Clavius, Christoph, Geometria practica

Page concordance

< >
Scan Original
291 261
292 262
293 263
294 264
295 265
296 266
297 267
298 268
299 269
300 270
301 271
302 272
303 273
304 274
305 275
306 276
307 277
308 278
309 279
310 280
311 281
312 282
313 283
314 284
315 285
316 286
317 287
318 288
319 289
320 290
< >
page |< < (309) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div885" type="section" level="1" n="309">
          <p>
            <s xml:id="echoid-s14521" xml:space="preserve">
              <pb o="309" file="339" n="339" rhead="LIBER SEPTIMVS."/>
            ABC. </s>
            <s xml:id="echoid-s14522" xml:space="preserve">Dico corpus E, ſphæræ ABC, eſſe æquale. </s>
            <s xml:id="echoid-s14523" xml:space="preserve">Nam ſi non eſt æquale: </s>
            <s xml:id="echoid-s14524" xml:space="preserve">ſit, ſi
              <lb/>
            fieri poteſt, primum maius, ſitque exceſſus corporis E, ſupra ſphæram A B C,
              <lb/>
            quantitas F. </s>
            <s xml:id="echoid-s14525" xml:space="preserve">Intelligatur circa centrum D, deſcripta ſphæra GHK, maior quam
              <lb/>
            ſphæra ABC, ita tamen, vt exceſſus ſphæræ GHK, ſupra ſphęram ABC, non ſit
              <lb/>
            maior quantitate F, ſed vel æqualis, vel minor, hoc eſt, vt ſphæra GHK, ſit vel ę-
              <lb/>
            qualis ſolido E, quando nimirum ipſa excedit ſphærã A B C, præciſè quantitate
              <lb/>
            F; </s>
            <s xml:id="echoid-s14526" xml:space="preserve">vel minor, ſi nimirum ipſa excedit ſphæram A B C, minori quãtitate, quam F.
              <lb/>
            </s>
            <s xml:id="echoid-s14527" xml:space="preserve">Neceſſario enim aliqua ſphæra erit, quæ vel æqualis ſit magnitudini E, atq; </s>
            <s xml:id="echoid-s14528" xml:space="preserve">ad-
              <lb/>
            eo maior quam ſphæra ABC; </s>
            <s xml:id="echoid-s14529" xml:space="preserve">vel maior quidem quam ſphæra ABC, minor verò
              <lb/>
              <note symbol="a" position="right" xlink:label="note-339-01" xlink:href="note-339-01a" xml:space="preserve">17. duodec.</note>
            quam magnitudo E, quæ maior ponitur, quam ſphæra ABC. </s>
            <s xml:id="echoid-s14530" xml:space="preserve"> Inſcribatur de- inde intra ſphæram GHK, corpus, quod non tangat ſphæram A B C, ita vt vna-
              <lb/>
            quæque perpendicularium ex centro D, ad baſes iſtius corporis eductarum ma-
              <lb/>
            ior ſit ſemidiametro A D. </s>
            <s xml:id="echoid-s14531" xml:space="preserve">Siigitur à centro D, ad omnes angulos dicti corporis
              <lb/>
            ducantur lineæ rectæ, vt to tum corpus in pyramides diuidatur, quarum baſes
              <lb/>
            ſunt eædem, quæ corporis G H K, vertex autem communis centrum D; </s>
            <s xml:id="echoid-s14532" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-339-02" xlink:href="note-339-02a" xml:space="preserve">14. hui{us}.</note>
            quælibet pyramis æqualis ſolido rectangulo contento ſub eius perpendiculari,
              <lb/>
            & </s>
            <s xml:id="echoid-s14533" xml:space="preserve">tertia parte baſis; </s>
            <s xml:id="echoid-s14534" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s14535" xml:space="preserve">idcirco ſolidum
              <lb/>
              <figure xlink:label="fig-339-01" xlink:href="fig-339-01a" number="231">
                <image file="339-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/339-01"/>
              </figure>
            rectangulum contentum ſub ſemidiame-
              <lb/>
            tro AD, & </s>
            <s xml:id="echoid-s14536" xml:space="preserve">tertia parte baſis cuiuslibet py-
              <lb/>
            ramidis, minus ipſa pyramide erit. </s>
            <s xml:id="echoid-s14537" xml:space="preserve">Et quo-
              <lb/>
            niam omnia ſolida rectangula cõtenta ſub
              <lb/>
            ſingulis perpendicularibus ex centro D, ad
              <lb/>
            baſes corporis dicti protractis, & </s>
            <s xml:id="echoid-s14538" xml:space="preserve">ſingulis
              <lb/>
            tertijs partibus baſium, ſimul æqualia ſunt
              <lb/>
            toti corpori; </s>
            <s xml:id="echoid-s14539" xml:space="preserve">efficiunt autem omnes tertiæ
              <lb/>
            partes baſium ſimul tertiam partem ambi-
              <lb/>
            tus corporis; </s>
            <s xml:id="echoid-s14540" xml:space="preserve">erit ſolidum rectangulũ con-
              <lb/>
            tẽtum ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14541" xml:space="preserve">tertia par-
              <lb/>
            te ambitus præfati corporis inſcripti intra
              <lb/>
            ſphæram G H K, minus corpore inſcripto.
