Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s17037" xml:space="preserve">
              <pb o="363" file="391" n="391" rhead="LIBER OCTAVVS."/>
            B, ad interuallum ſemidiametri recta D E, ſecetur in E,) ſecante ar@um AB, in F,
              <lb/>
            diuideretur arcus AB, in F, vel angulus ADB, bifariam. </s>
            <s xml:id="echoid-s17038" xml:space="preserve">quod tamen in eius de-
              <lb/>
            ſcriptione non contingit, vt demonſtrabitur. </s>
            <s xml:id="echoid-s17039" xml:space="preserve">Non ergo eius linea A B, verum
              <lb/>
            latus eſt heptagoni. </s>
            <s xml:id="echoid-s17040" xml:space="preserve">Ductis enim rectis DB, DF, ſi AB, eſt ſeptima pars circum-
              <lb/>
            ferentiæ, continebit tam angulus ADB, quam DEB, ( quiæquales ſunt) {2/7}. </s>
            <s xml:id="echoid-s17041" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-391-01" xlink:href="note-391-01a" xml:space="preserve">5. primi.</note>
            {4/14}. </s>
            <s xml:id="echoid-s17042" xml:space="preserve">duorum rectorum. </s>
            <s xml:id="echoid-s17043" xml:space="preserve"> Ergo reliqui DAB, DBA, ſimul continebunt {5/7}. </s>
            <s xml:id="echoid-s17044" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-391-02" xlink:href="note-391-02a" xml:space="preserve">32. primi.</note>
            {10/14}. </s>
            <s xml:id="echoid-s17045" xml:space="preserve">duorum rectorum. </s>
            <s xml:id="echoid-s17046" xml:space="preserve">Ac proinde vterqueipſorum continebit {5/14}. </s>
            <s xml:id="echoid-s17047" xml:space="preserve">duorum
              <lb/>
            rectorum. </s>
            <s xml:id="echoid-s17048" xml:space="preserve"> Cum ergo DAB, æqualis ſit duobus E, & </s>
            <s xml:id="echoid-s17049" xml:space="preserve">ABE, continebunt
              <note symbol="c" position="right" xlink:label="note-391-03" xlink:href="note-391-03a" xml:space="preserve">32. primi.</note>
            hi ſimul {5/14}. </s>
            <s xml:id="echoid-s17050" xml:space="preserve">duorum rectorum. </s>
            <s xml:id="echoid-s17051" xml:space="preserve">Continet autem E, ſolus {4/14}. </s>
            <s xml:id="echoid-s17052" xml:space="preserve">duorum recto-
              <lb/>
            rum. </s>
            <s xml:id="echoid-s17053" xml:space="preserve">Igitur ABE, continebit {1/14}. </s>
            <s xml:id="echoid-s17054" xml:space="preserve">duorum rectorum.</s>
            <s xml:id="echoid-s17055" xml:space="preserve"> Et quia A D F, duplus
              <note symbol="d" position="right" xlink:label="note-391-04" xlink:href="note-391-04a" xml:space="preserve">20. tertij.</note>
            ipſius ABE, propter eandem baſem AF, continebit angulus ADF, {2/14}. </s>
            <s xml:id="echoid-s17056" xml:space="preserve">id eſt, {1/7}.
