Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.]
[71. THEOREMA VI. PROPOSITIO VI.]
[72. THE OREMA VII. PROPOSITIO VII.]
[73. THE OREMA VIII. PROPOSITIO VIII.]
[74. THE OREMA IX. PROPOSITIO IX.]
[75. PROBLEMA I. PROPOSITIO X.]
[76. PROBLEMA II. PROPOSITIO XI.]
[77. PROBLEMA III. PROPOSITIO XII.]
[78. PROBLEMA IIII. PROPOSITIO XIII.]
[79. THEOREMA X. PROPOSITIO XIIII.]
[80. THE OREMA XI. PROPOSITIO XV.]
[81. THE OREMA XII. PROPOSITIO XVI.]
[82. THE OREMA XIII. PROPOSITIO XVII.]
[83. THEOREMA XIIII. PROPOSITIO XVIII.]
[84. THEOREMA XV. PROPOSITIO XIX.]
[85. THE OREMA XVI. PROPOSITIO XX.]
[86. THEOREMA XVII. PROPOSITIO XXI.]
[87. THE OREMA XVIII. PROPOSITIO XXII.]
[88. THEOREMA XIX. PROPOSITIO XXIII.]
[89. PROBLEMA V. PROPOSITIO XXIIII.]
[90. THEOREMA XX. PROPOSITIO XXV.]
< >
page |< < (42) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="55">
          <p style="it">
            <s xml:space="preserve">
              <pb o="42" file="0095" n="95" rhead="DE IIS QVAE VEH. IN AQVA."/>
            clinata, ut baſis humidum non contingat, ſectur plano per axem,
              <lb/>
            recto ad ſuperficiem humidi, ut ſectio ſit a m o l rectanguli coni ſe-
              <lb/>
            ctio: </s>
            <s xml:space="preserve">ſuperficiei humidi ſectio ſit i o: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis
              <lb/>
            diameter b d; </s>
            <s xml:space="preserve">quæ in eaſdem, quas diximus, partes ſecetur: </s>
            <s xml:space="preserve">duca-
              <lb/>
            turq; </s>
            <s xml:space="preserve">m n quidem ipſi i o æquidiſtans, ut in puncto m ſectionem
              <lb/>
            cótingat: </s>
            <s xml:space="preserve">mt uero æquidiſtans ipſi b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">m s ad eandem perpen
              <lb/>
            dicularis. </s>
            <s xml:space="preserve">Demonſtrandum eſt non manere portionem, ſed inclinari
              <lb/>
            ita, ut in uno puncto contingat ſuperficiem humidi. </s>
            <s xml:space="preserve">ducatur enim p c
              <lb/>
            ad ipſam b d perpendicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a f uſque ad ſectionem
              <lb/>
            producatur in q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per p ducatur p φ ipſi a q æquidiſtans. </s>
            <s xml:space="preserve">erunt
              <lb/>
            iam ex ijs, quæ demonſtrauimus a f, f q inter ſe ſe æquales. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cum
              <lb/>
            portio ad humi-
              <lb/>
              <anchor type="figure" xlink:label="fig-0095-01a" xlink:href="fig-0095-01"/>
            dum eam in gra-
              <lb/>
            uitate proportio
              <lb/>
            nem habeat, quá
              <lb/>
            quadratú p f ad
              <lb/>
            b d quadratum:
              <lb/>
            </s>
            <s xml:space="preserve">atque eandem ha
              <lb/>
            beat portio ipſi-
              <lb/>
            us demerſa ad to
              <lb/>
            tam portionem; </s>
            <s xml:space="preserve">
              <lb/>
            hoc eſt quadratú
              <lb/>
            m t ad quadratú
              <lb/>
              <anchor type="note" xlink:label="note-0095-01a" xlink:href="note-0095-01"/>
            b d: </s>
            <s xml:space="preserve">erit quadra
              <lb/>
            tum m t quadra-
              <lb/>
            to p f æquale: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            idcirco linea m t
              <lb/>
            æqualis lmeæ p
              <lb/>
            f. </s>
            <s xml:space="preserve">Itaque quoniam in portionibus æqualibus, & </s>
            <s xml:space="preserve">ſimilibus a p q l, a
              <lb/>
            m o l ductæ ſunt lineæ a q, i o, quæ æquales portiones abſcindunt;
              <lb/>
            </s>
            <s xml:space="preserve">illa quidem ab extremitate baſis; </s>
            <s xml:space="preserve">hæc uero non ab extremitate: </s>
            <s xml:space="preserve">ſe-
              <lb/>
            quitur ut a q, quæ ab extremitate ducitur, minorem acutum angulú
              <lb/>
            contineat cum diametro portionis, quàm ipſa i o. </s>
            <s xml:space="preserve">Sed linea p φ li-
              <lb/>
            neæ a q æquidiſtat, & </s>
            <s xml:space="preserve">m n ipſi i o. </s>
            <s xml:space="preserve">angulus igitur ad φ angulo ad n</s>
          </p>
        </div>
      </text>
    </echo>