Valerio, Luca, De centro gravitatis solidorum, 1604

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              <s>
                <pb xlink:href="043/01/094.jpg" pagenum="7"/>
              quantacumque magnitudine propoſita, nomina­
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              tam habuerit proportionem; prima ad ſecundam
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              eandem nominatam habebit proportionem. </s>
            </p>
            <p type="main">
              <s>Sint duæ magnitudines A, B duarum autem aliarum
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              EF vnà maiorum, vel minorum quàm AB minori ex­
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              ceſsu vel defectu quantacumque magnitudine propo­
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              ſita, habeat E maior vel minor quàm A ad F vnà
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              maiorem, vel minorem quàm B certam ali quam nomina­
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              tam proportionem, verbi gratia, ſeſquialteram. </s>
              <s>Dico A
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              ad B, eandem nominatam habere proportionem: vt A
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              ipſius B eſse ſeſquialteram. </s>
              <s>Quoniam
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              enim omnis proportio in aliquibus ma­
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              gnitudinibus conſiſtit; ſit magnitudo C
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              ipſius D ſeſquialtera: ſed & E eſt ipſius
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              F ſeſquialtera; vtigitur C, tertia ad D
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              quartam, ita erit E maior, vel minor quàm
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              A prima, ad F vnà maiorem, vel minorem
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              ſecunda, minori, vt ponitur, vtriuſque ex­
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              ceſsu, vel defectu magnitudine propoſita
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              eiuſdem generis cum A, B, quæcumque
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              illa, & quantacumque ſit; erit per præ­
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              cedentem eadem proportio A ad B,
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              quæ C ad D: ſed proportio quam ha­
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              bet C ad D, eſt ſeſquialtera; ergo & A
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              ipſius B erit ſeſquialtera. </s>
              <s>Similiter quo­
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              cumque alio nomine notatam proportio­
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              nem habeat E ad F, eandem habere A
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                <figure id="id.043.01.094.1.jpg" xlink:href="043/01/094/1.jpg" number="68"/>
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              ad B, oſtenderemus, vt duplam, ſeſquitertiam, alicuius du
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              plicatam, vel triplicatam, & ſic de ſingulis. </s>
              <s>Manifeſtum
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              eſt igitur propoſitum. </s>
            </p>
            <p type="main">
              <s>Hæc autem propoſitio in paucis exemplaribus, quæ do­
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              no quibuſdam
                <expan abbr="dederã">dederam</expan>
              , non extat; poſterius enim eam exco-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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