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 |< < (40) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="92">
          <p>
            <s xml:space="preserve">
              <pb o="40" file="0191" n="191" rhead="DE CENTRO GRAVIT. SOLID."/>
            eſſe pun ctum g. </s>
            <s xml:space="preserve">Sequitur ergo uticoſahedri centrum gra
              <lb/>
            uitatis fit idem, quodipſius ſphæræ centrum.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">13. primi</note>
            <note position="left" xlink:label="note-0190-02" xlink:href="note-0190-02a" xml:space="preserve">14. primi</note>
            <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a">
              <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0190-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Sit dodecahedrum a ſin ſphæra deſignatum, ſitque ſphæ
              <lb/>
            ræ centrum m. </s>
            <s xml:space="preserve">Dico m centrum eſſe grauitatis ipſius do-
              <lb/>
            decahedri. </s>
            <s xml:space="preserve">Sit enim pentagonum a b c d e una ex duode-
              <lb/>
            cim baſibus ſolidi a f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a m producatur ad ſphæræ
              <lb/>
            ſuperficiem. </s>
            <s xml:space="preserve">cadetin angulum ipſi a oppoſitum; </s>
            <s xml:space="preserve">quod col-
              <lb/>
            ligitur ex decima ſeptima propoſitione tertiidecimilibri
              <lb/>
            elementorum. </s>
            <s xml:space="preserve">cadat in f. </s>
            <s xml:space="preserve">at ſi ab aliis angulis b c d e per cẽ
              <lb/>
            trum itidem lineæ ducantur ad ſuperficiem ſphæræ in pun
              <lb/>
            cta g h k l; </s>
            <s xml:space="preserve">cadent hæ in alios angulos baſis, quæ ipſi a b c d
              <lb/>
            baſi opponitur. </s>
            <s xml:space="preserve">tranſeant ergo per pentagona a b c d e,
              <lb/>
            f g h K l plana ſphæram ſecantia, quæ facient ſectiones cir-
              <lb/>
            culos æquales inter ſe ſe poſtea ducantur ex centro ſphæræ
              <lb/>
            m perpen diculares ad pla-
              <lb/>
              <anchor type="figure" xlink:label="fig-0191-01a" xlink:href="fig-0191-01"/>
            na dictorum circulorũ; </s>
            <s xml:space="preserve">ad
              <lb/>
            circulum quidem a b c d e
              <lb/>
            perpendicularis m n: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad
              <lb/>
            circulum f g h K l ipſa m o,
              <lb/>
              <anchor type="note" xlink:label="note-0191-01a" xlink:href="note-0191-01"/>
            erunt puncta n o circulorũ
              <lb/>
            centra: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">lineæ m n, m o in
              <lb/>
            ter ſe æquales: </s>
            <s xml:space="preserve">quòd circu-
              <lb/>
            li æquales ſint. </s>
            <s xml:space="preserve">Eodem mo
              <lb/>
              <anchor type="note" xlink:label="note-0191-02a" xlink:href="note-0191-02"/>
            do, quo ſupra, demonſtrabi
              <lb/>
            mus lineas m n, m o in unã
              <lb/>
            atque eandem lineam con-
              <lb/>
            uenire. </s>
            <s xml:space="preserve">ergo cum puncta n o ſint centra circulorum, con-
              <lb/>
            ſtat ex prima huius & </s>
            <s xml:space="preserve">pentagonorũ grauitatis eſſe centra:
              <lb/>
            </s>
            <s xml:space="preserve">idcircoq; </s>
            <s xml:space="preserve">m n, m o pyramidum a b c d e m, ſ g h _K_ l m axes. </s>
            <s xml:space="preserve">
              <lb/>
            ponatur a b c d e m pyramidis grauitatis centrum p: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">py
              <lb/>
            ramidis f g h
              <emph style="sc">K</emph>
            l m ipſum q centrum. </s>
            <s xml:space="preserve">erunt p m, m q æqua-
              <lb/>
            les, & </s>
            <s xml:space="preserve">punctum m grauitatis centrum magnitudinis, quæ
              <lb/>
            ex ipſis pyramidibus conſtat. </s>
            <s xml:space="preserve">eodẽ modo probabitur qua-
              <lb/>
            rumlibet pyramidum, quæ è regione opponuntur, centrũ</s>
          </p>
        </div>
      </text>
    </echo>