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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            <s xml:id="echoid-s3103" xml:space="preserve">
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            teſt in portione, quæ recta linea & </s>
            <s xml:id="echoid-s3104" xml:space="preserve">obtuſianguli coni ſe-
              <lb/>
            ctione, ſeu hyperbola continetur.</s>
            <s xml:id="echoid-s3105" xml:space="preserve"/>
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        <div xml:id="echoid-div204" type="section" level="1" n="67">
          <head xml:id="echoid-head74" xml:space="preserve">THE OREMA IIII. PROPOSITIO IIII.</head>
          <p>
            <s xml:id="echoid-s3106" xml:space="preserve">
              <emph style="sc">In</emph>
            circulo & </s>
            <s xml:id="echoid-s3107" xml:space="preserve">ellipſiidem eſt figuræ & </s>
            <s xml:id="echoid-s3108" xml:space="preserve">graui-
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            tatis centrum.</s>
            <s xml:id="echoid-s3109" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3110" xml:space="preserve">SIT circulus, uel ellipſis, cuius centrum a. </s>
            <s xml:id="echoid-s3111" xml:space="preserve">Dico a gra-
              <lb/>
            uitatis quoque centrum eſſe. </s>
            <s xml:id="echoid-s3112" xml:space="preserve">Si enim fieri poteſt, ſit b cen-
              <lb/>
            trum grauitatis: </s>
            <s xml:id="echoid-s3113" xml:space="preserve">& </s>
            <s xml:id="echoid-s3114" xml:space="preserve">iuncta a b extra figuram in c produca
              <lb/>
            tur: </s>
            <s xml:id="echoid-s3115" xml:space="preserve">quam uero proportionem habetlinea c a ad a b, ha-
              <lb/>
            beat circulus a ad alium circulum, in quo d; </s>
            <s xml:id="echoid-s3116" xml:space="preserve">uel ellipſis ad
              <lb/>
            aliam ellipſim: </s>
            <s xml:id="echoid-s3117" xml:space="preserve">& </s>
            <s xml:id="echoid-s3118" xml:space="preserve">in circulo, uel ellipſi ſigura rectilinea pla-
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            ne deſcribatur adeo, ut tandem relinquantur portiones
              <lb/>
            quædam minores circulo, uel ellipſid; </s>
            <s xml:id="echoid-s3119" xml:space="preserve">quæ figura ſit e f g
              <lb/>
            h _k_ l m n. </s>
            <s xml:id="echoid-s3120" xml:space="preserve">Illud uero in circulo fieri poſſe ex duodecimo
              <lb/>
            elementorum libro, propoſitione ſecunda manifeſte con-
              <lb/>
            ſtat; </s>
            <s xml:id="echoid-s3121" xml:space="preserve">at in ellipſi nos demonſtra-
              <lb/>
              <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="78">
                <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0122-01"/>
              </figure>
            uinius in commentariis in quin-
              <lb/>
            tam propoſitionem Archimedis
              <lb/>
            de conoidibus, & </s>
            <s xml:id="echoid-s3122" xml:space="preserve">ſphæroidibus.
              <lb/>
            </s>
            <s xml:id="echoid-s3123" xml:space="preserve">erit igitur a centrum grauitatis
              <lb/>
            ipſius figuræ, quod proxime oſtē
              <lb/>
            dimus. </s>
            <s xml:id="echoid-s3124" xml:space="preserve">Itaque quoniam circulus
              <lb/>
            a ad circulum d; </s>
            <s xml:id="echoid-s3125" xml:space="preserve">uel ellipſis a ad
              <lb/>
            ellipſim d eandem proportionē
              <lb/>
            habet, quam linea c a ad a b: </s>
            <s xml:id="echoid-s3126" xml:space="preserve">
              <lb/>
            portiones uero ſunt minores cir
              <lb/>
              <note position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">8. quinti.</note>
            culo uel ellipſi d: </s>
            <s xml:id="echoid-s3127" xml:space="preserve">habebit circu-
              <lb/>
            lus, uel ellipſis ad portiones ma-
              <lb/>
            iorem proportionem, quàm c a
              <lb/>
              <note position="left" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">19. quinti
                <lb/>
              apud Cã
                <lb/>
              panum.</note>
            ad a b: </s>
            <s xml:id="echoid-s3128" xml:space="preserve">& </s>
            <s xml:id="echoid-s3129" xml:space="preserve">diuidendo figura recti-
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            linea e f g h _k_ l m n ad </s>
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