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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ARCHIMEDIS
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          <p>
            <s xml:space="preserve">
              <pb file="0086" n="86" rhead="ARCHIMEDIS"/>
            ipſi my æquidiſtans. </s>
            <s xml:space="preserve">Demonſtrandum eſt portionem in
              <lb/>
              <anchor type="note" xlink:label="note-0086-01a" xlink:href="note-0086-01"/>
            humidum demiſſam, inclinatamq; </s>
            <s xml:space="preserve">adeo, ut baſis ipſius nõ
              <lb/>
            contingat humidum, inclinatam conſiſtere ita, ut baſis ſu-
              <lb/>
            perficiem humidi nullo modo contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis cum ea fa
              <lb/>
            ciat angulum angulo χ maiorem. </s>
            <s xml:space="preserve">Demittatur enim in hu-
              <lb/>
            midum, conſiſtatq; </s>
            <s xml:space="preserve">ita, ut baſis ipſius in uno puncto cõtin
              <lb/>
            gat humidi ſuperficiem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecta ipſa portione per axem,
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            plano ad humidi ſuperficiem recto; </s>
            <s xml:space="preserve">ſuperficiei quidẽ por-
              <lb/>
            tionis ſectio ſit a p o l rectanguli coni ſectio: </s>
            <s xml:space="preserve">ſuperficiei
              <lb/>
            humidi ſectio ſit a o: </s>
            <s xml:space="preserve">axis autem portionis, & </s>
            <s xml:space="preserve">ſectionis dia
              <lb/>
            meter b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur b d in punctis k r, ut dictum eſt: </s>
            <s xml:space="preserve">du-
              <lb/>
              <anchor type="note" xlink:label="note-0086-02a" xlink:href="note-0086-02"/>
            catur etiam p g æquidiſtans ipſi a o, quæ ſectionem a p o l
              <lb/>
            contingat in p: </s>
            <s xml:space="preserve">atque ab eo puncto ducatur p t æquidiſtãs
              <lb/>
            ipſi b d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p s ad b d perpendicularis. </s>
            <s xml:space="preserve">Itaque quoniam
              <lb/>
            portio ad humidum in grauitate eam proportionem ha-
              <lb/>
            bet, quam qua-
              <lb/>
              <anchor type="figure" xlink:label="fig-0086-01a" xlink:href="fig-0086-01"/>
            dratũ, quod fit
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            à linea χ ad qua
              <lb/>
            dratum b d: </s>
            <s xml:space="preserve">quã
              <lb/>
            uero proportio
              <lb/>
            nem habet por-
              <lb/>
            tio ad humidũ,
              <lb/>
            eandem pars ip
              <lb/>
            ſius demerſa ha
              <lb/>
            bet ad totã por
              <lb/>
            tionẽ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam
              <lb/>
            pars demerſa ad
              <lb/>
            totam, eandem
              <lb/>
            habet quadra-
              <lb/>
            tum t p ad b d
              <lb/>
            quadratum: </s>
            <s xml:space="preserve">erit
              <lb/>
            linea ψ æqualis
              <lb/>
            ipſi t p. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">lineæ m n, p t; </s>
            <s xml:space="preserve">itemq, portiones a m q,
              <lb/>
            a p o inter ſe ſunt æquales. </s>
            <s xml:space="preserve">Quòd cumin portionibus
              <lb/>
              <anchor type="note" xlink:label="note-0086-03a" xlink:href="note-0086-03"/>
            </s>
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