Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < (43) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div281" type="section" level="1" n="94">
          <p>
            <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>
          </p>
        </div>
      </text>
    </echo>
Impressum