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

Table of contents

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[11.] THEOREMA VI. PROPOS. VI.
[12.] THEOREMA VII. PROPOS. VII.
[13.] PROBLEMA I. PROPOS. VIII.
[14.] Exemplum.
[15.] PROBLEMA II. PROPOS. IX.
[16.] Exemplum.
[17.] PROBLEMA III. PROPOS. X.
[18.] Exemplum.
[19.] PROBLEMA IV. PROPOS. XI.
[20.] Exemplum.
[21.] PROBLEMAV. PROPOS. XII.
[22.] Exemplum.
[23.] PROBLEMA VI. PROPOS. XIII.
[24.] Exemplum.
[25.] PROBLEMA VII. PROPOS. XIV.
[26.] Exemplum.
[27.] PROBLEMA VIII. PROPOS. XV.
[28.] Exemplum.
[29.] THEOREMA VIII. PROPOS. XVI.
[30.] ALITER.
[31.] THEOREMA IX. PROPOS. XVII.
[32.] Ad comparandum inter ſe duodecim corporum genera grauitate, & magnitudine tabella.
[33.] Altera, ad comparandum inter ſe duodecim corporum genera, grauitate, & magnitudine, tabella.
[34.] Hic ſequitur tabula, ad inueniendas ſphærarum grauita-tes, ex data diametrorum magnitudine, cuius hæc eſt explicatio.
[35.] Qua ratione hanc Tabulam compoſuimus.
[36.] Ad inueniendas ſphæra-diametrorum TAB
[37.] Sequitur, ad inueniendas diametrorum magnitudines ex data ſphæ-rarum grauitate, tabula.
[38.] Hactenus Vitruuius.
[39.] PROBLEMA IX. PROPOS. XVIII.
[40.] Exemplum. I.
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          <head xml:id="echoid-head28" xml:space="preserve">PROBLEMA VII. PROPOS. XIV.</head>
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            <s xml:id="echoid-s561" xml:space="preserve">PRopoſitis duobus liquidis corporibus magnitudine
              <lb/>
            ęqualibus, data grauitate vnius, grauitatem alte-
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            rius inuenire.</s>
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          <p>
            <s xml:id="echoid-s563" xml:space="preserve">SINT propoſita duo cor-
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              <figure xlink:label="fig-0034-01" xlink:href="fig-0034-01a" number="15">
                <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0034-01"/>
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            ra liquida, magnitudine æqualia
              <lb/>
            A, B, ſit autem vnius, vtpote li-
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            quidi A, data grauitas G, & </s>
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              <lb/>
            oporteat alterius liquidi B, gra-
              <lb/>
            uitatem inuenire. </s>
            <s xml:id="echoid-s565" xml:space="preserve">Accipiatur
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            aliquod corpus ſolidum C, & </s>
            <s xml:id="echoid-s566" xml:space="preserve">li-
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            quidi, quod ſit H, eiuſdem ge-
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            neris cum liquido A, magnitu-
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              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">8
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              . huius</note>
            dine æqualis ſolido C, inuenia- tur grauitas, quæ ſit D, ſimiliter
              <lb/>
            & </s>
            <s xml:id="echoid-s567" xml:space="preserve">liquidi, quod ſit I, eiuſdem
              <lb/>
            generis cum liquido B, magni-
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            tudine æqualis eidem ſolido C,
              <lb/>
              <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">8. huius</note>
            inueniatur grauitas, quæ ſit & </s>
            <s xml:id="echoid-s568" xml:space="preserve">fiat vt D, ad E, ita G, ad aliam grauitatem, quæ ſit F. </s>
            <s xml:id="echoid-s569" xml:space="preserve">Quoniam
              <lb/>
            igitur eſt vt A, ad B, ita H, ad I, æquale videlicet ad æquale, erit per-
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            mutando vt A, ad H, ita B, ad I, & </s>
            <s xml:id="echoid-s570" xml:space="preserve">quoniam eiuſdem ſunt generis cor-
              <lb/>
              <note position="left" xlink:label="note-0034-03" xlink:href="note-0034-03a" xml:space="preserve">4. buius</note>
            pora A, H, ſimiliter & </s>
            <s xml:id="echoid-s571" xml:space="preserve">corpora B, I, erit vt grauitas G, ad grauita- tem D, ita liquidi B, grauitas, ad grauitatem E, & </s>
            <s xml:id="echoid-s572" xml:space="preserve">permutando vt
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            grauitas G, ad grauitatem liquidi B, ita D, grauitas, ad grauitatem
              <lb/>
            E, ſed vt grauitas D, ad grauitatem E, ita eſt grauitas G, ad graui-
              <lb/>
            tatem F; </s>
            <s xml:id="echoid-s573" xml:space="preserve">ergo grauitas F, æqualis erit grauitati liquidi B. </s>
            <s xml:id="echoid-s574" xml:space="preserve">inuenta
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            igitur eſt liquidi corporis B, grauitas F, quod facere oportebat.</s>
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          <head xml:id="echoid-head29" xml:space="preserve">Exemplum.</head>
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            <s xml:id="echoid-s576" xml:space="preserve">QVidam proponit aliquod corpus liquidum notæ
              <lb/>
            grauitatis, & </s>
            <s xml:id="echoid-s577" xml:space="preserve">vult ſcire, quanta erit grauitas alte-
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            rius liquidi, magnitudinem habentis propoſito corpori
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            liquido æqualem.</s>
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            <s xml:id="echoid-s579" xml:space="preserve">Sit propoſitum aliquod olei corpus A, cuius grauitas 550, & </s>
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            oporteat inuenire, quanta erit grauitas aquæ, magnitudinem </s>
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