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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FED. COMMANDINI
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              <pb file="0190" n="190" rhead="FED. COMMANDINI"/>
            ctiones circuli ex prima propofitione ſphæricorum Theo
              <lb/>
            doſii: </s>
            <s xml:space="preserve">unus quidem circa triangulum a b c deſcriptus: </s>
            <s xml:space="preserve">al-
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            ter uero circa d e f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam triangula a b c, d e f æqua-
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            lia ſunt, & </s>
            <s xml:space="preserve">ſimilia; </s>
            <s xml:space="preserve">erunt ex prima, & </s>
            <s xml:space="preserve">ſecunda propoſitione
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            duodecimi libri elementorum, circuli quoque inter ſe ſe
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            æquales. </s>
            <s xml:space="preserve">poſtremo a centro g ad circulum a b c perpendi
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            cularis ducatur g h; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia perpendicularis ducatur ad cir
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            culum d e f, quæ ſit g _k_; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur a h, d k. </s>
            <s xml:space="preserve">perſpicuum
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            eſt ex corollario primæ ſphæricorum Theodoſii, punctum
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            h centrum eſſe circuli a b c, & </s>
            <s xml:space="preserve">k centrum circuli d e f. </s>
            <s xml:space="preserve">Quo
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            niam igitur triangulorum g a h, g d K latus a g eſt æquale la
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            teri g d; </s>
            <s xml:space="preserve">ſunt enim à centro ſphæræ ad ſuperficiem: </s>
            <s xml:space="preserve">atque
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            eſt a h æquale d k: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex ſexta propoſitione libri primi ſphæ
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            ricorum Theodoſii g h ipſi g K: </s>
            <s xml:space="preserve">triangulum g a h æquale
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            erit, & </s>
            <s xml:space="preserve">ſimile g d k triangulo: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">angulus a g h æqualis an-
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            gulo d g _K_. </s>
            <s xml:space="preserve">ſed anguli a g h, h g d ſunt æquales duobus re-
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              <anchor type="note" xlink:label="note-0190-01a" xlink:href="note-0190-01"/>
            ctis. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ipſi h g d, d g k duobus rectis æquales erunt.
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco h g, g _K_ una, atque eadem erit linea. </s>
            <s xml:space="preserve">cum autem
              <lb/>
              <anchor type="note" xlink:label="note-0190-02a" xlink:href="note-0190-02"/>
            h ſit centrũ circuli, & </s>
            <s xml:space="preserve">tri-
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              <anchor type="figure" xlink:label="fig-0190-01a" xlink:href="fig-0190-01"/>
            anguli a b c grauitatis cen
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            trũ probabitur ex iis, quæ
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            in prima propoſitione hu
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            ius tradita funt. </s>
            <s xml:space="preserve">quare g h
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            erit pyramidis a b c g axis.
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ob eandem cauſſam g k
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            axis pyramidis d e f g. </s>
            <s xml:space="preserve">Ita-
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            que centrum grauitatis py
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            ramidis a b c g ſit púctum
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            l, & </s>
            <s xml:space="preserve">pyramidis d e f g ſit m. </s>
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              <lb/>
            Similiter ut ſupra demon-
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            ſtrabimus m g, g linter ſe æquales eſſe, & </s>
            <s xml:space="preserve">punctum g graui
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            tatis centrum magnitudinis, quæ ex utriſque pyramidibus
              <lb/>
            conſtat. </s>
            <s xml:space="preserve">eodem modo demonſtrabitur, quarumcunque
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            duarum pyramidum, quæ opponuntur, grauitatis centrũ</s>
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