Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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            <p type="main">
              <s id="s.000774">
                <pb pagenum="37" xlink:href="023/01/081.jpg"/>
              ducta ſuerint, ita ut in unum punctum y coeant, erunt
                <expan abbr="triã">trian</expan>
                <lb/>
              gula uyl, xyp, tyk inter ſe ſimilia: & ſimilia etiam triangu
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              la lyr, pys, kyq quare ut in 19 huius, demonſtrabitur
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              xp, ad ps:
                <expan abbr="itemq;">itemque</expan>
              tk ad kq eandem habere
                <expan abbr="proportionẽ">proportionem</expan>
              ,
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              quam ul ad lr. </s>
              <s id="s.000775">Sed ut ul ad lr, ita eſt triangulum abc ad
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              triangulum acd: & ut tk ad Kq, ita triangulum efg ad
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              triangulum egh. </s>
              <s id="s.000776">Vt autem triangulum abc ad triangu­
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              lum acd, ita pyramis abcy ad pyramidem acdy. </s>
              <s id="s.000777">& ut
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              triangulum efg ad triangulum egh, ita pyramis efgy
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              ad pyramidem eghy; ergo ut pyramis abcy ad
                <expan abbr="pyramidẽ">pyramidem</expan>
                <lb/>
                <arrow.to.target n="marg93"/>
                <lb/>
              a cdy, ita pyramis efgy ad pyramidem eghy. </s>
              <s id="s.000778">reliquum
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              igitur
                <expan abbr="fruſtũ">fruſtum</expan>
              lf ad reliquum
                <expan abbr="fruſtũ">fruſtum</expan>
              lh eſt ut pyramis abcy
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              ad pyramidem acdy, hoc eſt ut ul ad r, & ut xp ad ps. </s>
              <lb/>
              <s id="s.000779">Quòd cum fruſti lf centrum grauitatis ſits: & fruſti lh ſit
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                <arrow.to.target n="marg94"/>
                <lb/>
              centrum x: conſtat punctum p totius fruſti ag grauitatis
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              eſſe centrum. </s>
              <s id="s.000780">Eodem modo fiet demonſtratio etiam in
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              aliis pyramidibus.</s>
            </p>
            <p type="margin">
              <s id="s.000781">
                <margin.target id="marg92"/>
              a. </s>
              <s id="s.000782">ſexti.</s>
            </p>
            <p type="margin">
              <s id="s.000783">
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              19. quinti</s>
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            <p type="margin">
              <s id="s.000784">
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              8. Archi­
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              medis.</s>
            </p>
            <p type="main">
              <s id="s.000785">Sit fruſtum ad à cono, uel coni portione abſciſſum, eu­
                <lb/>
              ius maior baſis circulus, uel ellipſis circa diametrum ab;
                <lb/>
              minor circa diametrum cd: & axis ef. </s>
              <s id="s.000786">diuidatur
                <expan abbr="autẽ">autem</expan>
              ef
                <lb/>
              in g, ita ut eg ad gf eandem proportionem habeat, quam
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              duplum diametri ab unà cum diametro ed ad duplum cd
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              unà cum ab. </s>
              <s id="s.000787">
                <expan abbr="Sitq;">Sitque</expan>
              gh quarta pars lineæ ge: & ſit ſ K item
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              quarta pars totius fe axis. </s>
              <s id="s.000788">Rurſus quam proportionem
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              habet fruſtum ad ad conum, uel coni portionem, in
                <expan abbr="eadẽ">eadem</expan>
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              baſi, & æquali altitudine, habeat linea Kh ad hl. </s>
              <s id="s.000789">Dico pun­
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              ctum l fruſti ad grauitatis centrum eſſe. </s>
              <s id="s.000790">Si enim fieri po­
                <lb/>
              teſt, ſit m centrum:
                <expan abbr="producaturq;">producaturque</expan>
              lm extra fruſtum in n:
                <lb/>
              & ut nl ad lm, ita fiat circulus, uel ellipſis circa
                <expan abbr="diametrũ">diametrum</expan>
                <lb/>
              ab ad aliud ſpacium, in quo ſit o. </s>
              <s id="s.000791">Itaque in circulo, uel
                <lb/>
              ellipſi circa diametrum ab rectilinea figura plane deſcri­
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              batur, ita ut quæ relinquuntur portiones ſint o ſpacio mi­
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              nores: & intelligatur pyramis apb, baſim habens rectili­
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              neam figuram in circulo, uel ellipſi ab deſcriptam: à qua </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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