              <lb/>
            </s>
            <s xml:id="echoid-s14542" xml:space="preserve">Quoniam verò ambitus corporis inſcripti
              <lb/>
            maior eſt ambitu ſphęræ ABC, vt demon-
              <lb/>
            ſtrat Archimedes lib. </s>
            <s xml:id="echoid-s14543" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14544" xml:space="preserve">de ſphęra & </s>
            <s xml:id="echoid-s14545" xml:space="preserve">cylin-
              <lb/>
            dro propoſ. </s>
            <s xml:id="echoid-s14546" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14547" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s14548" xml:space="preserve">tertia pars
              <lb/>
            ambitus dicti corporis maior tertia parte ambitus ſphęrę ABC: </s>
            <s xml:id="echoid-s14549" xml:space="preserve">erit ſolidum re-
              <lb/>
            ctangulum contentum ſub ſemidiametro AD, & </s>
            <s xml:id="echoid-s14550" xml:space="preserve">tertia parte ambitus ſphęrę A-
              <lb/>
            B C, hoc eſt, ſolidum E, multo minus corpore inſcripto intra ſphęram G H K: </s>
            <s xml:id="echoid-s14551" xml:space="preserve">
              <lb/>
            Poſita eſt autem ſphæra GHK, vel æqualis ſolido E, vel minor. </s>
            <s xml:id="echoid-s14552" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s14553" xml:space="preserve">ſphę-
              <lb/>
            ra G H K, minor erit corpore intra ipſam deſcripto, totum parte quod eſt ab-
              <lb/>
            ſurdum. </s>
            <s xml:id="echoid-s14554" xml:space="preserve">Quo circa ſolidum E, maius non erit ſphęra ABC.</s>
            <s xml:id="echoid-s14555" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14556" xml:space="preserve">
              <emph style="sc">Sit</emph>
              <emph style="sc">Deinde</emph>
            , ſi fieri poteſt, ſolidum E, minus, quam ſphęra ABC, exce-
              <lb/>
            datur que à ſphęra ABC, quantitate F. </s>
            <s xml:id="echoid-s14557" xml:space="preserve">Intelligatur circa centrum D, ſphęra de-
              <lb/>
            ſcripta L M N, minor quàm ſphęra A B C, ita tamen vt exceſſus, quo ſphęra
              <lb/>
            LMN, ſuperatur à ſphęra ABC, non ſit maior quantitate F, ſed vel æqualis, vel
              <lb/>
            minor, hoc eſt, vt ſphęra LMN, ſit vel æqualis ſolido E, ſi nimirum ipſa exceda-
              <lb/>
            tur à ſphęra ABC, quantitate F, vel maior ſolido E, ſi videlicet ſphęra L M N, à
              <lb/>
            ſphęra ABC, ſuperetur minori quantitate, quam F. </s>
            <s xml:id="echoid-s14558" xml:space="preserve">Neceſſario enim aliqua </s>
          </p>
        </div>
      </text>
    </echo>
Impressum