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-s4256" xml:space="preserve">
              <pb file="0170" n="170" rhead="FED. COMMANDINI"/>
            & </s>
            <s xml:id="echoid-s4257" xml:space="preserve">denique punctum h pyramidis a b c d e f grauitatis eſſe
              <lb/>
            centrum, & </s>
            <s xml:id="echoid-s4258" xml:space="preserve">ita in aliis.</s>
            <s xml:id="echoid-s4259" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4260" xml:space="preserve">Sit conus, uel coni portio axem habens b d: </s>
            <s xml:id="echoid-s4261" xml:space="preserve">ſecetur que
              <lb/>
            plano per axem, quod ſectionem faciat triangulum a b c:
              <lb/>
            </s>
            <s xml:id="echoid-s4262" xml:space="preserve">& </s>
            <s xml:id="echoid-s4263" xml:space="preserve">b d axis diuidatur in e, ita ut b e ipſius e d ſit tripla. </s>
            <s xml:id="echoid-s4264" xml:space="preserve">
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            Dico punctum e coni, uel coni portionis, grauitatis
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            eſſe centrum. </s>
            <s xml:id="echoid-s4265" xml:space="preserve">Sienim fieri poteſt, ſit centrum f: </s>
            <s xml:id="echoid-s4266" xml:space="preserve">& </s>
            <s xml:id="echoid-s4267" xml:space="preserve">pro-
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            ducatur e f extra figuram in g. </s>
            <s xml:id="echoid-s4268" xml:space="preserve">quam uero proportionem
              <lb/>
            habet g e ad e f, habeat baſis coni, uel coni portionis, hoc
              <lb/>
            eſt circulus, uel ellipſis circa diametrum a c ad aliud ſpa-
              <lb/>
            cium, in quo h. </s>
            <s xml:id="echoid-s4269" xml:space="preserve">Itaque in circulo, uel ellipſi plane deſcri-
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            batur rectilinea figura a k l m c n o p, ita ut quæ relinquũ-
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            tur portiones ſint minores ſpacio h: </s>
            <s xml:id="echoid-s4270" xml:space="preserve">& </s>
            <s xml:id="echoid-s4271" xml:space="preserve">intelligatur pyra-
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            mis baſim habens rectilineam figuram a K l m c n o p, & </s>
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              <lb/>
            axem b d; </s>
            <s xml:id="echoid-s4273" xml:space="preserve">cuius quidem grauitatis centrum erit punctum
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            e, ut iam demonſtrauimus. </s>
            <s xml:id="echoid-s4274" xml:space="preserve">Et quoniam portiones ſunt
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            minores ſpacio h, circulus, uel ellipſis ad portiones ma-
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              <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a" number="125">
                <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0170-01"/>
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            iorem proportionem habet, quam g e a d e f. </s>
            <s xml:id="echoid-s4275" xml:space="preserve">ſed ut circu-
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            lus, uel ellipſis ad figuram rectilineam ſibi inſcriptam, ita
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            conus, uel coni portio ad pyramidem, quæ figuram rectili-
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            neam pro baſi habet; </s>
            <s xml:id="echoid-s4276" xml:space="preserve">& </s>
            <s xml:id="echoid-s4277" xml:space="preserve">altitudinem æqualem: </s>
            <s xml:id="echoid-s4278" xml:space="preserve">etenim </s>
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