Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
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              <pb o="47" file="0205" n="205" rhead="DE CENTRO GRAVIT. SOLID."/>
            eani proportionem habeat, quam a b c d fruſtum ad por-
              <lb/>
            tionem a g d; </s>
            <s xml:id="echoid-s5122" xml:space="preserve">erit punctum l eius fruſti grauitatis cẽtrum:
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            </s>
            <s xml:id="echoid-s5123" xml:space="preserve">habebitq; </s>
            <s xml:id="echoid-s5124" xml:space="preserve">componendo K l ad 1 h proportionem eandem,
              <lb/>
            quam portio conoidis b gc ad a g d portionem. </s>
            <s xml:id="echoid-s5125" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s5126" xml:space="preserve">quo
              <lb/>
              <note position="right" xlink:label="note-0205-01" xlink:href="note-0205-01a" xml:space="preserve">20. I. coni
                <lb/>
              corum.</note>
            niam quadratum b f ad quadratum a e, hoc eſt quadratum
              <lb/>
            b c ad quadratum a d eſt, ut linea f g ad g e: </s>
            <s xml:id="echoid-s5127" xml:space="preserve">erunt duæ ter-
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            tiæ quadrati b c ad duas tertias quadrati a d, ut h g ad g _k_:
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            </s>
            <s xml:id="echoid-s5128" xml:space="preserve">& </s>
            <s xml:id="echoid-s5129" xml:space="preserve">ſi à duabus tertiis quadrati b c demptæ fuerint duæ ter-
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            tiæ quadrati a d: </s>
            <s xml:id="echoid-s5130" xml:space="preserve">erit diuidẽdo id, quod relinquitur ad duas
              <lb/>
            tertias quadrati a d, ut h k ad k g. </s>
            <s xml:id="echoid-s5131" xml:space="preserve">Rurſus duæ tertiæ quadra
              <lb/>
            ti a d ad duas tertias quadrati b c ſunt, ut _k_ g ad g h: </s>
            <s xml:id="echoid-s5132" xml:space="preserve">& </s>
            <s xml:id="echoid-s5133" xml:space="preserve">duæ
              <lb/>
            tertiæ quadrati b c ad tertiã partẽ ipſius, ut g h ad h f. </s>
            <s xml:id="echoid-s5134" xml:space="preserve">ergo
              <lb/>
            ex æ quali id, quod relinquitur ex duabus tertiis quadrati
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            b c, demptis ab ipſis quadrati a d duabus tertiis, ad tertiã
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            partem quadrati b c, ut _k_ h ad h f: </s>
            <s xml:id="echoid-s5135" xml:space="preserve">& </s>
            <s xml:id="echoid-s5136" xml:space="preserve">ad portionem eiuſdẽ
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            tertiæ partis, ad quam unà cum ipſa portione, duplam pro
              <lb/>
            portionem habeat eius, quæ eſt quadrati b c ad quadratũ
              <lb/>
            a d, ut K 1 ad 1 h. </s>
            <s xml:id="echoid-s5137" xml:space="preserve">habet enim _K_l ad 1 h ean dem proportio-
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            nem, quam conoidis portio b g c ad portionem a g d: </s>
            <s xml:id="echoid-s5138" xml:space="preserve">por-
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            tio autem b g c ad portionem a g d duplam proportionem
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            habet eius, quæ eſt baſis b c ad baſim a d: </s>
            <s xml:id="echoid-s5139" xml:space="preserve">hoc eſt quadrati
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            b c ad quadratum a d; </s>
            <s xml:id="echoid-s5140" xml:space="preserve">ut proxime demonſtratum eſt. </s>
            <s xml:id="echoid-s5141" xml:space="preserve">quare
              <lb/>
              <note position="right" xlink:label="note-0205-02" xlink:href="note-0205-02a" xml:space="preserve">30. huius</note>
            dempto a d quadrato à duabus tertiis quadrati b c, erit id,
              <lb/>
            quod relin quitur unà cum dicta portione tertiæ partis ad
              <lb/>
            reliquam eiuſdem portionem, ut el ad 1 f. </s>
            <s xml:id="echoid-s5142" xml:space="preserve">Cum igitur cen-
              <lb/>
            trum grauitatis fruſti a b c d ſit l, à quo axis e f in eam, quã
              <lb/>
            diximus, proportionem diuidatur; </s>
            <s xml:id="echoid-s5143" xml:space="preserve">conſtat uerũ eſſe illud,
              <lb/>
            quod demonſtrandum propoſuimus.</s>
            <s xml:id="echoid-s5144" xml:space="preserve"/>
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        <div xml:id="echoid-div288" type="section" level="1" n="97">
          <head xml:id="echoid-head104" xml:space="preserve">FINIS LIBRI DE CENTRO
            <lb/>
          GRAVITATIS SOLIDORVM.</head>
          <p>
            <s xml:id="echoid-s5145" xml:space="preserve">Impreſſ. </s>
            <s xml:id="echoid-s5146" xml:space="preserve">Bononiæ cum licentia Superiorum.</s>
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