Clavius, Christoph, Geometria practica

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          <pb o="216" file="246" n="246" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s9754" xml:space="preserve">
              <emph style="sc">Datvm</emph>
            iam ſit AB, latus Dodecaedri, ſupra quod extruatur pentagonum
              <lb/>
            æquilaterum, & </s>
            <s xml:id="echoid-s9755" xml:space="preserve">æquiangulum ABCDE, pro baſe Dodecaedri. </s>
            <s xml:id="echoid-s9756" xml:space="preserve">Iuncta autem re-
              <lb/>
            cta CE, quæ latus erit cubi in Dodecaedro, & </s>
            <s xml:id="echoid-s9757" xml:space="preserve">in eadem cumip ſo ſphæra
              <note symbol="a" position="left" xlink:label="note-246-01" xlink:href="note-246-01a" xml:space="preserve">2. coroll. 17.
                <lb/>
              @rtijdec.</note>
            pti, atque lateri AB, parallela: </s>
            <s xml:id="echoid-s9758" xml:space="preserve">ſecetur AB, bifariam in S, connectatur que recta S D. </s>
            <s xml:id="echoid-s9759" xml:space="preserve"> quæ angulum CDE, bifariam ſecabit: </s>
            <s xml:id="echoid-s9760" xml:space="preserve">d ac proinde & </s>
            <s xml:id="echoid-s9761" xml:space="preserve">rectam CE,
              <note symbol="b" position="left" xlink:label="note-246-02" xlink:href="note-246-02a" xml:space="preserve">coroll. 8.
                <lb/>
              quintidec.</note>
            & </s>
            <s xml:id="echoid-s9762" xml:space="preserve">ad angulos rectos diuidet: </s>
            <s xml:id="echoid-s9763" xml:space="preserve">ideo que & </s>
            <s xml:id="echoid-s9764" xml:space="preserve">anguli ad S, recti erunt. </s>
            <s xml:id="echoid-s9765" xml:space="preserve">Fiat ſupra
              <lb/>
            CE, Iſoſceles CGE, cuius vtrum que laterum CG, EG, perpendiculari SF, ſitæ-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-246-03" xlink:href="note-246-03a" xml:space="preserve">ſchol. 12.
                <lb/>
              quarti.</note>
              <note symbol="d" position="left" xlink:label="note-246-04" xlink:href="note-246-04a" xml:space="preserve">4. primi.</note>
              <figure xlink:label="fig-246-01" xlink:href="fig-246-01a" number="158">
                <image file="246-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/246-01"/>
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            quale. </s>
            <s xml:id="echoid-s9766" xml:space="preserve">Sumptis quo que FH, FI, ſemiſsi lateris AB, æqualibus, erigantur ad EC,
              <lb/>
            perpendiculares HK, IL, quæ ex C, E, ad interuallum FD, ſecentur in K, L, iun-
              <lb/>
            ganturq; </s>
            <s xml:id="echoid-s9767" xml:space="preserve">rectæ EL, CK. </s>
            <s xml:id="echoid-s9768" xml:space="preserve">His paratis, fiat angulo CGE, æqualis angulus MNO,
              <lb/>
            ponatur que N O, ipſi SD, æqualis: </s>
            <s xml:id="echoid-s9769" xml:space="preserve">Item angulo ELK, fiat æqualis angulus N-
              <lb/>
            OP, ponaturque OP, lateri AB, æqualis: </s>
            <s xml:id="echoid-s9770" xml:space="preserve">ac tandem demittatur ex P, ad MN,
              <lb/>
            perpendicularis PQ, quæ bifariam ſecetur in R. </s>
            <s xml:id="echoid-s9771" xml:space="preserve">Dico RQ, altitudinem eſſe py-
              <lb/>
            ramidis vnius in Dodecaedro. </s>
            <s xml:id="echoid-s9772" xml:space="preserve">Nam quia, vt ad finem Euclidis ex Hypſicle de-
              <lb/>
            monſtrauimus, angulus C G E, in clinationem vnius baſis ad alteram metitur, ſi
              <lb/>
            MN, concipiatur eſſe perpendicularis, quæ in baſe infima ex angulo pentagoni
              <lb/>
            ad medium punctum lateris oppoſiti ducitur, reſpondebit NO, perpendiculari,
              <lb/>
            quæin pentagono ad illam baſem inclinato ex eodem medio puncto ad oppo-
              <lb/>
            ſitum angulum ducitur: </s>
            <s xml:id="echoid-s9773" xml:space="preserve">propterea quod angulum M N O, angulo inclinatio-
              <lb/>
            nis CGE, & </s>
            <s xml:id="echoid-s9774" xml:space="preserve">rectam NO, perpendiculari S D, æqualem poſuimus. </s>
            <s xml:id="echoid-s9775" xml:space="preserve">Recta autem
              <lb/>
            OP, refert latus Dodecaedri inter angulum dicti pentagoni inclinati, & </s>
            <s xml:id="echoid-s9776" xml:space="preserve">angu-
              <lb/>
            lũ ſupremæ baſis poſitũ: </s>
            <s xml:id="echoid-s9777" xml:space="preserve">ꝓpterea ꝙ recta OP, poſita eſt æqualis lateri Dodeca-
              <lb/>
            edri, & </s>
            <s xml:id="echoid-s9778" xml:space="preserve">angulus NOP, angulo ELK, qui quidem æqualis eſt illi, quem dictum la-
              <lb/>
            tus efficit cum perpendiculari ex angulo ſupradicti pentagoni inclinatiad ba-
              <lb/>
            ſemin medium punctum lateris oppoſiti ductæ, vt conſtat, ſi vna baſis cubi Do-
              <lb/>
            decaedro inſcripti intelligatur dicto lateri Dodecaedri ſubſtrata, ita vt duo late-
              <lb/>
            ra baſis cubi ſubtendant duos angulos duorum pentagonorũ, quorum vnum
              <lb/>
            ad baſem Dodecaedri inclinatum eſt, alterum vero ò ſupremum in Dodecaedro.
              <lb/>
            </s>
            <s xml:id="echoid-s9779" xml:space="preserve">Erit enim tuncrecta CE, æqualis rectæ duo puncta media duorum laterum di-
              <lb/>
            ctorum baſis cubi connectenti. </s>
            <s xml:id="echoid-s9780" xml:space="preserve">Rectæ autem EL, CK, reſpondebunt rectis ex
              <lb/>
            eiſdem punctis medijs laterum illorum baſis cubi, ad angulos prædictorũ pen-
              <lb/>
            tagonorum ductis: </s>
            <s xml:id="echoid-s9781" xml:space="preserve">Ac proinde angulus ELK, æqualis erit ei, quem </s>
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