Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4926" xml:space="preserve">
              <pb o="43" file="0197" n="197" rhead="DE CENTRO GRAVIT. SOLID."/>
            b m. </s>
            <s xml:id="echoid-s4927" xml:space="preserve">ergo circulus a c circuli _k_ g: </s>
            <s xml:id="echoid-s4928" xml:space="preserve">& </s>
            <s xml:id="echoid-s4929" xml:space="preserve">idcirco cylindrus
              <lb/>
            a h cylindri _k_ l duplus erit. </s>
            <s xml:id="echoid-s4930" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s4931" xml:space="preserve">linea o p dupla
              <lb/>
            ipſius p n. </s>
            <s xml:id="echoid-s4932" xml:space="preserve">Deinde inſcripta & </s>
            <s xml:id="echoid-s4933" xml:space="preserve">circumſcripta portioni
              <lb/>
            alia figura, ita ut inſcripta conſtituatur ex tribus cylin-
              <lb/>
            dris q r, s g, tu: </s>
            <s xml:id="echoid-s4934" xml:space="preserve">circumſcripta uero ex quatuor a x, y z,
              <lb/>
            _K_ ν, θ λ: </s>
            <s xml:id="echoid-s4935" xml:space="preserve">diuidantur b o, o m, m n, n d bifariam in punctis
              <lb/>
            μ ν π ρ. </s>
            <s xml:id="echoid-s4936" xml:space="preserve">Itaque cylindri θ λ centrum grauitætis eſt punctum
              <lb/>
            μ: </s>
            <s xml:id="echoid-s4937" xml:space="preserve">& </s>
            <s xml:id="echoid-s4938" xml:space="preserve">cylindri
              <emph style="sc">K</emph>
            ν centrum ν. </s>
            <s xml:id="echoid-s4939" xml:space="preserve">ergo ſi linea μ ν diuidatur in σ,
              <lb/>
            ita ut μ σ ad σ ν proportionẽ eã habeat, quam cylindrus K ν
              <lb/>
            ad cylindrum θ λ, uidelicet quam quadratum
              <emph style="sc">K</emph>
            m ad qua-
              <lb/>
            dratum θ o, hoc eſt, quam linea m b ad b o: </s>
            <s xml:id="echoid-s4940" xml:space="preserve">erit σ centrum
              <lb/>
              <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">20. primi
                <lb/>
              conicorũ</note>
            magnitudinis compoſitæ ex cylindris
              <emph style="sc">K</emph>
            ν, θ λ. </s>
            <s xml:id="echoid-s4941" xml:space="preserve">& </s>
            <s xml:id="echoid-s4942" xml:space="preserve">cum linea
              <lb/>
            m b ſit dupla b o, erit & </s>
            <s xml:id="echoid-s4943" xml:space="preserve">μ σ ipſius σ ν dupla. </s>
            <s xml:id="echoid-s4944" xml:space="preserve">præterea quo-
              <lb/>
            niam cylindri y z centrum grauitatis eſt π, linea σ π ita diui
              <lb/>
            ſa in τ, ut σ τ ad τ π eam habeat proportionem, quam cylin
              <lb/>
            drus y z ad duos cylindros K ν, θ λ: </s>
            <s xml:id="echoid-s4945" xml:space="preserve">erit τ centrum magnitu
              <lb/>
            dinis, quæ ex dictis tribus cylindris conſtat. </s>
            <s xml:id="echoid-s4946" xml:space="preserve">cylindrus au-
              <lb/>
            tẽ y z ad cylindrum θ λ eſt, ut linea n b ad b o, hoc eſt ut 3
              <lb/>
            ad 1: </s>
            <s xml:id="echoid-s4947" xml:space="preserve">& </s>
            <s xml:id="echoid-s4948" xml:space="preserve">ad cylindrum k ν, ut n b ad b m, uidelicet ut 3 ad 2.
              <lb/>
            </s>
            <s xml:id="echoid-s4949" xml:space="preserve">quare y z cylĩdrus duobus cylindris k ν, θ λ æqualis erit. </s>
            <s xml:id="echoid-s4950" xml:space="preserve">& </s>
            <s xml:id="echoid-s4951" xml:space="preserve">
              <lb/>
            propterea linea σ τ æqualis ipſi τ π. </s>
            <s xml:id="echoid-s4952" xml:space="preserve">denique cylindri a x
              <lb/>
            centrum grauitatis eſt punctum ρ. </s>
            <s xml:id="echoid-s4953" xml:space="preserve">& </s>
            <s xml:id="echoid-s4954" xml:space="preserve">cum τ ζ diuiſa fuerit
              <lb/>
            in eã proportionem, quam habet cylindrus a x ad tres cy-
              <lb/>
            lindros y z, _k_ ν, θ λ: </s>
            <s xml:id="echoid-s4955" xml:space="preserve">erit in eo puncto centrum grauitatis
              <lb/>
            totius figuræ circũſcriptæ. </s>
            <s xml:id="echoid-s4956" xml:space="preserve">Sed cylindrus a x ad ipſum y z
              <lb/>
            eſt ut linea d b ad b n: </s>
            <s xml:id="echoid-s4957" xml:space="preserve">hoc eſt ut 4 ad 3: </s>
            <s xml:id="echoid-s4958" xml:space="preserve">& </s>
            <s xml:id="echoid-s4959" xml:space="preserve">duo cylindri _k_ ν
              <lb/>
            θ λ cylindro y z ſunt æquales. </s>
            <s xml:id="echoid-s4960" xml:space="preserve">cylindrns igitur a x ad tres
              <lb/>
            iam dictos cylindros eſt ut 2 ad 3. </s>
            <s xml:id="echoid-s4961" xml:space="preserve">Sed quoniã μ σ eſt dua-
              <lb/>
            rum partium, & </s>
            <s xml:id="echoid-s4962" xml:space="preserve">σ ν unius, qualium μ π eſt ſex; </s>
            <s xml:id="echoid-s4963" xml:space="preserve">erit σ π par-
              <lb/>
            tium quatuor: </s>
            <s xml:id="echoid-s4964" xml:space="preserve">proptereaq; </s>
            <s xml:id="echoid-s4965" xml:space="preserve">τ π duarum, & </s>
            <s xml:id="echoid-s4966" xml:space="preserve">ν π, hoc eſt π ρ
              <lb/>
            trium. </s>
            <s xml:id="echoid-s4967" xml:space="preserve">quare ſequitur ut punctum π totius figuræ circum
              <lb/>
            ſcriptæ ſit centrum. </s>
            <s xml:id="echoid-s4968" xml:space="preserve">Itaque fiat ν υ ad υ π, ut μ σ ad σ ν. </s>
            <s xml:id="echoid-s4969" xml:space="preserve">& </s>
            <s xml:id="echoid-s4970" xml:space="preserve">υ ρ
              <lb/>
            bifariam diuidatur in φ. </s>
            <s xml:id="echoid-s4971" xml:space="preserve">Similiter ut in circumſcripta figu
              <lb/>
            ra oſtendetur centrum magnitudinis compoſitæ ex </s>
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