita G, ad F, quod igitur fit ex EK,
              <lb/>
            & </s>
            <s xml:id="echoid-s1138" xml:space="preserve">F, nempe ex extremis, æquale erit ei, quod fit ex E, & </s>
            <s xml:id="echoid-s1139" xml:space="preserve">G, hoc eſt
              <lb/>
            ex medijs.</s>
            <s xml:id="echoid-s1140" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1141" xml:space="preserve">Similiter quoniam eſt, vt D, ad Q, ita C, ad L, æquale videlicet ad
              <lb/>
            æquale, erit permutando, vt D, ad C, ita Q, ad L, & </s>
            <s xml:id="echoid-s1142" xml:space="preserve">quoniam ſunt
              <lb/>
            eiuſdem generis D, C, ſimiliter & </s>
            <s xml:id="echoid-s1143" xml:space="preserve">Q, L, * erit vt grauitas ipſius D,
              <lb/>
              <note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">4. huius</note>
            hoc eſt vt EK, ad K, ita H, ad V; </s>
            <s xml:id="echoid-s1144" xml:space="preserve">quare quod fit ex EK, & </s>
            <s xml:id="echoid-s1145" xml:space="preserve">V, ex extre-
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            mis, æquabitur ei, quod ex H, fit & </s>
            <s xml:id="echoid-s1146" xml:space="preserve">K, ex medijs.</s>
            <s xml:id="echoid-s1147" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1148" xml:space="preserve">Sed oſtenſum eſt id quod ex EK, fit & </s>
            <s xml:id="echoid-s1149" xml:space="preserve">F. </s>
            <s xml:id="echoid-s1150" xml:space="preserve">æquale eſſe ei quod fit ex
              <lb/>
            G, & </s>
            <s xml:id="echoid-s1151" xml:space="preserve">E, ergo quod fit ex EK, & </s>
            <s xml:id="echoid-s1152" xml:space="preserve">F, vna cum eo, quod ex EK, & </s>
            <s xml:id="echoid-s1153" xml:space="preserve">V, hoc
              <lb/>
            eſb id quod fit ex EK, & </s>
            <s xml:id="echoid-s1154" xml:space="preserve">FV, æquale erit ei quod ex G, fit & </s>
            <s xml:id="echoid-s1155" xml:space="preserve">E, vna
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            cum eo quod ex H, & </s>
            <s xml:id="echoid-s1156" xml:space="preserve">K, ſed quod ex G, fit & </s>
            <s xml:id="echoid-s1157" xml:space="preserve">E, æquale eſt ei quod fit
              <lb/>
            ex G, & </s>
            <s xml:id="echoid-s1158" xml:space="preserve">EK, minus eo quod ex G, & </s>
            <s xml:id="echoid-s1159" xml:space="preserve">K, quod enim additur, idem &</s>
            <s xml:id="echoid-s1160" xml:space="preserve"/>
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