Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[1. None]
[2. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBRI DVO. A FEDERICO COMMANDINO VRBINATE IN PRISTINVM NITOREM RESTITVTI, ET COMMENTARIIS ILLVSTRATI.]
[3. CVM PRIVILEGIO IN ANNOS X. BONONIAE,]
[4. M D LXV.]
[5. RANVTIO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[6. Federicus Commandinus.]
[7. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER PRIMVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. POSITIO.]
[8. PROPOSITIO I.]
[9. PROPOSITIO II.]
[10. PROPOSITIO III.]
[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.]
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DE IIS QVAE VEH. IN AQVA.
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              <pb o="26" file="0063" n="63" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _humidi ſuperficiem.</s>
            <s xml:space="preserve">]_ Est enim t ω æqualis κ r, hoc eſt ei, quæ
              <lb/>
            uſque ad axem. </s>
            <s xml:space="preserve">quare ex ijs, quæ ſuperius demonſtrata ſunt, linea
              <lb/>
            t h ducta erit ad humidi ſuperficiem perpendicularis.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="13">
            <note position="left" xlink:label="note-0062-10" xlink:href="note-0062-10a" xml:space="preserve">N</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Minorem igitur proportionem habet quadratum p i_
              <lb/>
              <anchor type="note" xlink:label="note-0063-01a" xlink:href="note-0063-01"/>
            _ad quadratum i y, quàm quadratum e ψ ad ψ b quadratũ]_
              <lb/>
            Hæc & </s>
            <s xml:space="preserve">alia, quæ ſequuntur, tum in hac, tum in ſequenti propoſitio-
              <lb/>
            ne non alio, quàm quo ſupra modo demonstrabimus.</s>
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          </p>
          <div type="float" level="2" n="14">
            <note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">O</note>
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          <p style="it">
            <s xml:space="preserve">_Itaque per z g ductis perpendicularibus ad humidi ſu-_
              <lb/>
              <anchor type="note" xlink:label="note-0063-02a" xlink:href="note-0063-02"/>
            _perficiem, quæ i pſi t h æ quidiftent; </s>
            <s xml:space="preserve">ſequitur portionem ip_
              <lb/>
            _ſam non manere, ſed reuolui adeo, ut axis cum ſuperſicie_
              <lb/>
            _humidi angulum faciat maiorem eo, quem nunc facit.</s>
            <s xml:space="preserve">]_
              <lb/>
            Nam cum perpendicularis, quæ per g, ducitur ad eas partes cadat,
              <lb/>
            in quibus eſt l; </s>
            <s xml:space="preserve">quæ autem per Z ad eis in quibus a: </s>
            <s xml:space="preserve">neceſſarium eſt
              <lb/>
            centrum g deorſum ferri, & </s>
            <s xml:space="preserve">Z ſurſum. </s>
            <s xml:space="preserve">quare partes ſolidi, quæ
              <lb/>
            ſunt ad l deorſum; </s>
            <s xml:space="preserve">quæ uero ad a ſurſum ferentur, ut axis cum ſu-
              <lb/>
            perficie humidi maiorem angulum contineat.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="15">
            <note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">P</note>
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          <p>
            <s xml:space="preserve">Sic enim erit i o æ qualis ψ b, itẽq; </s>
            <s xml:space="preserve">ω i æ qualis ψ r, & </s>
            <s xml:space="preserve">p h
              <lb/>
              <anchor type="note" xlink:label="note-0063-03a" xlink:href="note-0063-03"/>
            ipſi f.</s>
            <s xml:space="preserve">] _Hoc in tertia figura, quam nos addidimus, perſpicue apparet_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="16">
            <note position="right" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve">Q</note>
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        <div type="section" level="1" n="38">
          <head xml:space="preserve">PROPOSITIO IX.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            axem habuerit maiorem quidem, quàm ſeſquial-
              <lb/>
            terum eius, quæ uſque ad axem; </s>
            <s xml:space="preserve">minorem uero,
              <lb/>
            quàm ut ad eam, quæ uſque ad axem proportio-
              <lb/>
            nem habeat, quam quindecim ad quatuor; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in
              <lb/>
            grauitate ad humidum proportionem habeat ma
              <lb/>
            iorem, quàm exceſſus, quo quadratum, quod fit
              <lb/>
            ab axe maius eſt quadrato, quod ab exceſſu, quo
              <lb/>
            axis eſt maior, quàm ſeſquialter eius, quæ uſq; </s>
            <s xml:space="preserve">ad
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            axem, habet ad quadratum, quod ab axe: </s>
            <s xml:space="preserve">in hu-</s>
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