Valerio, Luca, De centro gravitatis solidorum, 1604

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/100.jpg" pagenum="13"/>
              C ad B, ita fiat HM, ad
                <expan abbr="Mq.">Mque</expan>
              & vt B ad A, ita QM, ad
                <lb/>
              MP, & ipſi GK, parallelæ TPR, VQS, ducantur.
                <lb/>
              </s>
              <s>Quoniam igitur eſt vt C, ad duplam ipſius F, ita GH, ad
                <lb/>
              HK; erit vt C ad F, ita eſt par llelogrammum GM, ad
                <lb/>
              triangulum MHK: ſed vt C, ad B, ita eſt HM, ad
                <expan abbr="Mq;">Mque</expan>
                <lb/>
              hoc eſt parallelogrammum GM, ad parallelogrammum
                <lb/>
              MV: & vt F, ad E, ita triangulum MHK, ad triangu­
                <lb/>
              lum MQS, ob duplicatam proportionem eius, quæ eſt
                <lb/>
              HM ad
                <expan abbr="Mq.">Mque</expan>
              hoc eſt ipſius C ad B; vt igitur trapezium
                <lb/>
              NK, ad NS trapezium, ita erit, per præcedentem, CF,
                <lb/>
              ſimul ad BE ſimul. </s>
              <s>Rurſus quoniam eſt conuertendo, vt
                <lb/>
              parallelogrammum MV, ad parallelogrammum GM, ita
                <lb/>
              B ad C. ſed vt parallelogrammum GM, ad triangulum
                <lb/>
              KHM, ita erat C, ad F: & vt triangulum KHM, ad
                <lb/>
              triangulum QSM, ita F ad E; erit ex æquali, vt paral­
                <lb/>
              lelogrammum MV, ad triangulum SQM, ita B, ad E.
                <lb/>
              </s>
              <s>Similiter ergo vt ante erit vt trapezium NS, ad NR tra­
                <lb/>
              pezium, ita EB, ſimul ad AD, ſimul. </s>
              <s>Rurſus, quoniam
                <lb/>
              æque excedit LV, ipſam LT, atque LG, ipſam LV;
                <lb/>
              minor erit proportio LT ad LV, quam LV, ad LG: eſt
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              autem trianguli LTR ad triangulum LVS, duplicata
                <lb/>
              proportio ipſius LT, ad LV, & trianguli LVS, ad trian­
                <lb/>
              gulum LGK, duplicata ipſius LV, ad LG, propter ſi­
                <lb/>
              militudinem triangulorum; minor igitur proportio erit
                <lb/>
              trianguli LTR, ad triangulum LVS, quam trianguli
                <lb/>
              LVS, ad triangulum LGK; dempto igitur triangulo
                <lb/>
              LNM, communi, minor erit proportio trapezij NR, ad
                <lb/>
              trapezium NS, quam trapezij NS, ad trapezium NK.
                <lb/>
              </s>
              <s>Sed vt trapezium NR, ad trapezium NS, ita eſt conuer­
                <lb/>
              tendo AD ſimul ad BE, ſimul: & vt trapezium NS, ad
                <lb/>
              trapezium NK, ita BE, ſimul ad CF, ſimul; minor igi­
                <lb/>
              tur proportio erit AD, ſimul ad BE ſimul, quam BE ſi­
                <lb/>
              mul ad CF, ſimul. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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