              <lb/>
            </s>
            <s xml:id="echoid-s17057" xml:space="preserve">duorum rectorum. </s>
            <s xml:id="echoid-s17058" xml:space="preserve">Cum ergo totus ADB, complectatur {2/7}. </s>
            <s xml:id="echoid-s17059" xml:space="preserve">vt dictum eſt, con-
              <lb/>
            tinebit quoq; </s>
            <s xml:id="echoid-s17060" xml:space="preserve">BDF, {1/7}. </s>
            <s xml:id="echoid-s17061" xml:space="preserve">duorum rectorum; </s>
            <s xml:id="echoid-s17062" xml:space="preserve">ideoque æquales erunt ADF, BDF.</s>
            <s xml:id="echoid-s17063" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17064" xml:space="preserve">
              <emph style="sc">Sed</emph>
            iam AB, ſit inuenta per conſtructionem prædicti auctoris; </s>
            <s xml:id="echoid-s17065" xml:space="preserve">eritque EB,
              <lb/>
            æqualis ipſi DB. </s>
            <s xml:id="echoid-s17066" xml:space="preserve">Si ergo AB, eſſet verum latus heptagoni, caderet DI, perpendi-
              <lb/>
            cularis, diuidens nimirum angulum A D B, bifariam, in F, quod verum non eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s17067" xml:space="preserve">Poſita enim BE, 4. </s>
            <s xml:id="echoid-s17068" xml:space="preserve">erit tota CE, 9. </s>
            <s xml:id="echoid-s17069" xml:space="preserve">& </s>
            <s xml:id="echoid-s17070" xml:space="preserve">DE, 5.</s>
            <s xml:id="echoid-s17071" xml:space="preserve"> Cum ergo ſit, vt BD, ad DE, ita
              <note symbol="e" position="right" xlink:label="note-391-05" xlink:href="note-391-05a" xml:space="preserve">3. ſexti.</note>
            ad F E; </s>
            <s xml:id="echoid-s17072" xml:space="preserve">(quod angulus A D B, ſectus ſit bifariam) erit componendo, ſumma ex
              <lb/>
            BD, DE, nimirum 9. </s>
            <s xml:id="echoid-s17073" xml:space="preserve">ad DE, 5. </s>
            <s xml:id="echoid-s17074" xml:space="preserve">vt BE, ad FE. </s>
            <s xml:id="echoid-s17075" xml:space="preserve">Si igitur fiat, vt 9. </s>
            <s xml:id="echoid-s17076" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s17077" xml:space="preserve">ita BE, 4. </s>
            <s xml:id="echoid-s17078" xml:space="preserve">ad
              <lb/>
            aliud, inuenietur FE, 2 {2/9}. </s>
            <s xml:id="echoid-s17079" xml:space="preserve">ac propterea rectangulum ſub BE, 4. </s>
            <s xml:id="echoid-s17080" xml:space="preserve">& </s>
            <s xml:id="echoid-s17081" xml:space="preserve">EF, 2 {2/9}. </s>
            <s xml:id="echoid-s17082" xml:space="preserve">erit
              <lb/>
            8 {8/9}. </s>
            <s xml:id="echoid-s17083" xml:space="preserve">& </s>
            <s xml:id="echoid-s17084" xml:space="preserve">rectangulum ſub CE, 9. </s>
            <s xml:id="echoid-s17085" xml:space="preserve">& </s>
            <s xml:id="echoid-s17086" xml:space="preserve">EA, 1. </s>
            <s xml:id="echoid-s17087" xml:space="preserve">erit 9. </s>
            <s xml:id="echoid-s17088" xml:space="preserve">quod eſt abſurdum; </s>
            <s xml:id="echoid-s17089" xml:space="preserve"> cum
              <note symbol="f" position="right" xlink:label="note-391-06" xlink:href="note-391-06a" xml:space="preserve">1. coroll. 36.
                <lb/>
              tertij.</note>
            ctangula ſint æqualia. </s>
            <s xml:id="echoid-s17090" xml:space="preserve">Non ergo recta DI, cadit in punctum F, interſectionis re-
              <lb/>
            ctæ BE, cum arcu AB, quando quidem rectangulum ſub BE, EF, æquale non eſt
              <lb/>
            rectangulo ſub CE, EA, ſed minus: </s>
            <s xml:id="echoid-s17091" xml:space="preserve">Ac proindenonrectè illa ratione latus he-
              <lb/>
            ptagoni inuenitur.</s>
            <s xml:id="echoid-s17092" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17093" xml:space="preserve">
              <emph style="sc">Albertvs</emph>
            Durerus ad KL, latus trianguli æquilateri (ſumptis videlicet ar-
              <lb/>
            cubus AK, AL, quorum vterque ſextam partẽ circumferentiæ contineat) per-
              <lb/>
            pendicularem ducit A H, dicitque K H, ſemiſſem illius lateris eſſe latus hepta-
              <lb/>
            goni. </s>
            <s xml:id="echoid-s17094" xml:space="preserve">quod ſimiliter falſum eſt. </s>
            <s xml:id="echoid-s17095" xml:space="preserve">Nam KH, omnino æqualis eſt rectæ AB, quam
              <lb/>
            proximè demonſtrauimus non eſſelatus heptagoni. </s>
            <s xml:id="echoid-s17096" xml:space="preserve">Si enim iungeretur recta
              <lb/>
            AK, fieret triangulum æquilaterum AKD. </s>
            <s xml:id="echoid-s17097" xml:space="preserve"> Igitur perpendicularis K H,
              <note symbol="g" position="right" xlink:label="note-391-07" xlink:href="note-391-07a" xml:space="preserve">ſchol 26.
