Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000729">
                <pb xlink:href="023/01/078.jpg"/>
              nis, quouſque in unum punctum r conueniant; erit pyra­
                <lb/>
              midis abcr, & pyramidis defr grauitatis centrum in li­
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              nea rh. </s>
              <s id="s.000730">ergo & reliquæ magnitudinis, uidelicet fruſti cen­
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              trum in eadem linea neceſſario comperietur. </s>
              <s id="s.000731">Iungantur
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              db, dc, dh, dm: & per lineas db, dc ducto altero plano
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              intelligatur fruſtum in duas pyramides diuiſum: in pyra­
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              midem quidem, cuius baſis eſt triangulum abc, uertex d:
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              & in eam, cuius idem uertex, & baſis trapezium bcfe. </s>
              <s id="s.000732">erit
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              igitur pyramidis abcd axis dh, & pyramidis bcfed axis
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              d m: atque erunt tres axes gh, dh, dm in eodem plano
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              daKl.</s>
              <s id="s.000733"> ducatur præterea per o linea ſt ipſi aK
                <expan abbr="æquidiſtãs">æquidiſtans</expan>
              ,
                <lb/>
              quæ lineam dh in u ſecet: per p uero ducatur xy æquidi­
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                <figure id="id.023.01.078.1.jpg" xlink:href="023/01/078/1.jpg" number="69"/>
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              ſtans eidem, ſecansque dm in
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              z: & iungatur zu, quæ ſecet
                <lb/>
              gh in
                <foreign lang="grc">φ.</foreign>
              tranſibit ea per q: &
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              erunt
                <foreign lang="grc">φ</foreign>
              q unum, atque idem
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              punctum; ut inferius appare­
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              bit. </s>
              <s id="s.000734">Quoniam igitur linea uo
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                <arrow.to.target n="marg89"/>
                <lb/>
              æquidiſtat ipſi dg, erit du ad
                <lb/>
              uh, ut go ad oh. </s>
              <s id="s.000735">Sed go tri­
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              pla eſt oh. </s>
              <s id="s.000736">quare & du ipſius
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              uh eſt tripla: & ideo pyrami­
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              dis abcd centrum grauitatis
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              erit punctum u. </s>
              <s id="s.000737">Rurſus quo­
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              niam zy ipſi dl æquidiſtat, dz
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              ad zm eſt, ut ly ad ym: eſtque
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              ly ad ym, ut gp ad pn. </s>
              <s id="s.000738">ergo
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              dz ad zm eſt, ut gp ad pn. </s>
              <lb/>
              <s id="s.000739">Quòd cum gp ſit tripla pn;
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              erit etiam dz ipſius zm tri­
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              pla. </s>
              <s id="s.000740">atque ob eandem cauſ­
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              ſam punctum z eſt
                <expan abbr="centrũ">centrum</expan>
              gra­
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              uitatis pyramidis bcfed. </s>
              <s id="s.000741">iun
                <lb/>
              cta igitur zu, in ea erit
                <expan abbr="cẽtrum">centrum</expan>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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