Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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ARCHIMEDIS
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            extet ex humidi ſuperficie. </s>
            <s xml:space="preserve">conſiſtat autem humidum, ma
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            neatq;</s>
            <s xml:space="preserve">: & </s>
            <s xml:space="preserve">intelligatur aliquod planum ductum per centrũ
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            terræ, per humidum, & </s>
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              <lb/>
              <anchor type="figure" xlink:label="fig-0018-01a" xlink:href="fig-0018-01"/>
            per magnitudinem ſoli-
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            dam: </s>
            <s xml:space="preserve">à quo ſuperficies
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            quidem humidi ſecetur
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            ſecundum circunferen-
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            tiam a b c; </s>
            <s xml:space="preserve">ſolida autem
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            magnitudo ſecundum fi
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            guram, in qua r: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cen-
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            trum terræ ſit K. </s>
            <s xml:space="preserve">Intelli
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            gatur etiam quædam py
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            ramis comprehendens
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            figuram r, ſicuti prius, quæ pũctum K pro uertice habeat:
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            </s>
            <s xml:space="preserve">fecenturq; </s>
            <s xml:space="preserve">ipſius plana à ſuperficie plani a b c ſecundum
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            a K K b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſumatur pyramis alia æ qualis, & </s>
            <s xml:space="preserve">ſimilis ſuperio
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            ri, cuius plana ſecentur à plano a b c, ſecundum b K K c: </s>
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            deinde alterius ſphæræ ſuperficies quædam deſcribatur in
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            humido circa centrum K, ſub ſolida magnitudine: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſece-
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            tur ab eodem plano ſecundum x o p: </s>
            <s xml:space="preserve">poſtremo intelliga-
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            tur alia magnitudo h in poſteriori pyramide, quæ ex humi
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            do conſtet, & </s>
            <s xml:space="preserve">ſolidæ magnitudini r ſit æ qualis. </s>
            <s xml:space="preserve">partes igi-
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            tur humidi, & </s>
            <s xml:space="preserve">quæ in prima pyramide continetur ſuperfi-
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            cie x o; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ in ſecunda ſuperficie o p continetur, æquali
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            ter iacent, & </s>
            <s xml:space="preserve">continuatæ inter ſe ſe; </s>
            <s xml:space="preserve">non tamen ſimiliter
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            premuntur: </s>
            <s xml:space="preserve">nam quæ eſt in prima pyramide premitur ma
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            gnitudine ſolida r, & </s>
            <s xml:space="preserve">humido cõtinente ipſam, quod eſt in
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            loco pyramidis a b o x: </s>
            <s xml:space="preserve">quæ uero in altera pyramide pre-
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            mitur ſolida magnitudineh, & </s>
            <s xml:space="preserve">humido ipſam continente
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            in loco pyramidis p o b c. </s>
            <s xml:space="preserve">At grauitas ſolidæ magnitudi-
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            nis r, minor eſt grauitate humidi, in quo h: </s>
            <s xml:space="preserve">quoniam ma-
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            gnitudo ſolida mole quidem æqualis, & </s>
            <s xml:space="preserve">humido leuior po
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            nitur: </s>
            <s xml:space="preserve">grauitas autem humidi continentis magnitudines
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            r h eſt æqualis; </s>
            <s xml:space="preserve">cum pyramides æquales ſint. </s>
            <s xml:space="preserve">magis ergo</s>
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