Clavius, Christoph, Geometria practica

Table of figures

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          <p>
            <s xml:id="echoid-s10746" xml:space="preserve">
              <pb o="231" file="261" n="261" rhead="LIBER QVINTVS."/>
            ctorem ſphæræ.) </s>
            <s xml:id="echoid-s10747" xml:space="preserve">hac ratione inueſtigabitur. </s>
            <s xml:id="echoid-s10748" xml:space="preserve">Quoniam per propoſ. </s>
            <s xml:id="echoid-s10749" xml:space="preserve">42. </s>
            <s xml:id="echoid-s10750" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10751" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10752" xml:space="preserve">Ar-
              <lb/>
            chimedis de ſphęra & </s>
            <s xml:id="echoid-s10753" xml:space="preserve">cylindro, ſectoriſphęræ ęqualis eſt conus baſem habens
              <lb/>
            circulum ęqualem ſuperficiei conuexæ portionis ſphęræ, altitudinem verò ſe-
              <lb/>
            midiametro ſphęræ ęqualem: </s>
            <s xml:id="echoid-s10754" xml:space="preserve">Conus autem pro ducitur, vt c. </s>
            <s xml:id="echoid-s10755" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10756" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10757" xml:space="preserve">Nu.
              <lb/>
            </s>
            <s xml:id="echoid-s10758" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10759" xml:space="preserve">declarauimus, vel ex baſe in {1/3}. </s>
            <s xml:id="echoid-s10760" xml:space="preserve">altitudinis: </s>
            <s xml:id="echoid-s10761" xml:space="preserve">Vel ex tota altitudine in {1/3}. </s>
            <s xml:id="echoid-s10762" xml:space="preserve">baſis; </s>
            <s xml:id="echoid-s10763" xml:space="preserve">
              <lb/>
            fit vt ſector ſphęræ gignatur vel ex ſuperficie conuexa portionis ſphęræ in {1/3}. </s>
            <s xml:id="echoid-s10764" xml:space="preserve">ſe-
              <lb/>
            midiametri, hoc eſt, in {1/6}. </s>
            <s xml:id="echoid-s10765" xml:space="preserve">totius diametri: </s>
            <s xml:id="echoid-s10766" xml:space="preserve">Vel ex ſemidiametro in {1/3}. </s>
            <s xml:id="echoid-s10767" xml:space="preserve">ſuperfi-
              <lb/>
            ciei conuexæ portionis ſphæræ.</s>
            <s xml:id="echoid-s10768" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Soliditas cæ
            <unsure/>
          -
            <lb/>
          iuslibet portio
            <lb/>
          nis ſphæræ.</note>
          <p>
            <s xml:id="echoid-s10769" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10770" xml:space="preserve">
              <emph style="sc">Soliditas</emph>
            verò cuiuſcunque portionis ſphęræ hoc modo procrea-
              <lb/>
            bitur. </s>
            <s xml:id="echoid-s10771" xml:space="preserve">Inueſtigetur ſoliditas ſectoris ſphæræ, vt proximè tra ditum eſt. </s>
            <s xml:id="echoid-s10772" xml:space="preserve">Nam ſi,
              <lb/>
            quando portio propoſita minor eſt hemiſphærio, ex hoc ſectore dematur co-
              <lb/>
            nus eandem habens cum portione baſem, altitudinem verò perpendicularem
              <lb/>
            ex centro ſphęræ in baſem portionis cadentem, reliqua fiet ſoliditas portionis
              <lb/>
            minoris: </s>
            <s xml:id="echoid-s10773" xml:space="preserve">At verò ſi, quando portio propof
              <unsure/>
            ita hemiſphęrio maior eſt, idem co-
              <lb/>
            nus ad ſectorem adijciatur, conflabitur ſoliditas portionis maioris. </s>
            <s xml:id="echoid-s10774" xml:space="preserve">Id quod
              <lb/>
            perſpicuum eſt in ſuperiorifigura, cum conus BFD, ablatus ex ſectore ABFDA,
              <lb/>
            reliquam faciat portionem minorem BAD: </s>
            <s xml:id="echoid-s10775" xml:space="preserve">Idem vero conus BFD, ad ditus ſe-
              <lb/>
            ctori CBFDC, conſtituat maiorem portionem BCD. </s>
            <s xml:id="echoid-s10776" xml:space="preserve">Conus porrò prædictus
              <lb/>
            B F D, cognitus fiet ex baſe, nimirum ex circulo diametri B D, & </s>
            <s xml:id="echoid-s10777" xml:space="preserve">altitudine E F,
              <lb/>
            cognitis, vt cap. </s>
            <s xml:id="echoid-s10778" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10779" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10780" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s10781" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10782" xml:space="preserve">docuimus.</s>
            <s xml:id="echoid-s10783" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div665" type="section" level="1" n="233">
          <head xml:id="echoid-head251" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s10784" xml:space="preserve">
              <emph style="sc">Sit</emph>
            in ſphæra circulus maximus ABCD, & </s>
            <s xml:id="echoid-s10785" xml:space="preserve">portiones ſphęræ, quarum ba-
              <lb/>
            ſis communis circulus diametri B D, & </s>
            <s xml:id="echoid-s10786" xml:space="preserve">vertices A, C, quarum ſoliditates ex-
              <lb/>
            quirendæ ſunt. </s>
            <s xml:id="echoid-s10787" xml:space="preserve">Ex centro H, ducatur ad B D, perpendicularis H E, quæ
              <note symbol="a" position="right" xlink:label="note-261-02" xlink:href="note-261-02a" xml:space="preserve">3. tertij.</note>
            B D, ſecabit bifariam, ac proinde & </s>
            <s xml:id="echoid-s10788" xml:space="preserve">vtrum que
              <figure xlink:label="fig-261-01" xlink:href="fig-261-01a" number="166">
                <image file="261-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/261-01"/>
              </figure>
              <note symbol="b" position="right" xlink:label="note-261-03" xlink:href="note-261-03a" xml:space="preserve">ſchol. 27.
