Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s11925" xml:space="preserve">
              <pb o="259" file="289" n="289" rhead="LIBER SEXTVS."/>
            pterea ad reliquum ml C B A, reliquo rectangulo K M. </s>
            <s xml:id="echoid-s11926" xml:space="preserve"> Igitur erit A B C l
              <note symbol="a" position="right" xlink:label="note-289-01" xlink:href="note-289-01a" xml:space="preserve">7. quinti.</note>
            a d l m D, vt G M, ad K M: </s>
            <s xml:id="echoid-s11927" xml:space="preserve">hoc eſt vt G L, ad L K, vel vt E, ad F. </s>
            <s xml:id="echoid-s11928" xml:space="preserve">quod eſt pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s11929" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11930" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            prorſus modo quamlibet aliam figuram, quotquot habeat latera,
              <lb/>
            in datam prop ortionem ſecabimus per lineam, quæ vni lateri vel cuiuis alij re-
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            ctæ lineæ æquidiſtet. </s>
            <s xml:id="echoid-s11931" xml:space="preserve">Sit enim datum heptagonum qualecunque A B C D E F G,
              <lb/>
            ſecandum per lineam lateri A G, parallelam, in duas partes, vt ea, quæ ad D, ver-
              <lb/>
            git, ad reliquam habeat proportionem eandem, quam M, ad N habet. </s>
            <s xml:id="echoid-s11932" xml:space="preserve">Conſtitu-
              <lb/>
            to quadrato H I K L, æquali ipſi heptagono, per ea, quæin ſchol. </s>
            <s xml:id="echoid-s11933" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s11934" xml:space="preserve">14.
              <lb/>
            </s>
            <s xml:id="echoid-s11935" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11936" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11937" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11938" xml:space="preserve">vel potius per ea, quæ Num. </s>
            <s xml:id="echoid-s11939" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11940" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s11941" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11942" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11943" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11944" xml:space="preserve">huius ſcripſimus; </s>
            <s xml:id="echoid-s11945" xml:space="preserve">& </s>
            <s xml:id="echoid-s11946" xml:space="preserve">
              <lb/>
            diuiſo latere H I, in O, in proportionem M, ad N, ductaque O P, lateri H L, pa-
              <lb/>
            rellela: </s>
            <s xml:id="echoid-s11947" xml:space="preserve"> fiat ſuper rectam A G, inter rectas A B, G F, rectangulo I P,
              <note symbol="b" position="right" xlink:label="note-289-02" xlink:href="note-289-02a" xml:space="preserve">2. hui{us}.</note>
            le rectilineum A G Q R, habens latus Q R, lateri A G, parallelum. </s>
            <s xml:id="echoid-s11948" xml:space="preserve">Et quo-
              <lb/>
            niam Q R, cadit vltra F, B, conſtituemus
              <figure xlink:label="fig-289-01" xlink:href="fig-289-01a" number="192">
                <image file="289-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/289-01"/>
              </figure>
              <note symbol="c" position="right" xlink:label="note-289-03" xlink:href="note-289-03a" xml:space="preserve">2. hui{us}.</note>
            ſum ſuper rectam S T, inter rectas S C, T E, per
              <lb/>
            rectam V X, ipſi S T, parallelam, recti-
              <lb/>
            lineum æquale triangulis F Q T, B R S, extra
              <lb/>
            heptagonum exiſtentibus; </s>
            <s xml:id="echoid-s11949" xml:space="preserve">factumque erit
              <lb/>
            quod proponitur. </s>
            <s xml:id="echoid-s11950" xml:space="preserve">Cum enim rectilineum
              <lb/>
            A G Q R, ac proinde & </s>
            <s xml:id="echoid-s11951" xml:space="preserve">rectilineum A B V X-
              <lb/>
            F G, rectangulo I P, ſit æquale, erit quo que re-
