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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            ioris baſis ad quadratum minoris: </s>
            <s xml:id="echoid-s5104" xml:space="preserve">centrum ſit in
              <lb/>
            eo axis puncto, quo ita diuiditur ut pars, quæ mi
              <lb/>
            norem baſim attingit ad alteram partem eandem
              <lb/>
            proportionem habeat, quam dempto quadrato
              <lb/>
            minoris baſis à duabus tertiis quadrati maioris,
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            habet id, quod reliquum eſt unà cum portione à
              <lb/>
            tertia quadrati maioris parte dempta, ad reliquà
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            eiuſdem tertiæ portionem.</s>
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            <s xml:id="echoid-s5106" xml:space="preserve">SIT fruſtum à portione rectanguli conoidis abſciſſum
              <lb/>
            a b c d, cuius maior baſis circulus, uel ellipſis circa diame-
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            trum b c, minor circa diametrum a d; </s>
            <s xml:id="echoid-s5107" xml:space="preserve">& </s>
            <s xml:id="echoid-s5108" xml:space="preserve">axis e f. </s>
            <s xml:id="echoid-s5109" xml:space="preserve">deſcriba-
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            tur autem portio conoidis, à quo illud abſciſſum eſt, & </s>
            <s xml:id="echoid-s5110" xml:space="preserve">pla-
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              <figure xlink:label="fig-0204-01" xlink:href="fig-0204-01a" number="150">
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            no per axem ducto ſecetur; </s>
            <s xml:id="echoid-s5111" xml:space="preserve">ut ſuperficiei ſectio ſit parabo-
              <lb/>
            le b g c, cuius diameter, & </s>
            <s xml:id="echoid-s5112" xml:space="preserve">axis portionis g f: </s>
            <s xml:id="echoid-s5113" xml:space="preserve">deinde g f diui
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            datur in puncto h, ita ut g h ſit dupla h f: </s>
            <s xml:id="echoid-s5114" xml:space="preserve">& </s>
            <s xml:id="echoid-s5115" xml:space="preserve">rurſus g e in ean
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            dem proportionem diuidatur: </s>
            <s xml:id="echoid-s5116" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s5117" xml:space="preserve">g _k_ ipſius k e dupla. </s>
            <s xml:id="echoid-s5118" xml:space="preserve">Iã
              <lb/>
            ex iis, quæ proxime demonſtrauimus, conſtat centrum gra
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            uitatis portionis b g c eſſe h punctum: </s>
            <s xml:id="echoid-s5119" xml:space="preserve">& </s>
            <s xml:id="echoid-s5120" xml:space="preserve">portionis a g c
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            punctum k. </s>
            <s xml:id="echoid-s5121" xml:space="preserve">ſumpto igitur infra h punctol, ita ut k h ad h </s>
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