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="40" file="0091" n="91" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ipſi i m æquidiſtãs, & </s>
            <s xml:space="preserve">contingens ſectionem in p; </s>
            <s xml:space="preserve">pt uero
              <lb/>
            æquidiſtans b d, & </s>
            <s xml:space="preserve">p s ad ipſam b d perpendicularis. </s>
            <s xml:space="preserve">Demõ
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            ſtrandũ eſt, portionẽ non cõſiſtereita, ſed inclinari, donec
              <lb/>
            baſis in uno puncto ſuperficiem humidi cõtingat. </s>
            <s xml:space="preserve">Maneãt
              <lb/>
            enim eadem, quæ in ſuperiori figura: </s>
            <s xml:space="preserve">ducaturq; </s>
            <s xml:space="preserve">o c ad b d
              <lb/>
            perpendicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a x ad q producatur. </s>
            <s xml:space="preserve">erit a x
              <lb/>
            æqualis ipſi x q. </s>
            <s xml:space="preserve">deĩde ducatur o χ ipſi a q æquidiſtãs. </s>
            <s xml:space="preserve">Quo
              <lb/>
            niã igitur portio ad humidũ eã in grauitate proportione
              <lb/>
            habere ponitur, quam quadratum x o ad quadratum b d:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eandem proportionem habet pars ipſius demerſa ad to
              <lb/>
            tam; </s>
            <s xml:space="preserve">hoc eſt quadratum t p ad quadratum b d: </s>
            <s xml:space="preserve">æqualis uti
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            que erit t p ipſi x o: </s>
            <s xml:space="preserve">cumq; </s>
            <s xml:space="preserve">portionum i p m, a o q diame-
              <lb/>
            tri ſint æquales, & </s>
            <s xml:space="preserve">portiones ipſæ æquales erunt. </s>
            <s xml:space="preserve">Rurſus
              <lb/>
              <anchor type="note" xlink:label="note-0091-01a" xlink:href="note-0091-01"/>
            quoniam in por
              <lb/>
              <anchor type="note" xlink:label="note-0091-02a" xlink:href="note-0091-02"/>
              <anchor type="figure" xlink:label="fig-0091-01a" xlink:href="fig-0091-01"/>
            tionibus æquali
              <lb/>
            bus, & </s>
            <s xml:space="preserve">ſimilibus
              <lb/>
            a o q l, a p m l,
              <lb/>
            ductæ ſunt lineæ
              <lb/>
            a q, i m, quæ æ-
              <lb/>
            quales portio-
              <lb/>
            nes auferunt; </s>
            <s xml:space="preserve">il-
              <lb/>
            la quidem ab ex
              <lb/>
            tremitate baſis,
              <lb/>
            hæc autem non
              <lb/>
            ab extremitate:
              <lb/>
            </s>
            <s xml:space="preserve">cõſtat eam, quæ
              <lb/>
            ab extremitate
              <lb/>
            baſis ducta eſt,
              <lb/>
            minorem facere
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            angulum acutũ
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            cum diametro totius portionis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam angulus, qui
              <lb/>
              <anchor type="note" xlink:label="note-0091-03a" xlink:href="note-0091-03"/>
            ad χ minor eſt angulo, qui ad n; </s>
            <s xml:space="preserve">maior erit b c, quàm b s:
              <lb/>
            </s>
            <s xml:space="preserve">cr autem, quàm ſr minor. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">o g minor, quàm p z: </s>
            <s xml:space="preserve">
              <lb/>
            & </s>
            <s xml:space="preserve">g x maior, quàm z t. </s>
            <s xml:space="preserve">ergo p z maior eſt, quàm dupla z t;</s>
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