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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            ſuperficiem recto, ſit portionis ſectio anzg; </s>
            <s xml:space="preserve">ſuperficiei
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            humidi ez: </s>
            <s xml:space="preserve">a-
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              <anchor type="figure" xlink:label="fig-0098-01a" xlink:href="fig-0098-01"/>
            xis portionis,
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            & </s>
            <s xml:space="preserve">ſectionis dia-
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            meter b d: </s>
            <s xml:space="preserve">ſece-
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            turq, b d in pũ-
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            ctis _K_r, ſicuti
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            prius; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">duca-
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            tur n l quidem
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            ipſi e z æquidi-
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            ſtans, quæ con-
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            tingat ſectionẽ
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            a n z g in n; </s>
            <s xml:space="preserve">& </s>
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              <lb/>
            n t æquidiſtans
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            ipſi b d; </s>
            <s xml:space="preserve">n s ue-
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            ro ad b d perpẽ
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            dicularis. </s>
            <s xml:space="preserve">Itaq;
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            </s>
            <s xml:space="preserve">quoniam portio ad humidum in grauitate eam proportio
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            nem habet, quam quadratum, quod fit à linea ψ ad quadra
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            tum b d: </s>
            <s xml:space="preserve">erit ψ ipſi n t æqualis: </s>
            <s xml:space="preserve">quod ſimiliter demonſtrabi
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            tur, ut ſuperius. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">n t eſt æqualis ipſi u i. </s>
            <s xml:space="preserve">portiones
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            igitur a u q, e n z inter ſe ſunt æquales. </s>
            <s xml:space="preserve">Et cum in æquali-
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            bus, & </s>
            <s xml:space="preserve">ſimilibus portionibus a u q l, a n z g ductæ ſint a q
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            e z, quæ æquales portiones auferunt; </s>
            <s xml:space="preserve">illa quidem ab extre
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            mitate baſis; </s>
            <s xml:space="preserve">hæc autem non ab extremitate: </s>
            <s xml:space="preserve">minorem fa-
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            ciet acutum angulum cum portionis diametro, quæ ab ex-
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            tremitate baſis ducitur. </s>
            <s xml:space="preserve">At triangulorum n l s, u ω c angu
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            lus ad l angulo ad ω maior eſt. </s>
            <s xml:space="preserve">ergo b s minor erit, quam
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            b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſ r maior, quàm c r: </s>
            <s xml:space="preserve">ideoq; </s>
            <s xml:space="preserve">n χ maior, quam u h; </s>
            <s xml:space="preserve">& </s>
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            χ t minor, quàm h i. </s>
            <s xml:space="preserve">Quoniam igitur u y dupla eſt ipſius
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            y i; </s>
            <s xml:space="preserve">conſtat n χ maiorem eſſe, quàm duplã χ t. </s>
            <s xml:space="preserve">Sit n m dupla
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            ipſius m t. </s>
            <s xml:space="preserve">perſpicuũ eſt ex iis, quæ dicta ſunt, non manere
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            portionẽ; </s>
            <s xml:space="preserve">ſed in clinari, donec eius baſis contingat ſuperfi-
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            ciem humidi: </s>
            <s xml:space="preserve">contingat autem in puncto uno, ut patet in fi</s>
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