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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          <head xml:id="echoid-head86" xml:space="preserve">THEOREMA X. PROPOSITIO XIIII.</head>
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            <s xml:id="echoid-s3761" xml:space="preserve">Cuiuslibet pyramidis, & </s>
            <s xml:id="echoid-s3762" xml:space="preserve">cuiuslibet coni, uel
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            coni portionis, centrum grauitatis in axe cõſiſtit.</s>
            <s xml:id="echoid-s3763" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3764" xml:space="preserve">SIT pyramis, cuius baſis triangulum a b c: </s>
            <s xml:id="echoid-s3765" xml:space="preserve">& </s>
            <s xml:id="echoid-s3766" xml:space="preserve">axis d e.
              <lb/>
            </s>
            <s xml:id="echoid-s3767" xml:space="preserve">Dico in linea d e ipſius grauitatis centrum ineſſe. </s>
            <s xml:id="echoid-s3768" xml:space="preserve">Si enim
              <lb/>
            fieri poteſt, ſit centrum f: </s>
            <s xml:id="echoid-s3769" xml:space="preserve">& </s>
            <s xml:id="echoid-s3770" xml:space="preserve">ab f ducatur ad baſim pyrami
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            dis linea f g, axi æquidiſtans: </s>
            <s xml:id="echoid-s3771" xml:space="preserve">iunctaq; </s>
            <s xml:id="echoid-s3772" xml:space="preserve">e g ad latera trian-
              <lb/>
            guli a b c producatur in h. </s>
            <s xml:id="echoid-s3773" xml:space="preserve">quam uero proportionem ha-
              <lb/>
            bet linea h e ad e g, habeat pyramis ad aliud ſolidum, in
              <lb/>
            quo K: </s>
            <s xml:id="echoid-s3774" xml:space="preserve">inſcribaturq; </s>
            <s xml:id="echoid-s3775" xml:space="preserve">in pyramide ſolida figura, & </s>
            <s xml:id="echoid-s3776" xml:space="preserve">altera cir
              <lb/>
            cumſcribatur ex priſmatibus æqualem habentibus altitu-
              <lb/>
            dinem, ita ut circumſcripta inſcriptam exuperet magnitu-
              <lb/>
            dine, quæ ſolido _k_ ſit minor. </s>
            <s xml:id="echoid-s3777" xml:space="preserve">Et quoniam in pyramide pla
              <lb/>
            num baſi æquidiſtans ductum ſectionem facit figuram ſi-
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            milem ei, quæ eſt baſis; </s>
            <s xml:id="echoid-s3778" xml:space="preserve">centrumq; </s>
            <s xml:id="echoid-s3779" xml:space="preserve">grauitatis in axe haben
              <lb/>
            tem: </s>
            <s xml:id="echoid-s3780" xml:space="preserve">erit priſmatis s t grauitatis centrũ in linear q; </s>
            <s xml:id="echoid-s3781" xml:space="preserve">priſ-
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            matis u x centrum in linea q p; </s>
            <s xml:id="echoid-s3782" xml:space="preserve">priſmatis y z in linea p o; </s>
            <s xml:id="echoid-s3783" xml:space="preserve">
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            priſmatis η θ in l_i_nea o n; </s>
            <s xml:id="echoid-s3784" xml:space="preserve">priſmatis λ μ in linea n m; </s>
            <s xml:id="echoid-s3785" xml:space="preserve">priſ-
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            matis ν π in m l; </s>
            <s xml:id="echoid-s3786" xml:space="preserve">& </s>
            <s xml:id="echoid-s3787" xml:space="preserve">denique priſmatis ρ σ in l e. </s>
            <s xml:id="echoid-s3788" xml:space="preserve">quare </s>
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