                <lb/>
              tertij.</note>
            cum BAD, B C D, bifariam, hoc eſt, per vertices A,
              <lb/>
              <note symbol="c" position="right" xlink:label="note-261-04" xlink:href="note-261-04a" xml:space="preserve">12. ſexti.</note>
            C, tranſibit. </s>
            <s xml:id="echoid-s10789" xml:space="preserve"> Fiat, vt C E, ad ſummam rectarum C H, C E, ita A E, ad E F: </s>
            <s xml:id="echoid-s10790" xml:space="preserve">Item, vt A E, ad ſummam
              <lb/>
            rectarum A H, A E, ita EC, ad E G. </s>
            <s xml:id="echoid-s10791" xml:space="preserve">Intelligantur que
              <lb/>
            duo coni, quorum baſis communis circulus diametri BD, & </s>
            <s xml:id="echoid-s10792" xml:space="preserve">vertices F, G. </s>
            <s xml:id="echoid-s10793" xml:space="preserve">Erit
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s10794" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10795" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10796" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10797" xml:space="preserve">Archimedis de ſphæra, & </s>
            <s xml:id="echoid-s10798" xml:space="preserve">cylindro, conus B F D, portioni
              <lb/>
            minori B A D, & </s>
            <s xml:id="echoid-s10799" xml:space="preserve">conus BGD, portioni maiori BCD, æqualis. </s>
            <s xml:id="echoid-s10800" xml:space="preserve">Quocirca, in-
              <lb/>
            uentis horum conorum ſoliditatibus, vt cap. </s>
            <s xml:id="echoid-s10801" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10802" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10803" xml:space="preserve">Numer. </s>
            <s xml:id="echoid-s10804" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10805" xml:space="preserve">traditum eſt
              <lb/>
            inuentę quoque erunt ſoliditates portionum B A D, B C D. </s>
            <s xml:id="echoid-s10806" xml:space="preserve">quod eſt propoſi-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s10807" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Soliditas c@-
            <lb/>
          iuslibet fru-
            <lb/>
          ſti ſphæræ.</note>
          <p>
            <s xml:id="echoid-s10808" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10809" xml:space="preserve">
              <emph style="sc">Soliditas</emph>
            denique cuiuſcunque fruſti ſphęrę, ſiue baſes ſint paralle-
              <lb/>
            Ię, cuiuſmodi eſt in 1. </s>
            <s xml:id="echoid-s10810" xml:space="preserve">figura huius cap. </s>
            <s xml:id="echoid-s10811" xml:space="preserve">fruſtum BDHG, inter circulos diametro-
              <lb/>
            rum BD, GH, incluſum, ſiue non parallelę, quale eſt fruſtum B D L K, hoc pa-
              <lb/>
            cto inuenietur. </s>
            <s xml:id="echoid-s10812" xml:space="preserve">Inueſtigetur, vt Num. </s>
            <s xml:id="echoid-s10813" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10814" xml:space="preserve">diximus, vtriuſque portionis ABD, A-
              <lb/>
            GH, ſoliditas. </s>
            <s xml:id="echoid-s10815" xml:space="preserve">Minori enim detra cta ex maiore, reliqua erit ſoliditas fruſti BD-
              <lb/>
            HG. </s>
            <s xml:id="echoid-s10816" xml:space="preserve">Sic etiam, inuento I, vertice portionis KIL, ſi inueniatur ſoliditas v-
              <lb/>
            triuſque portio nis BCD, KLI, minorque ex maiore tol-
              <lb/>
            latur, remanebit ſoliditas fruſti B D L K, nota.</s>
            <s xml:id="echoid-s10817" xml:space="preserve"/>
          </p>
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