Valerio, Luca, De centro gravitatis solidorum, 1604

List of thumbnails

< >
161
161 		162
162
163
163 		164
164
165
165 		166
166
167
167 		168
168
169
169 		170
170
< >
page |< < of 283 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/165.jpg" pagenum="78"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XLIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis conoidis hyperbolici centrum grauita­
                <lb/>
              tis eſt punctum illud, in quo duodecima pars axis
                <lb/>
              ordine quarta ab ea, quæ baſim attingit, ſic diui­
                <lb/>
              ditur, vt pars baſi propinquior ſit ad reliquam, vt
                <lb/>
              ſeſquialtera tranſuerſi lateris hyperboles, quæ
                <lb/>
              conoides deſcribit ad axim conoidis. </s>
            </p>
            <p type="main">
              <s>Sit conoides hyperbolicum ABC, cuius vertex B, axis
                <lb/>
              autem BD, qui etiam erit diameter hyperboles, quæ co­
                <lb/>
              noides deſcripſit, ad quam rectæ ordinatim applicantur:
                <lb/>
              eiuſdem autem hyperboles tranſuerſum latus ſit EB, cu­
                <lb/>
              ius ſit ſeſquialtera BEI, & ſumpta DQ quarta parte
                <lb/>
              axis BD, & DG, eiuſdem tertia, qua ratione erit FG
                <lb/>
              duodecima pars axis BD, & ordine quarta ab ea cuius
                <lb/>
              terminus D, fiat vt IB, ad BD, ita QH, ad HG.
                <lb/>
              </s>
              <s>Dico conoidis ABC, centrum grauitatis eſſe H. </s>
              <s>Sumpto
                <lb/>
              enim in linea AD quolibet puncto M, vt eſt EB ad
                <lb/>
              BD longitudine, ita fiat MD, ad DK ipſius AD po­
                <lb/>
              tentia: & abſcindatur DN, æqualis DM, & DL æqua­
                <lb/>
              lis DK; ſiue autem ſit DK minor, quàm DM, ſiue ma­
                <lb/>
              ior, ſiue eadem illi; omnibus caſibus communis erit demon
                <lb/>
              ſtratio. </s>
              <s>At per puncta M, N, vertice B, circa diametrum
                <lb/>
              BD, deſcribatur parabola MBN, & triangulum KBL.
                <lb/>
              </s>
              <s>Manente igitur BD, & circumductis figuris MBN,
                <lb/>
              KBL, deſcribantur conoides parabolicum MBN, &
                <lb/>
              conus KBL, quorum communis axis erit BD, baſes
                <lb/>
              autem circuli, quorum diametri KL, MN, in eodem
                <lb/>
              plano cum baſe conoidis ABC. </s>
              <s>Rurſus ſecto axe BD
                <lb/>
              bifariam, & ſingulis eius partibus ſemper bifariam in qua-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum