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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FED. COMMANDINI
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            quæ quidem in centro conueniunt. </s>
            <s xml:space="preserve">idem igitur eſt centrum
              <lb/>
            grauitatis quadrati, & </s>
            <s xml:space="preserve">circuli centrum.</s>
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            <figure xlink:label="fig-0115-02" xlink:href="fig-0115-02a">
              <image file="0115-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0115-02"/>
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            <note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">51. tortil.</note>
          </div>
          <p>
            <s xml:space="preserve">Sit pentagonum æquilaterum, & </s>
            <s xml:space="preserve">æquiangulum in circu-
              <lb/>
            lo deſcriptum a b c d e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iun-
              <lb/>
              <anchor type="figure" xlink:label="fig-0116-01a" xlink:href="fig-0116-01"/>
            cta b d, bifariamq́; </s>
            <s xml:space="preserve">in ſ diuiſa,
              <lb/>
            ducatur c f, & </s>
            <s xml:space="preserve">producatur ad
              <lb/>
            circuli circumferentiam in g;
              <lb/>
            </s>
            <s xml:space="preserve">quæ lineam a e in h ſecet: </s>
            <s xml:space="preserve">de-
              <lb/>
            inde iungantur a c, c e. </s>
            <s xml:space="preserve">Eodem
              <lb/>
            modo, quo ſupra demonſtra-
              <lb/>
            bimus angulum b c f æqualem
              <lb/>
            eſſe angulo d c f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">angulos
              <lb/>
            ad f utroſque rectos: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcir-
              <lb/>
            colineam c f g per circuli cen
              <lb/>
            trum tranſire. </s>
            <s xml:space="preserve">Quoniam igi-
              <lb/>
            tur latera c b, b a, & </s>
            <s xml:space="preserve">c d, d e æqualia ſunt; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">æquales anguli
              <lb/>
            c b a, c d e: </s>
            <s xml:space="preserve">erit baſis c a baſi c e, & </s>
            <s xml:space="preserve">angulus b c a angulo
              <lb/>
              <anchor type="note" xlink:label="note-0116-01a" xlink:href="note-0116-01"/>
            d c e æqualis. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliquus a c h, reliquo e c h. </s>
            <s xml:space="preserve">eſt au-
              <lb/>
            tem c h utrique triangulo a c h, e c h communis. </s>
            <s xml:space="preserve">quare
              <lb/>
            baſis a h æqualis eſt baſi h e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">anguli, quiad h recti: </s>
            <s xml:space="preserve">ſuntq́;
              <lb/>
            </s>
            <s xml:space="preserve">recti, qui ad f. </s>
            <s xml:space="preserve">ergo lineæ a e, b d inter ſe ſe æquidiſtant. </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0116-02a" xlink:href="note-0116-02"/>
            Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
              <lb/>
            nea fh bifariam diuidantur; </s>
            <s xml:space="preserve">centrum grauitatis ipſius erit
              <lb/>
            in linea f h, ex ultima eiuſdem libri Archimedis. </s>
            <s xml:space="preserve">Sed trian-
              <lb/>
              <anchor type="note" xlink:label="note-0116-03a" xlink:href="note-0116-03"/>
            guli b c d centrum grauitatis eſt in linea c f. </s>
            <s xml:space="preserve">ergo in eadem
              <lb/>
            linea c h eſt centrum grauitatis trapezij a b d e, & </s>
            <s xml:space="preserve">trian-
              <lb/>
            guli b c d: </s>
            <s xml:space="preserve">hoc eſt pentagoni ipſius centrum & </s>
            <s xml:space="preserve">centrum
              <lb/>
            circuli. </s>
            <s xml:space="preserve">Rurſus ſi iuncta a d, bifariamq́; </s>
            <s xml:space="preserve">ſecta in k, duca-
              <lb/>
            tur e k l: </s>
            <s xml:space="preserve">demonſtrabimus in ipſa utrumque centrum in
              <lb/>
            eſſe. </s>
            <s xml:space="preserve">Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
              <lb/>
            ueniunt, idem ſit centrum circuli, & </s>
            <s xml:space="preserve">centrum grauitatis
              <lb/>
            pentagoni.</s>
            <s xml:space="preserve"/>
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            <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a">
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            <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">4. Primi.</note>
            <note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">08. primi.</note>
            <note position="left" xlink:label="note-0116-03" xlink:href="note-0116-03a" xml:space="preserve">13. Archi-
              <lb/>
            medis.</note>
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          <p>
            <s xml:space="preserve">Sit hexagonum a b c d e f æquilaterum, & </s>
            <s xml:space="preserve">æquiangulum
              <lb/>
            in circulo deſignatum: </s>
            <s xml:space="preserve">iunganturq́; </s>
            <s xml:space="preserve">b d, a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam ſe-</s>
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