Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
191 40
192
193 41
194
195 42
196
197 43
198
199 44
200
201 45
202
203 46
204
205 47
206
207
208
209
210
211
212
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="95">
          <pb file="0202" n="202" rhead="FED. COMMANDINI"/>
          <p>
            <s xml:space="preserve">ABSCINDATVR à portione conoidis rectanguli
              <lb/>
            a b c alia portio e b f, plano baſi æquidiſtante: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eadem
              <lb/>
            portio ſecetur alio plano per axem; </s>
            <s xml:space="preserve">ut ſuperficiei ſectio ſit
              <lb/>
            parabole a b c: </s>
            <s xml:space="preserve">planorũ portiones abſcindentium rectæ
              <lb/>
            lineæ a c, e f: </s>
            <s xml:space="preserve">axis autem portionis, & </s>
            <s xml:space="preserve">ſectionis diameter
              <lb/>
            b d; </s>
            <s xml:space="preserve">quam linea e fin puncto g ſecet. </s>
            <s xml:space="preserve">Dico portionem co-
              <lb/>
            noidis a b c ad portionem e b f duplam proportionem ha-
              <lb/>
            bere eius, quæ eſt baſis a c ad baſim e f; </s>
            <s xml:space="preserve">uel axis d b ad b g
              <lb/>
            axem. </s>
            <s xml:space="preserve">Intelligantur enim duo coni, ſeu coni portiones
              <lb/>
            a b c, e b f, eãdem baſim, quam portiones conoidis, & </s>
            <s xml:space="preserve">æqua
              <lb/>
            lem habentes altitudinem. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam a b c portio conoi
              <lb/>
            dis ſeſquialtera eſt coni, ſeu portionis coni a b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portio
              <lb/>
            e b f coniſeu portionis coni e b feſt ſeſquialtera, quod de-
              <lb/>
              <anchor type="figure" xlink:label="fig-0202-01a" xlink:href="fig-0202-01"/>
            monſtrauit Archimedes in propoſitionibus 23, & </s>
            <s xml:space="preserve">24 libri
              <lb/>
            de conoidibus, & </s>
            <s xml:space="preserve">ſphæroidibus: </s>
            <s xml:space="preserve">erit conoidis portio ad
              <lb/>
            conoidis portionem, ut conus ad conum, uel ut coni por-
              <lb/>
            tio ad coni portionem. </s>
            <s xml:space="preserve">Sed conus, uel coni portio a b c ad
              <lb/>
            conum, uel coni portionem e b f compoſitam proportio-
              <lb/>
            nem habet ex proportione baſis a c ad baſim e f, & </s>
            <s xml:space="preserve">ex pro-
              <lb/>
            portione altitudinis coni, uel coni portionis a b c ad alti-
              <lb/>
            tudinem ipſius e b f, ut nos demonſtrauimus in com men-
              <lb/>
            tariis in undecimam propoſitionem eiuſdem libri A rchi-
              <lb/>
            medis: </s>
            <s xml:space="preserve">altitudo autem ad altitudinem eſt, ut axis ad axem.
              <lb/>
            </s>
            <s xml:space="preserve">quod quidem in conis rectis perſpicuum eſt, in ſcalenis ue</s>
          </p>
        </div>
      </text>
    </echo>