Valerio, Luca, De centro gravitatis solidorum, 1604

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/133.jpg" pagenum="46"/>
              LMN, ſimul centrum grauitatis. </s>
              <s>Quod demonſtran­
                <lb/>
              dum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              ALITER.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Poſito enim R centro grauitatis duarum
                <expan abbr="magnitudinũ">magnitudinum</expan>
              G,
                <lb/>
              H, & S
                <expan abbr="duarũ">duarum</expan>
              L,M, vel punctum V cadit in puncto E, vel in
                <lb/>
              linea EB, vel in linea AE, ſi in puncto E vel in linea EB,
                <lb/>
              cum igitur T ſit
                <expan abbr="centrũ">centrum</expan>
              grauitatis trium
                <expan abbr="magnitudinũ">magnitudinum</expan>
              G,H,I
                <lb/>
              ſimul, & E ipſius I, erit punctum T propinquius termino
                <lb/>
              A quàm punctum V. </s>
              <s>Sed punctum V in linea AE cadat.
                <lb/>
              </s>
              <s>Veligitur S centrum grauitatis duarum magnitudinum L,
                <lb/>
              M, ſimul cadit in puncto D, ſiue in linea DB, vel in li­
                <lb/>
              nea AD. ſi in puncto D, vel in linea DB; centrum gra­
                <lb/>
              uitatis R duarum magnitudinum GH erit termino A
                <lb/>
              propinquius quàm ipſum S, & recta ER maior quàm ES,
                <lb/>
                <figure id="id.043.01.133.1.jpg" xlink:href="043/01/133/1.jpg" number="104"/>
                <lb/>
              Sed cadat punctum S in linea AD. </s>
              <s>Quoniam igitur ma­
                <lb/>
              ior eſt proportio G ad H, quàm L ad M: & vt G ad H,
                <lb/>
              ita eſt DR ad RG, & vt L ad M, ita PS ad SO, ma­
                <lb/>
              ior erit proportio DR ad RC, quàm PS ad SO; mul­
                <lb/>
              to ergo maior DR ad RC, quàm DS ad SO, & multo
                <lb/>
              maior quàm DS ad SC, & componendo maior propor­
                <lb/>
              tio DC ad CR, quàm DC ad CS; erit igitur CR mi­
                <lb/>
              nor quàm CS, atque adeo RD maior DS, addita igitur
                <lb/>
              ED communi, erit ER maior quàm ES. </s>
              <s>Rurſus quia
                <lb/>
              componendo, & ex æquali maior eſt proportio totius GH
                <lb/>
              ad I quàm totius LM ad N, hoc eſt maior longitudinis
                <lb/>
              ET ad TR, quàm QV ad VS, & multo maior quàm </s>
            </p>
          </chap>
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