Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.]
< >
page |< < (44) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="56">
          <p>
            <s xml:space="preserve">
              <pb o="44" file="0099" n="99" rhead="DE IIS QVAE VEH. IN AQVA."/>
            gura: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia eadem diſponantur demonſtrabimus rurſum
              <lb/>
            n t æqualem eſſe ipſi u i: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portiones a u q, a n z inter
              <lb/>
            ſe ſe æquales.
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="figure" xlink:label="fig-0099-01a" xlink:href="fig-0099-01"/>
            Itaque quoniã
              <lb/>
            ĩ portionibus
              <lb/>
            æqualibus, & </s>
            <s xml:space="preserve">ſi
              <lb/>
            milibus a u q l,
              <lb/>
            a n z g ductæ
              <lb/>
            sũt a q, a z, por
              <lb/>
            tiones æqua-
              <lb/>
            les auferentes;
              <lb/>
            </s>
            <s xml:space="preserve">cum diametris
              <lb/>
            portionum æ-
              <lb/>
            quales angu-
              <lb/>
            los cõtinebũt. </s>
            <s xml:space="preserve">
              <lb/>
            ergo triangulo
              <lb/>
            rum n l s, u ω c
              <lb/>
            anguli, qui cõ-
              <lb/>
            ſiſtũt ad l ω pũ-
              <lb/>
            cta, æquales ſunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b s recta linea æqualis ipſi b c: </s>
            <s xml:space="preserve">ſ r ipſi cr,
              <lb/>
            n χ ipſi u h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">χ tipſi h i. </s>
            <s xml:space="preserve">quòd cum u y dupla ſit ipſius y i,
              <lb/>
            erit n χ maior, quàm dupla χ t. </s>
            <s xml:space="preserve">Sit igitur n m ipſius m t du
              <lb/>
            pla. </s>
            <s xml:space="preserve">Rurſus ex his manifeſtum eſt, non manere ipſam por-
              <lb/>
            tionem; </s>
            <s xml:space="preserve">ſed inclinari ex parte a: </s>
            <s xml:space="preserve">ponebatur autem portio
              <lb/>
            humidi ſuperficiem in uno puncto contingere. </s>
            <s xml:space="preserve">ergo ne-
              <lb/>
            ceſſe eſt, ut eius baſis in humidum magis demergatur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a">
              <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0097-01"/>
            </figure>
            <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a">
              <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0098-01"/>
            </figure>
            <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a">
              <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0099-01"/>
            </figure>
          </div>
        </div>
        <div type="section" level="1" n="57">
          <head xml:space="preserve">DEMONSTRATIO QVINT AE PARTIS.</head>
          <p>
            <s xml:space="preserve">HABEAT denique portio ad humidum in grauitate
              <lb/>
            minorem proportionem, quàm quadratum f p ad quadra-
              <lb/>
            tum b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet portio ad humidũ
              <lb/>
            in grauitate, eandem quadratum, quod fit à linea ψ habeat
              <lb/>
            ad quadratum b d. </s>
            <s xml:space="preserve">erit χ minor ipſa p f. </s>
            <s xml:space="preserve">Rurſus aptetur</s>
          </p>
        </div>
      </text>
    </echo>