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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            <s xml:id="echoid-s1287" xml:space="preserve">
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            tur ex parte 1. </s>
            <s xml:id="echoid-s1288" xml:space="preserve">Quod ſi n o non ſecuerit ipſam ω k,
              <lb/>
            eadem nihilominus demonſtrabuntur.</s>
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          <head xml:id="echoid-head41" xml:space="preserve">PROPOSITIO VIII.</head>
          <p>
            <s xml:id="echoid-s1290" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            axem habuerit maiorem quidem, quàm ſeſqui-
              <lb/>
            alterum eius, quæ uſque ad axem; </s>
            <s xml:id="echoid-s1291" xml:space="preserve">minorem ue-
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            ro, quàm ut ad eam, quæ uſque ad axem propor-
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            tionem habeat, quam quindecim ad quatuor: </s>
            <s xml:id="echoid-s1292" xml:space="preserve">ſi
              <lb/>
            in grauitate ad humidum habeat proportionem
              <lb/>
            minorem ea, quam quadratum, quod fit ab exceſ
              <lb/>
            ſu, quo axis maior eſt, quàm ſeſquialter eius, quæ
              <lb/>
            uſque ad axem, habet ad quadratum, quod ab
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            axe: </s>
            <s xml:id="echoid-s1293" xml:space="preserve">demiſſa in humidum, ita ut baſis ipſius humi
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            dum non contingat; </s>
            <s xml:id="echoid-s1294" xml:space="preserve">neque in rectum reſtitue-
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            tur, neque manebit inclinata, niſi quando axis
              <lb/>
            cum ſuperficie humidi angulum fecerit æqualẽ
              <lb/>
            ei, de quo infra dicetur.</s>
            <s xml:id="echoid-s1295" xml:space="preserve"/>
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            <s xml:id="echoid-s1296" xml:space="preserve">SIT portio qualis dicta eſt; </s>
            <s xml:id="echoid-s1297" xml:space="preserve">ſitque b d æqualis axi: </s>
            <s xml:id="echoid-s1298" xml:space="preserve">& </s>
            <s xml:id="echoid-s1299" xml:space="preserve">
              <lb/>
            b k quidem dupla ipſius _K_ d: </s>
            <s xml:id="echoid-s1300" xml:space="preserve">r _K_ uero æqualis ei, quæ uſ-
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            que ad axem: </s>
            <s xml:id="echoid-s1301" xml:space="preserve">& </s>
            <s xml:id="echoid-s1302" xml:space="preserve">ſit c b ſeſquialtera b r. </s>
            <s xml:id="echoid-s1303" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s1304" xml:space="preserve">c d ipſius
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            _k_ r ſeſquialtera. </s>
            <s xml:id="echoid-s1305" xml:space="preserve">Quam uero portionem habet portio ad
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              <note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">A</note>
            humidum in grauitate, habeat quadratum f q ad quadra-
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            tum d b: </s>
            <s xml:id="echoid-s1306" xml:space="preserve">& </s>
            <s xml:id="echoid-s1307" xml:space="preserve">ſit f dupla ipſius q. </s>
            <s xml:id="echoid-s1308" xml:space="preserve">perſpicuum igitur eſt f q
              <lb/>
            ad d b proportionem minorem habere ea, quam habet
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            c b ad b d. </s>
            <s xml:id="echoid-s1309" xml:space="preserve">eſt enim c b exceſſus, quo axis maior eſt, quàm
              <lb/>
            ſeſquialter eins, quæ uſque ad axem: </s>
            <s xml:id="echoid-s1310" xml:space="preserve">quare f q minor eſt
              <lb/>
              <note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">B</note>
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