Valerio, Luca, De centro gravitatis solidorvm libri tres

List of thumbnails

< >
111
111
112
112
113
113
114
114
115
115
116
116
117
117
118
118
119
119
120
120
< >
page |< < of 283 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/118.jpg" pagenum="31"/>
              ABC circumſcripta ad AE cylindrum: vtraque autem
                <lb/>
              circumſcriptarum figurarum excedit ſibi inſcriptam mino­
                <lb/>
              ri ſpacio quantacumque magnitudine propoſita, vt igitur
                <lb/>
              triangulum ABC, ad parallelogrammum AE, ita erit co­
                <lb/>
              noides ABC, ad cylindrum AE. </s>
              <s>Sed triangulum ABC
                <lb/>
              eſt parallelogrammi AE dimidium; igitur conoides ABC
                <lb/>
              eſt cylindro AE dimidium: ſed cylindrus AE eſt coni
                <lb/>
              ABC, triplum: igitur conoides ABC, erit coni ABC
                <lb/>
              ſeſquialterum. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XIX.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis priſmatis triangulam baſim habentis
                <lb/>
              centrum grauitatis rectam lineam, quæ cuiuſlibet
                <lb/>
              trium laterum bipartiti ſectionem, & oppoſiti pa­
                <lb/>
              rallelogrammi centrum iungit, ita diuidit, vt
                <lb/>
              pars, quæ attingit latus ſit dupla reliquæ. </s>
            </p>
            <p type="main">
              <s>Sit priſma, quale diximus AB
                <lb/>
              CDEF, ſectoque vno ipſius la­
                <lb/>
              tere BF in puncto G, bifariam
                <lb/>
              parallelogrammi oppoſiti ſit cen
                <lb/>
              trum H, & iuncta GH, cuius
                <lb/>
              pars GK ſit dupla reliquæ
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              H.
                <lb/>
              </s>
              <s>Dico priſmatis ABCDEF, cen
                <lb/>
              trum grauitatis eſſe K. </s>
              <s>Per pun
                <lb/>
              ctum enim H ducatur NO ip­
                <lb/>
              ſi AE, vel CD parallela, quæ
                <lb/>
              ipſas AC, ED, ſecabit
                <expan abbr="bifariã">bifariam</expan>
              :
                <lb/>
              iunctisque BN, FO, ducatur per
                <lb/>
              punctum
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              , ipſi FB, vel NO
                <lb/>
                <figure id="id.043.01.118.1.jpg" xlink:href="043/01/118/1.jpg" number="90"/>
                <lb/>
              parallela LM. </s>
              <s>Quoniam igitur eſt vt HK ad KG, ita
                <lb/>
              NL ad LB, & OM ad MF, erit NL, ipſius LB, & OM </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>