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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DE IIS QVAE VEH. IN AQVA.
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              <pb o="23" file="0057" n="57" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ipſa b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco f minor ipſa b r. </s>
            <s xml:space="preserve">ſit ipſi f æqualis r ψ:
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            </s>
            <s xml:space="preserve">
              <anchor type="note" xlink:label="note-0057-01a" xlink:href="note-0057-01"/>
            ducaturq; </s>
            <s xml:space="preserve">ad b d perpendicularis ψ e, quæ posſit dimidiũ
              <lb/>
            eius, quod lineis _k_ r, ψ b continetur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur b c. </s>
            <s xml:space="preserve">De-
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            monſtrandum eſt portionem in humidum demiſſam, ſicu-
              <lb/>
            ti dictum eſt, conſiſtere inclinatam ita, ut axis cum ſuperſi-
              <lb/>
            cie humidi angulum faciat angulo c b ψ æqualem. </s>
            <s xml:space="preserve">demit-
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            tatur enim aliqua portio in humidum, ut baſis ipſius hu-
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            midi ſuperficiem non contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi fieri poteſt, axis cum
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            ſuperficie humidi non faciat angulum æqualem angulo
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            e b ψ; </s>
            <s xml:space="preserve">ſed primo maiorem. </s>
            <s xml:space="preserve">ſecta autẽ portione plano per
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            axem, recto ad ſu-
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              <anchor type="figure" xlink:label="fig-0057-01a" xlink:href="fig-0057-01"/>
            perficiem humi-
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            di, ſit ſectio a p o l
              <lb/>
            rectanguli coni ſe
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            ctio: </s>
            <s xml:space="preserve">ſuperficiei
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            humidi ſectio x s:
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            </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">axis portio-
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            nis, & </s>
            <s xml:space="preserve">ſectiõis dia
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            meter n o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">du-
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            catur p y quidem
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            ipſi x s æquidi-
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            ſtans, quæ ſectio-
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            nem a p o l contin
              <lb/>
            gat in p: </s>
            <s xml:space="preserve">p m ue-
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            ro æquidiſtans ip-
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            ſi n o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p i ad
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            n o perpendicularis. </s>
            <s xml:space="preserve">ſit præterea b r æqualis o ω. </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="note" xlink:label="note-0057-02a" xlink:href="note-0057-02"/>
            r k ipſi t _a_ & </s>
            <s xml:space="preserve">ω h perpendicularis ad axem. </s>
            <s xml:space="preserve">Itaque quo-
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            niam ponitut axis portionis cum ſuperficie humidi facere
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            angulum maiorem angulo b: </s>
            <s xml:space="preserve">erit angulus p y i angulo b
              <lb/>
              <anchor type="note" xlink:label="note-0057-03a" xlink:href="note-0057-03"/>
            maior. </s>
            <s xml:space="preserve">maiorem ergo proportionem habet quadratum
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            p i ad quadratum y i, quam quadratum e ψ ad ψ b qua-
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              <anchor type="note" xlink:label="note-0057-04a" xlink:href="note-0057-04"/>
            dratum. </s>
            <s xml:space="preserve">Sed quam proportionem habet quadratum p i
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            ad quadratum i y, eandem linea k r habet ad lineam i y:</s>
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