Clavius, Christoph, Geometria practica

Page concordance

< >
Scan Original
331 301
332 302
333 303
334 304
335 305
336 306
337 307
338 308
339 309
340 310
341 311
342 312
343 313
344 314
345 315
346 316
347 317
348 318
349 319
350 320
351 321
352 322
353 323
354 324
355 325
356 326
357 327
358 328
359 329
360 330
< >
page |< < (308) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div883" type="section" level="1" n="308">
          <pb o="308" file="338" n="338" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s14480" xml:space="preserve">
              <emph style="sc">Esto</emph>
            corpus planis ſuperficiebus contentum A B C D, circa ſphæram
              <lb/>
            EFGH, cuius centrum I, deſcriptum, in quo ducantur ex I, ad puncta conta-
              <lb/>
            ctuum lineæ rectæ IE, IF, IG, IH, quæ ad baſes ſolidi erunt perpendiculares. </s>
            <s xml:id="echoid-s14481" xml:space="preserve">Nam
              <lb/>
            ſi verbi gratia per rectam IE, ducatur planum faciens in ſphæra, per propoſ. </s>
            <s xml:id="echoid-s14482" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s14483" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-338-01" xlink:href="note-338-01a" xml:space="preserve">3. vndec.</note>
            lib. </s>
            <s xml:id="echoid-s14484" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14485" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s14486" xml:space="preserve">circulum EFGH, & </s>
            <s xml:id="echoid-s14487" xml:space="preserve">in baſi rectam AB; </s>
            <s xml:id="echoid-s14488" xml:space="preserve">tanget circulus EFGH, rectam A B, in puncto E, propterea quod ſphæra baſim non ſecat, ſed tangit.
              <lb/>
            </s>
            <s xml:id="echoid-s14489" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-338-02" xlink:href="note-338-02a" xml:space="preserve">18. tertii.</note>
            Igitur IE, ad rectam AB, perpendicularis erit. </s>
            <s xml:id="echoid-s14490" xml:space="preserve">Eadem ratione, ſi per I E, duca- tur aliud planum, à priori differens, fiet alius circulus in ſphæra, & </s>
            <s xml:id="echoid-s14491" xml:space="preserve">alia linea recta
              <lb/>
            in eadem baſi ſecans rectam A B, in E; </s>
            <s xml:id="echoid-s14492" xml:space="preserve">ad quam et-
              <lb/>
              <figure xlink:label="fig-338-01" xlink:href="fig-338-01a" number="230">
                <image file="338-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/338-01"/>
              </figure>
              <note symbol="c" position="left" xlink:label="note-338-03" xlink:href="note-338-03a" xml:space="preserve">4. vndec.</note>
            iam I E, perpendicularis erit: </s>
            <s xml:id="echoid-s14493" xml:space="preserve"> Ac propterea IE, ad baſim ſolidi per illas rectas ductam perpendicularis
              <lb/>
            erit. </s>
            <s xml:id="echoid-s14494" xml:space="preserve">Non aliter oſtendemus, rectas IF, IG, IH, ad alias
              <lb/>
            baſes eſſe perpendiculares. </s>
            <s xml:id="echoid-s14495" xml:space="preserve">Sit quo que ſolidum re-
              <lb/>
            ctangulum L R, cuius baſes KLMN, ſit æqualis ter-
              <lb/>
            tiæ parti ambitus corporis ABCD; </s>
            <s xml:id="echoid-s14496" xml:space="preserve">altitudo verò ſi-
              <lb/>
            ue perpendicularis L P, æqualis vni perpendicula-
              <lb/>
            rium ex centro I, ad baſes corporis A B C D, caden-
              <lb/>
            tium; </s>
            <s xml:id="echoid-s14497" xml:space="preserve">quæ omnes inter ſe æquales ſunt ex defin.
