Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11.] PROPOSITIO IIII.
[12.] PROPOSITIO V.
[13.] PROPOSITIO VI.
[14.] PROPOSITIO VII.
[15.] POSITIO II.
[16.] COMMENTARIVS.
[17.] PROPOSITIO VIII.
[18.] COMMENTARIVS.
[19.] PROPOSITIO IX.
[20.] COMMENTARIVS.
[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
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            <s xml:id="echoid-s4485" xml:space="preserve">
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            fruſtum a d. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">Sed pyramis q æqualis eſt fruſto à pyramide
              <lb/>
            abſciſſo, ut dem onſtrauimus. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s4488" xml:space="preserve">conus, uel coni por-
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            tio q, cuius baſis ex tribus circulis, uel ellipſibus a b, e f, c d
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            conſtat, & </s>
            <s xml:id="echoid-s4489" xml:space="preserve">altitudo eadem, quæ fruſti: </s>
            <s xml:id="echoid-s4490" xml:space="preserve">ipſi fruſto a d eſt æ-
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            qualis. </s>
            <s xml:id="echoid-s4491" xml:space="preserve">atque illud eſt, quod demonſtrare oportebat.</s>
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        <div xml:id="echoid-div268" type="section" level="1" n="91">
          <head xml:id="echoid-head98" xml:space="preserve">THEOREMA XXI. PROPOSITIO XXVI.</head>
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            <s xml:id="echoid-s4493" xml:space="preserve">
              <emph style="sc">Cvivslibet</emph>
            fruſti à pyramide, uel cono,
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            uel coni portione abſcisſi, centrum grauitatis eſt
              <lb/>
            in axe, ita ut eo primum in duas portiones diui-
              <lb/>
            ſo, portio ſuperior, quæ minorem baſim attingit
              <lb/>
            ad portionem reliquam eam habeat proportio-
              <lb/>
            nem, quam duplum lateris, uel diametri maioris
              <lb/>
            baſis, vnà cum latere, uel diametro minoris, ipſi
              <lb/>
            reſpondente, habet ad duplum lateris, uel diame-
              <lb/>
            tri minoris baſis vnà cũ latere, uel diametro ma-
              <lb/>
            ioris: </s>
            <s xml:id="echoid-s4494" xml:space="preserve">deinde à puncto diuiſionis quarta parte ſu
              <lb/>
            perioris portionis in ipſa ſumpta: </s>
            <s xml:id="echoid-s4495" xml:space="preserve">& </s>
            <s xml:id="echoid-s4496" xml:space="preserve">rurſus ab in-
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            ferioris portionis termino, qui eſt ad baſim maio
              <lb/>
            rem, ſumpta quarta parte totius axis: </s>
            <s xml:id="echoid-s4497" xml:space="preserve">centrum ſit
              <lb/>
            in linea, quæ his finibus continetur, atque in eo li
              <lb/>
            neæ puncto, quo ſic diuiditur, ut tota linea ad par
              <lb/>
            tem propinquiorem minori baſi, eãdem propor-
              <lb/>
            tionem habeat, quam fruſtum ad pyramidẽ, uel
              <lb/>
            conum, uel coni portionem, cuius baſis ſit ea-
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            dem, quæ baſis maior, & </s>
            <s xml:id="echoid-s4498" xml:space="preserve">altitudo fruſti altitudini
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            æqualis.</s>
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