Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[41. COMMENTARIVS.]
[42. LEMMA I.]
[43. LEMMA II.]
[44. LEMMA III.]
[45. LEMMA IIII.]
[46. LEMMA V.]
[47. LEMMA VI.]
[48. II.]
[49. III.]
[50. IIII.]
[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.]
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ARCHIMEDIS
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        <div type="section" level="1" n="39">
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            _erit conuertendo tota portio ad partem ipſius demerſam, ut quadrd-_
              <lb/>
            _tum b d ad exceſſum, quo quadratum f q excedit. </s>
            <s xml:space="preserve">quare per conuer-_
              <lb/>
            _ſionem rationis tota portio ad eam, quæ extra humidum est ut_
              <lb/>
            _qu.</s>
            <s xml:space="preserve">idratum b d ad quadratum f q: </s>
            <s xml:space="preserve">nam quadratum b d tanto maius_
              <lb/>
            _est exceſſu, quo excedit quadratum f q, quantum est ipſum f q qua-_
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            _dratum_.</s>
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            <note position="right" xlink:label="note-0067-08" xlink:href="note-0067-08a" xml:space="preserve">E</note>
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          <p style="it">
            <s xml:space="preserve">_Quoniam quæ ex parte 1 deorſum, quæ uero ex parte a_
              <lb/>
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            _ſurſum ferentur.</s>
            <s xml:space="preserve">]_ Hæc nos ita correximus, nam in translatione
              <lb/>
            mendoſe, ut opinor, legebatur, quoniam quæ ex parte l ad ſuperiora
              <lb/>
            ferentur, perpendicularis enim quæ tranſit per z ad partes l, & </s>
            <s xml:space="preserve">quæ
              <lb/>
            per g ad partes a cadit. </s>
            <s xml:space="preserve">quare centrum z unà cum p. </s>
            <s xml:space="preserve">trtibus ijs, quæ
              <lb/>
            ſunt ad l deorſum feretur, centrum uero g unà cum partibus quæ ad
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            a ſurſum.</s>
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            <s xml:space="preserve">Similiter demonſtrabitur non manere portionem, ſed
              <lb/>
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            inclinari, donec utique axis cum ſuperficie humidi faciat
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            angulum angulo b æqualem.</s>
            <s xml:space="preserve">] _Illud uero tum ex ijs, quæ in an_
              <lb/>
            _tecedenti dicta ſunt, tum ex figuris, quas appoſuimus, facile demon-_
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            _strari potest._</s>
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            <note position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">G</note>
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        <div type="section" level="1" n="40">
          <head xml:space="preserve">PROPOSITIO X.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem, quàm
              <lb/>
            ut ad eam, quæ uſque ad axem proportionem ha-
              <lb/>
            beat, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">in humidum
              <lb/>
            demiſſa, ita ut baſis ipſius non contingat humi-
              <lb/>
            dum: </s>
            <s xml:space="preserve">non nunquam quidem recta conſiſtet; </s>
            <s xml:space="preserve">non
              <lb/>
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            nunquam inclinata: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">interdum adeo inclinata,
              <lb/>
              <anchor type="note" xlink:label="note-0068-04a" xlink:href="note-0068-04"/>
            ut baſis ipſius in uno puncto contingat ſuperfi-
              <lb/>
            ciem humidi: </s>
            <s xml:space="preserve">idq; </s>
            <s xml:space="preserve">in duabus diſpoſitionibus:</s>
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