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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              <pb o="28" file="0167" n="167" rhead="DE CENTRO GRAVIT. SOLID."/>
            uel coni portionis axis à centro grauitatis ita diui
              <lb/>
            ditur, ut pars, quæ terminatur ad uerticem reli-
              <lb/>
            quæ partis, quæ ad baſim, ſit tripla.</s>
            <s xml:id="echoid-s4136" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4137" xml:space="preserve">Sit pyramis, cuius baſis triangulum a b c; </s>
            <s xml:id="echoid-s4138" xml:space="preserve">axis d e; </s>
            <s xml:id="echoid-s4139" xml:space="preserve">& </s>
            <s xml:id="echoid-s4140" xml:space="preserve">gra
              <lb/>
            uitatis centrum _K_. </s>
            <s xml:id="echoid-s4141" xml:space="preserve">Dico lineam d k ipſius _K_ e triplam eſſe.
              <lb/>
            </s>
            <s xml:id="echoid-s4142" xml:space="preserve">trianguli enim b d c centrum grauitatis ſit punctum f; </s>
            <s xml:id="echoid-s4143" xml:space="preserve">triã
              <lb/>
            guli a d c centrũ g; </s>
            <s xml:id="echoid-s4144" xml:space="preserve">& </s>
            <s xml:id="echoid-s4145" xml:space="preserve">trianguli a d b ſit h: </s>
            <s xml:id="echoid-s4146" xml:space="preserve">& </s>
            <s xml:id="echoid-s4147" xml:space="preserve">iungantur a f,
              <lb/>
            b g, c h. </s>
            <s xml:id="echoid-s4148" xml:space="preserve">Quoniam igitur centrũ grauitatis pyramidis in axe
              <lb/>
            cõſiſtit: </s>
            <s xml:id="echoid-s4149" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s4150" xml:space="preserve">d e, a f, b g, c h eiuſdẽ pyramidis axes: </s>
            <s xml:id="echoid-s4151" xml:space="preserve">conue
              <lb/>
              <note position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">17. huíus</note>
            nient omnes in idẽ punctũ _k_, quod eſt grauitatis centrum.
              <lb/>
            </s>
            <s xml:id="echoid-s4152" xml:space="preserve">Itaque animo concipiamus hanc pyramidem diuiſam in
              <lb/>
            quatuor pyramides, quarum baſes ſint ipſa pyramidis
              <lb/>
            triangula; </s>
            <s xml:id="echoid-s4153" xml:space="preserve">& </s>
            <s xml:id="echoid-s4154" xml:space="preserve">axis pun-
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              <handwritten xlink:label="hd-0167-01" xlink:href="hd-0167-01a" number="8"/>
              <figure xlink:label="fig-0167-01" xlink:href="fig-0167-01a" number="123">
                <image file="0167-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0167-01"/>
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            ctum k quæ quidem py-
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            ramides inter ſe æquales
              <lb/>
            ſunt, ut demõſtrabitur.
              <lb/>
            </s>
            <s xml:id="echoid-s4155" xml:space="preserve">Ducatur enĩ per lineas
              <lb/>
            d c, d e planum ſecãs, ut
              <lb/>
            ſit ipſius, & </s>
            <s xml:id="echoid-s4156" xml:space="preserve">baſis a b c cõ
              <lb/>
            munis ſectio recta linea
              <lb/>
            c e l: </s>
            <s xml:id="echoid-s4157" xml:space="preserve">eiuſdẽ uero & </s>
            <s xml:id="echoid-s4158" xml:space="preserve">triã-
              <lb/>
            guli a d b ſitlinea d h l. </s>
            <s xml:id="echoid-s4159" xml:space="preserve">
              <lb/>
            erit linea a l æqualis ipſi
              <lb/>
            l b: </s>
            <s xml:id="echoid-s4160" xml:space="preserve">nam centrum graui-
              <lb/>
            tatis trianguli conſiſtit
              <lb/>
            in linea, quæ ab angulo
              <lb/>
            ad dimidiam baſim per-
              <lb/>
            ducitur, ex tertia deci-
              <lb/>
            ma Archimedis. </s>
            <s xml:id="echoid-s4161" xml:space="preserve">quare
              <lb/>
              <note position="right" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">1. ſexti.</note>
            triangulum a c l æquale
              <lb/>
            eſt triangulo b c l: </s>
            <s xml:id="echoid-s4162" xml:space="preserve">& </s>
            <s xml:id="echoid-s4163" xml:space="preserve">propterea pyramis, cuius baſis trian-
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            gulum a c l, uertex d, eſt æqualis pyramidi, cuius baſis b c l
              <lb/>
            triangulum, & </s>
            <s xml:id="echoid-s4164" xml:space="preserve">idem uertex. </s>
            <s xml:id="echoid-s4165" xml:space="preserve">pyramides enim, quæ ab eodẽ
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              <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">5. duode-
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              cimi.</note>
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