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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            ceatinclinata. </s>
            <s xml:space="preserve">Demonſtrandum eſt non manere ipſam; </s>
            <s xml:space="preserve">ſed
              <lb/>
            rectam reſtitui. </s>
            <s xml:space="preserve">Itaque ſecta ipſa plano per axem, recto ad
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            planum, quod eſt in ſuperficie humidi, portionis ſectio ſit
              <lb/>
            a p o l rectanguli coni ſectio: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis
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            diameter n o: </s>
            <s xml:space="preserve">ſuperficiei autem humidi ſectio ſit i s. </s>
            <s xml:space="preserve">Si
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            igitur portio non eſt recta; </s>
            <s xml:space="preserve">non utique erit a l ipſi i s æ-
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            quidiſtans. </s>
            <s xml:space="preserve">quare n o cum i s non faciet angulos rectos.
              <lb/>
            </s>
            <s xml:space="preserve">ducatur crgo k ω contingens ſectionem coni in p [quæ
              <lb/>
              <anchor type="note" xlink:label="note-0032-01a" xlink:href="note-0032-01"/>
            ipſi i s æquidiſtet: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à puncto p ad i s ducatur p f æquidi
              <lb/>
            ſtans ipſi o n, quæ erit ſectionis i p o s diameter, & </s>
            <s xml:space="preserve">axis por
              <lb/>
              <anchor type="note" xlink:label="note-0032-02a" xlink:href="note-0032-02"/>
            tionis in humido demerſæ. </s>
            <s xml:space="preserve">ſumantur deinde centra graui
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            tatum: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ſolidæ magnitudinis a p o l grauitatis centrũ
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              <anchor type="note" xlink:label="note-0032-03a" xlink:href="note-0032-03"/>
            r; </s>
            <s xml:space="preserve">ipſius uero i p o s centrum ſit b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta b r produca-
              <lb/>
              <anchor type="note" xlink:label="note-0032-04a" xlink:href="note-0032-04"/>
            tur ad g, quod ſit centrum grauitatis reliquæ figuræ i s l a.
              <lb/>
            </s>
            <s xml:space="preserve">Quoniam igitur n o ipſius quidem r o ſeſquialtera eſt; </s>
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              <lb/>
            eius autẽ, quæ uſque ad axẽ minor, quam ſeſquialtera; </s>
            <s xml:space="preserve">erit
              <lb/>
              <anchor type="note" xlink:label="note-0032-05a" xlink:href="note-0032-05"/>
            r o minor, quàm quæ uſque ad axem. </s>
            <s xml:space="preserve">Quare angulus r p ω
              <lb/>
              <anchor type="note" xlink:label="note-0032-06a" xlink:href="note-0032-06"/>
            acutus erit: </s>
            <s xml:space="preserve">cum enim linea, quæ uſque ad axem maior ſit
              <lb/>
            ipſa r o; </s>
            <s xml:space="preserve">quæ à puncto r ad k ω perpendicularis ducitur,
              <lb/>
            uidelicet r t, cũ
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              <anchor type="figure" xlink:label="fig-0032-01a" xlink:href="fig-0032-01"/>
            linea f p extra
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            ſectionem con
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            ueniet: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pro-
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            pterea inter p
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            & </s>
            <s xml:space="preserve">ω puncta ca-
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            datneceſſe eſt.
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            </s>
            <s xml:space="preserve">Itaq; </s>
            <s xml:space="preserve">ſi per b g
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            ducantur lineæ
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            ipſi r t æquidi-
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            ſtantes; </s>
            <s xml:space="preserve">angu-
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            los rectos cum
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            ſuperficie humidi continebunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quod in humido eſt ſur-
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              <anchor type="note" xlink:label="note-0032-07a" xlink:href="note-0032-07"/>
            ſum feretur ſecundum perpendicularem, quæ per b ducta
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            eſt, ipſi r t æquidiſtans: </s>
            <s xml:space="preserve">quod uero eſt extra humi dum ſe-</s>
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