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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            dine, magnitudinem liquidi inuenire.</s>
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            <s xml:id="echoid-s382" xml:space="preserve">SINT duo propoſita corpora
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            æque grauia, A, quidem ſolidum B,
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            vero liquidum, ſit autem ſolidi A, da-
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            ta magnitudo C, & </s>
            <s xml:id="echoid-s383" xml:space="preserve">oporteat inuenire
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            quanta erit magnitudo liquidi B, Ac-
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            cipiatur aliquod corpus ſolidum D,
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            eiuſdem generis cum ſolido A, & </s>
            <s xml:id="echoid-s384" xml:space="preserve">ſit
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            eius grauitas G, & </s>
            <s xml:id="echoid-s385" xml:space="preserve">liquidi, quod ſit E,
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            eiuſdem generis cum liquido B, ma-
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            gnitudinem habentis æqualem ſolido
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            D, inueniatur grauitas quæ ſit H, &</s>
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            fiat vt grauitas H, ad grauitatem G,
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            ita magnitudo C, ad aliam magnitudinem quæ ſit F. </s>
            <s xml:id="echoid-s387" xml:space="preserve">Quoniam igitur
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            ſunt quatuor corpora grauia E, D, B, A, quorum primum E, & </s>
            <s xml:id="echoid-s388" xml:space="preserve">ſecun-
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            dum D, ſunt æqualia magnitudine, tertium vero B, & </s>
            <s xml:id="echoid-s389" xml:space="preserve">quartum A,
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            æque grauia, & </s>
            <s xml:id="echoid-s390" xml:space="preserve">ſunt eiuſdem generis corpora E, B, ſimiliter, & </s>
            <s xml:id="echoid-s391" xml:space="preserve">corpo-
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            ra D, A, erit vt grauitas H, ad grauitatem G, ita magnitudo C, ad
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            quidi B, magnitudinem, ſed vt grauitas H, ad grauitatem G, ita eſt
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            magnitudo C, ad magnitudinem F, ergo magnitudo F, æqualis erit
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            magnitudini liquidi B, inuenta igitur eſt liquidi corporis B, magni-
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            tudo F, quod facere oportebat.</s>
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            <s xml:id="echoid-s393" xml:space="preserve">Sed quoniam corporum regularium magnitudo quo-
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            que exprimitur latere eiuſdem corporis, vel diametro, ſi
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            propoſita duo corpora A, B, ſuerint regularia, vtpote ſphę
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            rica, fuerit autem ſphæræ A, data diameter C, & </s>
            <s xml:id="echoid-s394" xml:space="preserve">oporteat
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            inuenire quanta erit diameter ſphæræ B. </s>
            <s xml:id="echoid-s395" xml:space="preserve">ita faciendum
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            erit.</s>
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            <s xml:id="echoid-s397" xml:space="preserve">Accepto, vt diximus, aliquo corpore ſolido D, eiuſdem generis cũ
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            ſphæra A, & </s>
            <s xml:id="echoid-s398" xml:space="preserve">inuenta grauitate liquidi E, vt ſupra, fiat vt grauitas H,
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            ad grauitatem G, ita cubus ex C, ad alium cubum, cuius latus ſit F,
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            dico ipſum latus F, æquale eſſe diametro ſphæræ B. </s>
            <s xml:id="echoid-s399" xml:space="preserve">Quoniam enim
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            eadem ratione qua ſupra demonſtrabitur, vt grauitas H, ad grauita-
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            tem G, ita eſſe magnitudinem ſphæræ A, ad ſphæræ B, magnitudinem,
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            ſed magnitudo ſphæræ A, ad magnitudinem ſphæræ B,
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            rationem habet eius, quam C, diameter ſphæræ A, ad diametrum
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            ſphæræ B, ſimiliter & </s>
            <s xml:id="echoid-s400" xml:space="preserve">cubus ex C, ad cubum ex diametro ſphæræ </s>
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