              <lb/>
            </s>
            <s xml:id="echoid-s14498" xml:space="preserve">ſphæræ. </s>
            <s xml:id="echoid-s14499" xml:space="preserve">Dico ſolidum LR, corpori ABCD, æquale
              <lb/>
            eſſe. </s>
            <s xml:id="echoid-s14500" xml:space="preserve">Ducantur enim ex centro I, ad omnes angulos
              <lb/>
            corporis ABCD, rectælineæ, vt totum corpus in py-
              <lb/>
            ramides, ex quibus componitur, diuidatur: </s>
            <s xml:id="echoid-s14501" xml:space="preserve">quarum
              <lb/>
            quidem pyramidum baſes eædem ſunt quæ corpo-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-338-04" xlink:href="note-338-04a" xml:space="preserve">14. hui{us}.</note>
            ris, vertex autem communis centrum I. </s>
            <s xml:id="echoid-s14502" xml:space="preserve"> Quoniam igitur quælibet harum pyramidum æqualis eſt ſolido
              <lb/>
            rectangulo ſub perpendiculari L P, quæ ſingulis perpendicularibus corporis
              <lb/>
            ABCD, æqualis ponitur, & </s>
            <s xml:id="echoid-s14503" xml:space="preserve">tertia parte ſuæ baſis contento; </s>
            <s xml:id="echoid-s14504" xml:space="preserve">Si fiant tot ſolida
              <lb/>
            rectangula, quot ſunt pyramides, erunt omnia hæc ſimul æqualia ſolido rectan-
              <lb/>
            gulo LR. </s>
            <s xml:id="echoid-s14505" xml:space="preserve">(Si enim rectangulum K L M N, diuidatur in tot rectangula, quot
              <lb/>
            baſes ſunt in ſolido propoſito, ita vt primum æquale ſit tertiæ parti vnius baſis,
              <lb/>
            & </s>
            <s xml:id="echoid-s14506" xml:space="preserve">ſecundum tertiæ parti alterius, & </s>
            <s xml:id="echoid-s14507" xml:space="preserve">ita deinceps, quando quidem totum rectan-
              <lb/>
            gulum K L M N, æquale ponitur tertiæ parti totius ambitus ſolidi; </s>
            <s xml:id="echoid-s14508" xml:space="preserve">intelligan-
              <lb/>
            tur autem ſuper illa rectangula conſtitui parallelepipeda; </s>
            <s xml:id="echoid-s14509" xml:space="preserve">erunt omnia ſimul
              <lb/>
              <note symbol="e" position="left" xlink:label="note-338-05" xlink:href="note-338-05a" xml:space="preserve">14. hui{us}.</note>
            æqualia parallelepipedo L R.) </s>
            <s xml:id="echoid-s14510" xml:space="preserve"> Cum ergo ſingula parallelepipeda ſingulis pyramidibus ſint æqualia; </s>
            <s xml:id="echoid-s14511" xml:space="preserve">erunt quo que omnes pyramides, nempe corpus
              <lb/>
            A B C D, ex illis compoſitum, æquale ſolido rectangulo L R. </s>
            <s xml:id="echoid-s14512" xml:space="preserve">Quamobrem
              <lb/>
            area cuiuslibet corporis planis ſuperficiebus contenti, &</s>
            <s xml:id="echoid-s14513" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14514" xml:space="preserve">quod demonſtran-
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s14515" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div885" type="section" level="1" n="309">
          <head xml:id="echoid-head336" xml:space="preserve">THEOR. 14. PROPOS. 16.</head>
          <p>
            <s xml:id="echoid-s14516" xml:space="preserve">AREA cuiuslibet ſphæræ æqualis eſt ſolido rectangulo comprehenſo
              <lb/>
              <note position="left" xlink:label="note-338-06" xlink:href="note-338-06a" xml:space="preserve">Sphæræ quæ-
                <lb/>
              libet cui pa-
                <lb/>
              rallelepipedo
                <lb/>
              ſit æqualis.</note>
            ſub ſemidiametro ſphæræ, & </s>
            <s xml:id="echoid-s14517" xml:space="preserve">tertia parte ambitus ſphæræ.</s>
            <s xml:id="echoid-s14518" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14519" xml:space="preserve">
              <emph style="sc">Esto</emph>
            ſphæra ABC, cuius centrum D, ſemidiameter AD: </s>
            <s xml:id="echoid-s14520" xml:space="preserve">Solidum autem
              <lb/>
            rectangulum E, contentũ ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14521" xml:space="preserve">tertia parte ambitus </s>
          </p>
        </div>
      </text>
    </echo>
Impressum