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 style="it">
            <s xml:space="preserve">
              <pb file="0096" n="96" rhead="ARCHIMEDIS"/>
            minor erit: </s>
            <s xml:space="preserve">linea uero b c maior, quàm b s: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">s r; </s>
            <s xml:space="preserve">hoc eſt m χ ma-
              <lb/>
            ior, quàm c r, hoc eſt, quàm p y: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea χ t minor, quàm y f.
              <lb/>
            </s>
            <s xml:space="preserve">quòd cum p y ſit dupla y f, erit m χ maior, quàm dupla y f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            multo maior, quàm dupla χ t. </s>
            <s xml:space="preserve">fiat m h dupla ipſius h t: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">copu-
              <lb/>
            lata h k producatur. </s>
            <s xml:space="preserve">I am grauitatis centrum totius portionis erit
              <lb/>
            punctum k: </s>
            <s xml:space="preserve">eius, quæ in humido est, h: </s>
            <s xml:space="preserve">at rel iquæ partis, quæ ex-
              <lb/>
            tra humidum in linea h k producta; </s>
            <s xml:space="preserve">quod ſit ω. </s>
            <s xml:space="preserve">eodem modo demon
              <lb/>
            strabitur, & </s>
            <s xml:space="preserve">lineam k h, & </s>
            <s xml:space="preserve">quæ per h ω puncta ipſi k h æquidi-
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            ſtantes ducuntur, ad humidi ſuperficiem perpendiculares eſſe. </s>
            <s xml:space="preserve">non
              <lb/>
            igitur maneb it
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              <anchor type="figure" xlink:label="fig-0096-01a" xlink:href="fig-0096-01"/>
            portio, ſed cum
              <lb/>
            uſque eò inclina-
              <lb/>
            ta fuerit, ut in
              <lb/>
            uno puncto con-
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            tingat ſuperfi-
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            cié humidi, tunc
              <lb/>
            conſiſtet. </s>
            <s xml:space="preserve">an-
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            gulus enim ad n
              <lb/>
            angulo ad φ æ-
              <lb/>
            qualis erit; </s>
            <s xml:space="preserve">li-
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            neáq; </s>
            <s xml:space="preserve">b s lineæ
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            b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">s r ipſi
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            c r. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">m h
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            ipſi p y eſt æqua
              <lb/>
            lis. </s>
            <s xml:space="preserve">Itaque ducta
              <lb/>
            h k producatur.
              <lb/>
            </s>
            <s xml:space="preserve">erit totius portionis grauitatis centrum K; </s>
            <s xml:space="preserve">eius, quæ in humido eſt
              <lb/>
            h; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reliquæ partis centrum in linea producta; </s>
            <s xml:space="preserve">ſit autem ω. </s>
            <s xml:space="preserve">per ean
              <lb/>
            dem igitur rectam lineam k h, quæ eſt ad humidi ſuperficiem perpen
              <lb/>
            dicularis, id quod in humido eſt ſurſum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quod extra humidum de
              <lb/>
            orſum feretur. </s>
            <s xml:space="preserve">atque ob hác cauſſam portio non amplius mouebitur; </s>
            <s xml:space="preserve">
              <lb/>
            ſed conſiſtet, manebítq, ita, ut eius baſis ſuperficiem humidi in uno
              <lb/>
            punsto contingat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis, cum ipſa angulum faciat æqualem angulo
              <lb/>
            φ. </s>
            <s xml:space="preserve">at que illud eſt, quod demonſtrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
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            <note position="left" xlink:label="note-0094-08" xlink:href="note-0094-08a" xml:space="preserve">F</note>
            <figure xlink:label="fig-0094-01" xlink:href="fig-0094-01a">
              <image file="0094-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0094-01"/>
            </figure>
            <figure xlink:label="fig-0095-01" xlink:href="fig-0095-01a">
              <image file="0095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0095-01"/>
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            <note position="right" xlink:label="note-0095-01" xlink:href="note-0095-01a" xml:space="preserve">8. quinti.</note>
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