Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div263" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s4485" xml:space="preserve">
              <pb file="0180" n="180" rhead="FED. COMMANDINI"/>
            fruſtum a d. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">Sed pyramis q æqualis eſt fruſto à pyramide
              <lb/>
            abſciſſo, ut dem onſtrauimus. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s4488" xml:space="preserve">conus, uel coni por-
              <lb/>
            tio q, cuius baſis ex tribus circulis, uel ellipſibus a b, e f, c d
              <lb/>
            conſtat, & </s>
            <s xml:id="echoid-s4489" xml:space="preserve">altitudo eadem, quæ fruſti: </s>
            <s xml:id="echoid-s4490" xml:space="preserve">ipſi fruſto a d eſt æ-
              <lb/>
            qualis. </s>
            <s xml:id="echoid-s4491" xml:space="preserve">atque illud eſt, quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s4492" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div268" type="section" level="1" n="91">
          <head xml:id="echoid-head98" xml:space="preserve">THEOREMA XXI. PROPOSITIO XXVI.</head>
          <p>
            <s xml:id="echoid-s4493" xml:space="preserve">
              <emph style="sc">Cvivslibet</emph>
            fruſti à pyramide, uel cono,
              <lb/>
            uel coni portione abſcisſi, centrum grauitatis eſt
              <lb/>
            in axe, ita ut eo primum in duas portiones diui-
              <lb/>
            ſo, portio ſuperior, quæ minorem baſim attingit
              <lb/>
            ad portionem reliquam eam habeat proportio-
              <lb/>
            nem, quam duplum lateris, uel diametri maioris
              <lb/>
            baſis, vnà cum latere, uel diametro minoris, ipſi
              <lb/>
            reſpondente, habet ad duplum lateris, uel diame-
              <lb/>
            tri minoris baſis vnà cũ latere, uel diametro ma-
              <lb/>
            ioris: </s>
            <s xml:id="echoid-s4494" xml:space="preserve">deinde à puncto diuiſionis quarta parte ſu
              <lb/>
            perioris portionis in ipſa ſumpta: </s>
            <s xml:id="echoid-s4495" xml:space="preserve">& </s>
            <s xml:id="echoid-s4496" xml:space="preserve">rurſus ab in-
              <lb/>
            ferioris portionis termino, qui eſt ad baſim maio
              <lb/>
            rem, ſumpta quarta parte totius axis: </s>
            <s xml:id="echoid-s4497" xml:space="preserve">centrum ſit
              <lb/>
            in linea, quæ his finibus continetur, atque in eo li
              <lb/>
            neæ puncto, quo ſic diuiditur, ut tota linea ad par
              <lb/>
            tem propinquiorem minori baſi, eãdem propor-
              <lb/>
            tionem habeat, quam fruſtum ad pyramidẽ, uel
              <lb/>
            conum, uel coni portionem, cuius baſis ſit ea-
              <lb/>
            dem, quæ baſis maior, & </s>
            <s xml:id="echoid-s4498" xml:space="preserve">altitudo fruſti altitudini
              <lb/>
            æqualis.</s>
            <s xml:id="echoid-s4499" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum