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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          <p>
            <s xml:space="preserve">
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            ut baſis ipſius humidum non contingat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">poſi-
              <lb/>
            ta inclinata, non manebit inclinata, ſed recta re-
              <lb/>
            ſtituetur.</s>
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          </p>
          <p>
            <s xml:space="preserve">SIT portio conoidis rectanguli, qualis dicta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">de-
              <lb/>
            miſſa in humidum, ſi fieri poteſt, non ſitrecta; </s>
            <s xml:space="preserve">ſed inclina-
              <lb/>
            ta: </s>
            <s xml:space="preserve">ſecta autem ipſa plano per axem, recto ad ſuperficiem
              <lb/>
            humidi, portionis quidem ſectio ſit rectanguli coni ſectio
              <lb/>
            a p o l, axis portionis, & </s>
            <s xml:space="preserve">ſectionis diameter n o; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſuper-
              <lb/>
            ficiei humidi ſectio ſit is. </s>
            <s xml:space="preserve">ſi igitur portio non eſt recta, nõ
              <lb/>
            faciet n o cum is angulos æquales. </s>
            <s xml:space="preserve">Ducatur k ω contin-
              <lb/>
            gens rectanguli coni ſectionem in p; </s>
            <s xml:space="preserve">æquidiſtanſq; </s>
            <s xml:space="preserve">ipſi
              <lb/>
            is: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à puncto p ipſi o n æquidiſtans ducatur p f. </s>
            <s xml:space="preserve">Itaque
              <lb/>
            ſumantur centra grauitatum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſolidi quidem a p o l cen
              <lb/>
            trum ſit r; </s>
            <s xml:space="preserve">eius autem, quod intra humidum, centrum b:
              <lb/>
            </s>
            <s xml:space="preserve">iunctaq; </s>
            <s xml:space="preserve">b r pro-
              <lb/>
              <anchor type="figure" xlink:label="fig-0038-01a" xlink:href="fig-0038-01"/>
            ducatur ad g, ut
              <lb/>
            g ſit centrũ graui
              <lb/>
            tatis ſolidi, quod
              <lb/>
            extra humidum.
              <lb/>
            </s>
            <s xml:space="preserve">Quoniam igitur
              <lb/>
            n o ipſius quidem
              <lb/>
            r o ſeſquialtera ẽ; </s>
            <s xml:space="preserve">
              <lb/>
            eius autẽ, quæ uſ-
              <lb/>
            que ad axẽ maior,
              <lb/>
            quàm ſeſquialte-
              <lb/>
            ra: </s>
            <s xml:space="preserve">patet r o maio
              <lb/>
              <anchor type="note" xlink:label="note-0038-01a" xlink:href="note-0038-01"/>
            rẽ eſſe, quàm quæ
              <lb/>
            uſq; </s>
            <s xml:space="preserve">ad axẽ. </s>
            <s xml:space="preserve">Sit ei,
              <lb/>
              <anchor type="note" xlink:label="note-0038-02a" xlink:href="note-0038-02"/>
            quæ uſque ad axẽ
              <lb/>
            æqualis r h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">o h dupla ipſius h m. </s>
            <s xml:space="preserve">quòd cū n o ipſius r o
              <lb/>
              <anchor type="note" xlink:label="note-0038-03a" xlink:href="note-0038-03"/>
            ſeſquialtera ſit; </s>
            <s xml:space="preserve">item q; </s>
            <s xml:space="preserve">m o ipſius o h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reliqua n m reli
              <lb/>
              <anchor type="note" xlink:label="note-0038-04a" xlink:href="note-0038-04"/>
            quæ r h ſeſquialtera erit. </s>
            <s xml:space="preserve">ergo axis tanto maior eſt, quàm</s>
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