Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
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ARCHIMEDIS
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            ipſi my æquidiſtans. </s>
            <s xml:space="preserve">Demonſtrandum eſt portionem in
              <lb/>
              <anchor type="note" xlink:label="note-0086-01a" xlink:href="note-0086-01"/>
            humidum demiſſam, inclinatamq; </s>
            <s xml:space="preserve">adeo, ut baſis ipſius nõ
              <lb/>
            contingat humidum, inclinatam conſiſtere ita, ut baſis ſu-
              <lb/>
            perficiem humidi nullo modo contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis cum ea fa
              <lb/>
            ciat angulum angulo χ maiorem. </s>
            <s xml:space="preserve">Demittatur enim in hu-
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            midum, conſiſtatq; </s>
            <s xml:space="preserve">ita, ut baſis ipſius in uno puncto cõtin
              <lb/>
            gat humidi ſuperficiem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecta ipſa portione per axem,
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            plano ad humidi ſuperficiem recto; </s>
            <s xml:space="preserve">ſuperficiei quidẽ por-
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            tionis ſectio ſit a p o l rectanguli coni ſectio: </s>
            <s xml:space="preserve">ſuperficiei
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            humidi ſectio ſit a o: </s>
            <s xml:space="preserve">axis autem portionis, & </s>
            <s xml:space="preserve">ſectionis dia
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            meter b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur b d in punctis k r, ut dictum eſt: </s>
            <s xml:space="preserve">du-
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              <anchor type="note" xlink:label="note-0086-02a" xlink:href="note-0086-02"/>
            catur etiam p g æquidiſtans ipſi a o, quæ ſectionem a p o l
              <lb/>
            contingat in p: </s>
            <s xml:space="preserve">atque ab eo puncto ducatur p t æquidiſtãs
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            ipſi b d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p s ad b d perpendicularis. </s>
            <s xml:space="preserve">Itaque quoniam
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            portio ad humidum in grauitate eam proportionem ha-
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            bet, quam qua-
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              <anchor type="figure" xlink:label="fig-0086-01a" xlink:href="fig-0086-01"/>
            dratũ, quod fit
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            à linea χ ad qua
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            dratum b d: </s>
            <s xml:space="preserve">quã
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            uero proportio
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            nem habet por-
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            tio ad humidũ,
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            eandem pars ip
              <lb/>
            ſius demerſa ha
              <lb/>
            bet ad totã por
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            tionẽ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam
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            pars demerſa ad
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            totam, eandem
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            habet quadra-
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            tum t p ad b d
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            quadratum: </s>
            <s xml:space="preserve">erit
              <lb/>
            linea ψ æqualis
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            ipſi t p. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">lineæ m n, p t; </s>
            <s xml:space="preserve">itemq, portiones a m q,
              <lb/>
            a p o inter ſe ſunt æquales. </s>
            <s xml:space="preserve">Quòd cumin portionibus
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              <anchor type="note" xlink:label="note-0086-03a" xlink:href="note-0086-03"/>
            </s>
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