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 CENTRO GRA VIT. SOLID.
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              <pb o="38" file="0187" n="187" rhead="DE CENTRO GRA VIT. SOLID."/>
            ad portiones ſolidas maiorem habet proportioné, quàm
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            n l ad l m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo fruſtum pyramidis ad dictas por-
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            tiones maiorem proportionem habet, quàm n m ad m l.
              <lb/>
            </s>
            <s xml:space="preserve">fiat igitur ut fruſtum pyramidis ad portiones, ita q m ad
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            m l. </s>
            <s xml:space="preserve">Itaque quoniam à fruſto coni, uel coni portionis a d,
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            cuius grauitatis centrum eſtm, aufertur fruſtum pyrami-
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            dis habens centruml; </s>
            <s xml:space="preserve">erit reliquæ magnitudinis, quæ ex
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            portionibus ſolidis conſtat; </s>
            <s xml:space="preserve">grauitatis cẽtrum in linea l m
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            producta, atque in puncto q, extra figuram poſito. </s>
            <s xml:space="preserve">quod
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            fieri nullo modo poteſt. </s>
            <s xml:space="preserve">relinquitur ergo, ut punctum l ſit
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            fruſti a d grauitatis centrum. </s>
            <s xml:space="preserve">quæ omnia demonſtranda
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            proponebantur.</s>
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          </p>
          <div type="float" level="2" n="3">
            <figure xlink:label="fig-0186-01" xlink:href="fig-0186-01a">
              <image file="0186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0186-01"/>
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            <note position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">22. huius</note>
            <note position="left" xlink:label="note-0186-02" xlink:href="note-0186-02a" xml:space="preserve">19. quinti</note>
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        <div type="section" level="1" n="92">
          <head xml:space="preserve">THEOREMA XXII. PROPOSITIO XXVII.</head>
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              <emph style="sc">Omnivm</emph>
            ſolidorum in ſphæra deſcripto-
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            rum, quæ æqualibus, & </s>
            <s xml:space="preserve">ſimilibus baſibus conti-
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            nentur, centrum grauitatis eſt idem, quod ſphæ-
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            ræ centrum.</s>
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          </p>
          <p>
            <s xml:space="preserve">Solida eiuſmodi corpora regularia appellare ſolent, de
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            quibus agitur in tribus ultimis libris elementorum: </s>
            <s xml:space="preserve">ſunt
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            autem numero quinque, tetrahedrum, uel pyramis, hexa-
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            hedrum, uel cubus, octahedrum, dodecahedrum, & </s>
            <s xml:space="preserve">icoſa-
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            hedrum.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sit primo a b c d pyramis ĩ ſphæra deſcripta, cuíus ſphæ
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            ræ centrum ſit e. </s>
            <s xml:space="preserve">Dico e pyramidis a b c d grauitatis eſſe
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            centrum. </s>
            <s xml:space="preserve">Si enim iuncta d e producatur ad baſim a b c in
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            f; </s>
            <s xml:space="preserve">ex iis, quæ demonſtrauit Campanus in quartodecimo li
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            bro elementorum, propoſitione decima quinta, & </s>
            <s xml:space="preserve">decima
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            ſeptima, erit f centrum circuli circa triangulum a b c de-
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            ſcripti: </s>
            <s xml:space="preserve">atque erit e f ſexta pars ipſius ſphæræ axis. </s>
            <s xml:space="preserve">quare
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            ex prima huius conſtat trianguli a b c grauitatis centrum
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            eſſe punctum f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco lineam d f eſſe pyramidis axem.</s>
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