Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s9781" xml:space="preserve">
              <pb o="217" file="247" n="247" rhead="LIBER QVINTVS."/>
            cularis in pentagono inclinato cum prædicto latere Dodecaedri efficit. </s>
            <s xml:id="echoid-s9782" xml:space="preserve">Ex quo
              <lb/>
            fit punctum P, in plano ſupremæ baſis exiſtere, atque idcirco perpendicularem
              <lb/>
              <figure xlink:label="fig-247-01" xlink:href="fig-247-01a" number="159">
                <image file="247-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/247-01"/>
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            P Q, ad planum baſis per M N, ductum demiſſam, æqualem eſſe altitudini Do-
              <lb/>
            decaedri; </s>
            <s xml:id="echoid-s9783" xml:space="preserve">eiuſque ſemiſſem R Q, altitudini vnius pyramidis pentagonæ eſſe æ-
              <lb/>
            qualem. </s>
            <s xml:id="echoid-s9784" xml:space="preserve">Quæ omnia facil@ intelligentur, ſi Dodecaedrum aliquod materiale ad-
              <lb/>
            hibeatur.</s>
            <s xml:id="echoid-s9785" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9786" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            datum ſit Ico ſaedri latus a b, ſupra quod extruatur pentagonum
              <lb/>
            æquilaterum, & </s>
            <s xml:id="echoid-s9787" xml:space="preserve">æquiangulum a b c d e, pro baſe pyramidis ex quin que baſibus
              <lb/>
            Icoſaedri conflatæ. </s>
            <s xml:id="echoid-s9788" xml:space="preserve">Iuncta autem recta c e, ſeceturlatus a b, in ſ, bifariam, & </s>
            <s xml:id="echoid-s9789" xml:space="preserve">re-
              <lb/>
            cta ducaturſd, quæ vt in Dodecaedro oſtendimus proximè, perpendicularis e-
              <lb/>
            rit ad vtramque a b, c e. </s>
            <s xml:id="echoid-s9790" xml:space="preserve">Fiat ſupra latus Icoſaedri c d, triangulum æquilaterum
              <lb/>
            c d h, probaſe vna Icoſaedri; </s>
            <s xml:id="echoid-s9791" xml:space="preserve">& </s>
            <s xml:id="echoid-s9792" xml:space="preserve">diuiſo latere c d, bifariam in k, iungatur recta h-
              <lb/>
            k, quæ ad c d, erit perpendicularis. </s>
            <s xml:id="echoid-s9793" xml:space="preserve">Præterea ſupra c e, fiat Iſoſceles c g e,
              <note symbol="a" position="right" xlink:label="note-247-01" xlink:href="note-247-01a" xml:space="preserve">ſchol. 26.
                <lb/>
              Primi.</note>
            ius vtrum que laterum c g, e g, perpendicularihk, ſit æquale. </s>
            <s xml:id="echoid-s9794" xml:space="preserve">Poſt hæc ſupra ſ d,
              <lb/>
            conſtituatur triangulum ſdl, cuius latus ſl, perpendiculari h k, & </s>
            <s xml:id="echoid-s9795" xml:space="preserve">latus dl, lateri
              <lb/>
            Icoſaedri a b, fit æquale. </s>
            <s xml:id="echoid-s9796" xml:space="preserve">Denique angulo c g e, fiat æqualis angulus m n o, & </s>
            <s xml:id="echoid-s9797" xml:space="preserve">
              <lb/>
            recta n o, perpendiculari h k, æqualis: </s>
            <s xml:id="echoid-s9798" xml:space="preserve">Item angulus n o p, angulo d l s, rectaque
              <lb/>
            o p, lateri Icoſaedri a b, æqualis. </s>
            <s xml:id="echoid-s9799" xml:space="preserve">Dico perpendicularem p q, ad m n, demiſſam,
              <lb/>
            eſſe altitudinem Icoſaedri, eiuſque ſemiſſem r q, altitudinem vnius pyramidis in
              <lb/>
              <note position="right" xlink:label="note-247-02" xlink:href="note-247-02a" xml:space="preserve">Altitudo py-
                <lb/>
              ramidis Ico-
                <lb/>
              ſaedri.</note>
            Icoſaedro. </s>
            <s xml:id="echoid-s9800" xml:space="preserve">Quia enim, vt ex Hypſicle ad finem Euclidis demonſtrauimus, an-
              <lb/>
            gulus c g e, metitur in clinationem vnius baſis ad alteram, ſi m n, concipiatur eſ-
              <lb/>
            ſe perpendicularis, quæ in baſe infima Icoſaedri ex angulo trianguli ad medium
              <lb/>
            punctum lateris oppoſiti ducitur, reſpondebit n o, per pendiculari, quæ in trian-
              <lb/>
            gulo ad illam baſem inclinato ex eodem medio pũcto ad angulum oppoſitum
              <lb/>
            ducitur: </s>
            <s xml:id="echoid-s9801" xml:space="preserve">propterea quod angulum m n o, angulo inclinationis c g e, & </s>
            <s xml:id="echoid-s9802" xml:space="preserve">rectam
              <lb/>
            n o, perpendiculari h k, æqualem fecimus: </s>
            <s xml:id="echoid-s9803" xml:space="preserve">Recta verò o p, referet latus Icoſae-
              <lb/>
            dri inter angulum dicti trianguli inclinati, & </s>
            <s xml:id="echoid-s9804" xml:space="preserve">angulum ſupremæ baſis poſitum;
              <lb/>
            </s>
            <s xml:id="echoid-s9805" xml:space="preserve">propterea quod recta o p, poſita eſt æqualis lateri Icoſaedri, & </s>
            <s xml:id="echoid-s9806" xml:space="preserve">angulus n o p,
              <lb/>
            angulo d l s: </s>
            <s xml:id="echoid-s9807" xml:space="preserve"> qui quidem æqualis eſt illi, quẽ dictum latus efficit cum
              <note symbol="b" position="right" xlink:label="note-247-03" xlink:href="note-247-03a" xml:space="preserve">8. primi.</note>
            diculari ex angulo ſupradicti trianguli inclinati ad baſem, in medium punctum
              <lb/>
            lateris oppoſiti ducitur. </s>
            <s xml:id="echoid-s9808" xml:space="preserve">Eſt enim recta d s, æqualis perpendiculari ex angulo
              <lb/>
            pentagoni ad latus oppoſitum ductæ, & </s>
            <s xml:id="echoid-s9809" xml:space="preserve">latera sl, dl, æqualia </s>
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