                <lb/>
              primi.</note>
            AD, bifariam: </s>
            <s xml:id="echoid-s17098" xml:space="preserve">Acproinde poſita DK, vel DA, 4. </s>
            <s xml:id="echoid-s17099" xml:space="preserve">erit DH, 2. </s>
            <s xml:id="echoid-s17100" xml:space="preserve">Quocirca ſi detrahe-
              <lb/>
            mus 4. </s>
            <s xml:id="echoid-s17101" xml:space="preserve">quadratum DH, ex 16. </s>
            <s xml:id="echoid-s17102" xml:space="preserve">quadrato DK, reliquum erit quadratum KH 12.</s>
            <s xml:id="echoid-s17103" xml:space="preserve">
              <note symbol="h" position="right" xlink:label="note-391-08" xlink:href="note-391-08a" xml:space="preserve">47 primi.</note>
            At tantum etiam deprehendemus eſſe quadratum AB. </s>
            <s xml:id="echoid-s17104" xml:space="preserve">Quoniam enim quadra-
              <lb/>
            tum BE, eſt 16. </s>
            <s xml:id="echoid-s17105" xml:space="preserve">hoc eſt, {64/4}. </s>
            <s xml:id="echoid-s17106" xml:space="preserve">& </s>
            <s xml:id="echoid-s17107" xml:space="preserve">quadratum EG, {25/4}. </s>
            <s xml:id="echoid-s17108" xml:space="preserve">(Nam perpendicularis BG,
              <lb/>
            ſecat in Iſoſcele EBD, baſem ED, bifariam. </s>
            <s xml:id="echoid-s17109" xml:space="preserve">Cum ergo ED, ſit 5. </s>
            <s xml:id="echoid-s17110" xml:space="preserve">erit DG, 2 {1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s17111" xml:space="preserve">cuius quadratum eſt {25/4}) erit quadratum BG, {39/4}. </s>
            <s xml:id="echoid-s17112" xml:space="preserve">Sed quadratum A G, eſt {9/4}.</s>
            <s xml:id="echoid-s17113" xml:space="preserve">
              <note symbol="i" position="right" xlink:label="note-391-09" xlink:href="note-391-09a" xml:space="preserve">47. primi.</note>
            quodrecta A G, @@t 1 {1/2}. </s>
            <s xml:id="echoid-s17114" xml:space="preserve"> Igitur quadratum AB, erit {48/4}. </s>
            <s xml:id="echoid-s17115" xml:space="preserve">id eſt, 12. </s>
            <s xml:id="echoid-s17116" xml:space="preserve">quod eſt
              <note symbol="k" position="right" xlink:label="note-391-10" xlink:href="note-391-10a" xml:space="preserve">47. primi.</note>
            poſitum.</s>
            <s xml:id="echoid-s17117" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17118" xml:space="preserve">
              <emph style="sc">Franciscvs</emph>
            Fluſlas Candalla vir nobiliſsimus, ac
              <lb/>
              <figure xlink:label="fig-391-01" xlink:href="fig-391-01a" number="283">
                <image file="391-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/391-01"/>
              </figure>
            do ctiſsimus conatus eſt conſtruere triangulum Iſoſceles
              <lb/>
            habens vtrumuis angulorum æqualiũ ad baſem triplum re-
              <lb/>
            liqui anguli, vt beneficio ipſius in dato circulo heptagonum
              <lb/>
            inſcribatur, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s17119" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17120" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s17121" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17122" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s17123" xml:space="preserve">tradidi-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s17124" xml:space="preserve">Ita ergo ſcribit. </s>
            <s xml:id="echoid-s17125" xml:space="preserve">Sit triangulum æquilaterum DMN,
              <lb/>
            in quo perpendicularis DO, ad baſem ſecetur bifariam in P.
              <lb/>
            </s>
            <s xml:id="echoid-s17126" xml:space="preserve">Deſcripto deinde ex M, per N, D, circulo, quem ſecet </s>
          </p>
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