Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4135" xml:space="preserve">
              <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,
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            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-
              <lb/>
              <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"/>
              </figure>
            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
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            d c, d e planum ſecãs, ut
              <lb/>
            ſit ipſius, & </s>
            <s xml:id="echoid-s4156" xml:space="preserve">baſis a b c cõ
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            munis ſectio recta linea
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            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
              <lb/>
              <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">5. duode-
                <lb/>
              cimi.</note>
            </s>
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