Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.]
[61. ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[62. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.]
[63. PETITIONES.]
[64. THEOREMA I. PROPOSITIO I.]
[65. THEOREMA II. PROPOSITIO II.]
[66. THE OREMA III. PROPOSITIO III.]
[67. THE OREMA IIII. PROPOSITIO IIII.]
[68. ALITER.]
[69. THEOREMA V. PROPOSITIO V.]
[70. COROLLARIVM.]
< >
page |< < of 213 > >|
ARCHIMEDIS
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="19">
          <p>
            <s xml:space="preserve">
              <pb file="0028" n="28" rhead="ARCHIMEDIS"/>
            extra humidi ſuperficiem, axem habetin perpendiculari
              <lb/>
            per _k_: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propter ea, quæ ſuperius dicta ſunt, centrum gra-
              <lb/>
            uitatis ipſius eſt in linea n _k_, quod ſitr; </s>
            <s xml:space="preserve">totius autem por-
              <lb/>
            tionis centrum grauitatis eſt in linea f t, inter _k_ & </s>
            <s xml:space="preserve">f, quod
              <lb/>
            ſit x. </s>
            <s xml:space="preserve">reliquæ ergo figuræ, eius ſcilicet, quæ eſt in humido,
              <lb/>
            centrum erit in rectalinea r x producta ad partes x; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">aſ-
              <lb/>
              <anchor type="figure" xlink:label="fig-0028-01a" xlink:href="fig-0028-01"/>
            ſumpta ex ea linea quadam, quæ ad x r eandem habeat pro
              <lb/>
            portionem, quam grauitas portionis, quæ eſt extra humi-
              <lb/>
            dum, ad grauitatem figuræ, quæ in humido. </s>
            <s xml:space="preserve">Sit autem o
              <lb/>
            centrum dictæ figuræ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per o perpendicularis ducatur
              <lb/>
            l o. </s>
            <s xml:space="preserve">Feretur ergo grauitas portionis quidem, quæ eſt ex-
              <lb/>
            tra humidum, per rectam r l deorſum; </s>
            <s xml:space="preserve">figuræ autem, quæ
              <lb/>
            in humido, per rectam o l ſurſum. </s>
            <s xml:space="preserve">non manet igitur flgu-
              <lb/>
            ra; </s>
            <s xml:space="preserve">ſed partes eius, quæ ſuntad h, deorſum ferẽtur; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ
              <lb/>
            ad e ſurſum. </s>
            <s xml:space="preserve">atque hoc ſemper erit, donec f t ſecundum
              <lb/>
            perpendicularem fiat.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve">A</note>
            <figure xlink:label="fig-0028-01" xlink:href="fig-0028-01a">
              <image file="0028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0028-01"/>
            </figure>
          </div>
        </div>
        <div type="section" level="1" n="20">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:space="preserve">ITAQVE figura, quæ extra humidi ſuperficiem,
              <lb/>
              <anchor type="note" xlink:label="note-0028-01a" xlink:href="note-0028-01"/>
            axem habet in perpendiculari per _k_.</s>
            <s xml:space="preserve">]</s>
          </p>
          <div type="float" level="2" n="1">
            <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">A</note>
          </div>
          <p style="it">
            <s xml:space="preserve">
              <emph style="sc">D_vcatvr_</emph>
            enim b c, quæ ſecet lineam n k in m: </s>
            <s xml:space="preserve">ipſa uero
              <lb/>
            n k circunferentiam a b c d ſecet in g. </s>
            <s xml:space="preserve">eodem modo, quo ſupra, de-</s>
          </p>
        </div>
      </text>
    </echo>