Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[71.] THEOREMA VI. PROPOSITIO VI.
Page: 127 (8)
[72.] THE OREMA VII. PROPOSITIO VII.
Page: 129 (9)
[73.] THE OREMA VIII. PROPOSITIO VIII.
Page: 131 (10)
[74.] THE OREMA IX. PROPOSITIO IX.
Page: 143 (15)
[75.] PROBLEMA I. PROPOSITIO X.
Page: 145 (17)
[76.] PROBLEMA II. PROPOSITIO XI.
Page: 146
[77.] PROBLEMA III. PROPOSITIO XII.
Page: 147 (18)
[78.] PROBLEMA IIII. PROPOSITIO XIII.
Page: 148
[79.] THEOREMA X. PROPOSITIO XIIII.
Page: 149 (19)
[80.] THE OREMA XI. PROPOSITIO XV.
Page: 153 (21)
[81.] THE OREMA XII. PROPOSITIO XVI.
Page: 154
[82.] THE OREMA XIII. PROPOSITIO XVII.
Page: 155 (22)
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
Page: 156
[84.] THEOREMA XV. PROPOSITIO XIX.
Page: 157 (23)
[85.] THE OREMA XVI. PROPOSITIO XX.
Page: 160
[86.] THEOREMA XVII. PROPOSITIO XXI.
Page: 164
[87.] THE OREMA XVIII. PROPOSITIO XXII.
Page: 166
[88.] THEOREMA XIX. PROPOSITIO XXIII.
Page: 171 (30)
[89.] PROBLEMA V. PROPOSITIO XXIIII.
Page: 172
[90.] THEOREMA XX. PROPOSITIO XXV.
Page: 174
[91.] THEOREMA XXI. PROPOSITIO XXVI.
Page: 180
[92.] THEOREMA XXII. PROPOSITIO XXVII.
Page: 187 (38)
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
Page: 192
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
Page: 194
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
Page: 201 (45)
[96.] THEOREMA XXV. PROPOSITIO XXXI.
Page: 203 (46)
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
Page: 205 (47)
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            <s xml:id="echoid-s4878" xml:space="preserve">
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            tionem cadet: </s>
            <s xml:id="echoid-s4879" xml:space="preserve">Itaque cum à portione conoidis, cuius gra-
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            uitatis centrum e auferatur inſcripta figura, centrum ha-
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            bens p: </s>
            <s xml:id="echoid-s4880" xml:space="preserve">& </s>
            <s xml:id="echoid-s4881" xml:space="preserve">ſit l e ad e p, ut figura inſcripta ad portiones reli
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            quas: </s>
            <s xml:id="echoid-s4882" xml:space="preserve">erit magnitudinis, quæ ex reliquis portionibus con
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            ſtat, centrum grauitatis punctum l, extra portionem ca-
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            dens. </s>
            <s xml:id="echoid-s4883" xml:space="preserve">quod fieri nequit. </s>
            <s xml:id="echoid-s4884" xml:space="preserve">ergo linea p e minor eſt ip ſa g li-
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            nea propoſita.</s>
            <s xml:id="echoid-s4885" xml:space="preserve"/>
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            <s xml:id="echoid-s4886" xml:space="preserve">Ex quibus perſpicuum eſt centrum grauitatis
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            figuræ inſcriptæ, & </s>
            <s xml:id="echoid-s4887" xml:space="preserve">circumſcriptæ eo magis acce
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            dere ad portionis centrum, quo pluribus cylin-
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            dris, uel cylindri portionibus conſtet: </s>
            <s xml:id="echoid-s4888" xml:space="preserve">fiatq́ figu
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            ra inſcripta maior, & </s>
            <s xml:id="echoid-s4889" xml:space="preserve">circumſcripta minor. </s>
            <s xml:id="echoid-s4890" xml:space="preserve">& </s>
            <s xml:id="echoid-s4891" xml:space="preserve">
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            quanquam continenter ad portionis centrū pro-
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            pius admoueatur nunquam tamen ad ipſum per
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            ueniet. </s>
            <s xml:id="echoid-s4892" xml:space="preserve">ſequeretur enim figuram inſcriptam, nó
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            ſolum portioni, ſed etiam circumſcriptæ figuræ
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            æqualem eſſe. </s>
            <s xml:id="echoid-s4893" xml:space="preserve">quod eſt abſurdum.</s>
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          <head xml:id="echoid-head101" xml:space="preserve">THE OREMA XXIII. PROPOSITIO XXIX.</head>
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              <emph style="sc">Cvivslibet</emph>
            portionis conoidis rectangu-
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            li axis à cẽtro grauitatis ita diuiditur, ut pars quæ
              <lb/>
            terminatur ad uerticem, reliquæ partis, quæ ad ba
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            ſim ſit dupla.</s>
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            <s xml:id="echoid-s4897" xml:space="preserve">SIT portio conoidis rectanguli uel abſciſſa plano ad
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            axem recto, uel non recto: </s>
            <s xml:id="echoid-s4898" xml:space="preserve">& </s>
            <s xml:id="echoid-s4899" xml:space="preserve">ſecta ipſa altero plano per axé
              <lb/>
            ſit ſuperſiciei ſe ctio a b c r ectanguli coni ſectio, uel parabo
              <lb/>
            le; </s>
            <s xml:id="echoid-s4900" xml:space="preserve">plani abſcindentis portionem ſectio ſit recta linea a c:
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            </s>
            <s xml:id="echoid-s4901" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s4902" xml:space="preserve">ſectionis diameter b d. </s>
            <s xml:id="echoid-s4903" xml:space="preserve">Sumatur autem
              <lb/>
            in linea b d punctum e, ita ut b e ſit ipſius e d dupla. </s>
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