              <lb/>
            liquum D E X V C, reliquo rectangulo O L, æ-
              <lb/>
            quale. </s>
            <s xml:id="echoid-s11952" xml:space="preserve"> Igitur erit D E X V C, ad A B V X F
              <note symbol="d" position="right" xlink:label="note-289-04" xlink:href="note-289-04a" xml:space="preserve">7. quinti.</note>
            vt O L, ad I P, hoc eſt, vt H O, ad O I, vel
              <note symbol="e" position="right" xlink:label="note-289-05" xlink:href="note-289-05a" xml:space="preserve">1. ſexti.</note>
            M, ad N, quo derat faciendum.</s>
            <s xml:id="echoid-s11953" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11954" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi latus rectilinei ex heptagono ab-
              <lb/>
            ſciſsi æquidiſtare debeat rectæ Y, q̃ nulli lateri
              <lb/>
            heptagoni æꝗdiſter (ſinãq; </s>
            <s xml:id="echoid-s11955" xml:space="preserve">æquidiſtaret, vni
              <lb/>
            lateri, abſolueretur problema, vt proximè tra-
              <lb/>
            ditũ eſt) ducta ex angulo G, rectæ Y, parallela
              <lb/>
            G Z, quæ intra figurã cadat; </s>
            <s xml:id="echoid-s11956" xml:space="preserve"> cõſtruemus
              <note symbol="f" position="right" xlink:label="note-289-06" xlink:href="note-289-06a" xml:space="preserve">2. hui{us}.</note>
            lineo A G Z, ſuper rectã I K, æquale rectangulũ h K; </s>
            <s xml:id="echoid-s11957" xml:space="preserve">quod fiet, ſi rectilineo A G Z,
              <lb/>
            fiat æquale quadratum, cuius latus l, & </s>
            <s xml:id="echoid-s11958" xml:space="preserve">duabus I K, & </s>
            <s xml:id="echoid-s11959" xml:space="preserve">l, tertia proportiona-
              <lb/>
            lis reperiatur I h. </s>
            <s xml:id="echoid-s11960" xml:space="preserve">Ducta enim h i, ipſi I K, parallela, erit rectangulum h K,
              <note symbol="g" position="right" xlink:label="note-289-07" xlink:href="note-289-07a" xml:space="preserve">17. ſexti.</note>
            drato lateris l, hoc eſt, rectilineo A G Z, æquale. </s>
            <s xml:id="echoid-s11961" xml:space="preserve"> Deinde ſuper rectam G
              <note symbol="h" position="right" xlink:label="note-289-08" xlink:href="note-289-08a" xml:space="preserve">2. hui{us}.</note>
            inter rectas G F, Z B, conſtituemus rectangulo h P, per parallelam b a, æqua-
              <lb/>
            le rectilineum G Z b a. </s>
            <s xml:id="echoid-s11962" xml:space="preserve"> Nam ſi triangulis B b e, F a d, ſuper rectam d e,
              <note symbol="i" position="right" xlink:label="note-289-09" xlink:href="note-289-09a" xml:space="preserve">2. hui{us}.</note>
            ter rectas e C, d E, fiat per parallelam f g, rectilineum d e g f, æquale; </s>
            <s xml:id="echoid-s11963" xml:space="preserve">fa-
              <lb/>
            ctum erit, quod in problemate proponitur, vt ex dictis perſpicuum eſt. </s>
            <s xml:id="echoid-s11964" xml:space="preserve">Ea-
              <lb/>
            demque omninò ratio eſt in omnibus aliis rectilineis quamuis irregularibus,
              <lb/>
            dummodo in iis ducipoſsit vna linea parallela datærectæ, quæ rectilineum au-
              <lb/>
            ferat dato rectilineo æquale. </s>
            <s xml:id="echoid-s11965" xml:space="preserve">Non enim ſemper hoc fieri poſſe in figuris, cu-
              <lb/>
            ius anguli partim introrſum, & </s>
            <s xml:id="echoid-s11966" xml:space="preserve">partim extrorſum vergant, ad finem propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s11967" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11968" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s11969" xml:space="preserve">declarauimus. </s>
            <s xml:id="echoid-s11970" xml:space="preserve">Id quod conſtructio ipſa problematis perſpicuè
              <lb/>
            nos docebit.</s>
            <s xml:id="echoid-s11971" xml:space="preserve"/>
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