Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div769" type="section" level="1" n="265">
          <p>
            <s xml:id="echoid-s12305" xml:space="preserve">
              <pb o="267" file="297" n="297" rhead="LIBER SEXTVS."/>
            ABCD, cum diametris AC, BD, quæ ſe mutuo bifariam diuidentin E. </s>
            <s xml:id="echoid-s12306" xml:space="preserve">Satis
              <note symbol="a" position="right" xlink:label="note-297-01" xlink:href="note-297-01a" xml:space="preserve">ſchol. 34.
                <lb/>
              primi.</note>
            ſet vnam tantum diametrum ducere, eamquein E, ſecare bifariam. </s>
            <s xml:id="echoid-s12307" xml:space="preserve">Protractis
              <lb/>
            autemlateribus DA, DC, intelligatur circa punctum B, moueriregula hincinde,
              <lb/>
            donecita ſecet D A, D C, productas in F, & </s>
            <s xml:id="echoid-s12308" xml:space="preserve">G, vtrectæ emiſſæ E F, E G, ęquales
              <lb/>
            ſint. </s>
            <s xml:id="echoid-s12309" xml:space="preserve">Vel certè, vt vult Apollonius, ex E, plures circulideſcribantur LI, GF,
              <lb/>
            MN, donec chorda arcus vnius pręciſè per punctum B, incedat, qualis eſt GF.
              <lb/>
            </s>
            <s xml:id="echoid-s12310" xml:space="preserve">Quod ſi chorda ſupra B, tranſeat, cuiuſmodi eſt chorda LI, deſcribendus erit cir-
              <lb/>
            culus j
              <unsure/>
            . </s>
            <s xml:id="echoid-s12311" xml:space="preserve">L; </s>
            <s xml:id="echoid-s12312" xml:space="preserve">Si verò infra punctũ B, tranſeat, qualis
              <lb/>
              <figure xlink:label="fig-297-01" xlink:href="fig-297-01a" number="202">
                <image file="297-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/297-01"/>
              </figure>
            eſt chorda MN, deſcribẽdus erit circul
              <emph style="sub">9</emph>
            s
              <unsure/>
            .</s>
            <s xml:id="echoid-s12313" xml:space="preserve">M. </s>
            <s xml:id="echoid-s12314" xml:space="preserve">At-
              <lb/>
            que hoc opus toties iterandum, donec aliqua
              <lb/>
            chorda, qualis eſt GF, per B, incedat. </s>
            <s xml:id="echoid-s12315" xml:space="preserve">Erunt enim
              <lb/>
            hacratione EF, EG, ex centro E, ad circumferen-
              <lb/>
            tiam GF, interſe ęquales. </s>
            <s xml:id="echoid-s12316" xml:space="preserve">Quibus ita conſtructis.
              <lb/>
            </s>
            <s xml:id="echoid-s12317" xml:space="preserve">Dico A F, C G, eſſe medio loco proportionales
              <lb/>
            inter AB, BC: </s>
            <s xml:id="echoid-s12318" xml:space="preserve">hoc eſt, ita eſſe AB, ad AF, vt AF,
              <lb/>
            ad CG, & </s>
            <s xml:id="echoid-s12319" xml:space="preserve">CG, ad CB.</s>
            <s xml:id="echoid-s12320" xml:space="preserve">
              <unsure/>
            Diuiſis enim AD, CD, bi-
              <lb/>
              <note symbol="b" position="right" xlink:label="note-297-02" xlink:href="note-297-02a" xml:space="preserve">ſchol. 26.
                <lb/>
              primi.</note>
            fariam in K, & </s>
            <s xml:id="echoid-s12321" xml:space="preserve">H; </s>
            <s xml:id="echoid-s12322" xml:space="preserve"> erunt ductę E K, E H, ad A D, C D, perpendiculares. </s>
            <s xml:id="echoid-s12323" xml:space="preserve"> Quoniam verò
              <note symbol="c" position="right" xlink:label="note-297-03" xlink:href="note-297-03a" xml:space="preserve">6. ſecundi.</note>
            gulum ſub D F, A F, vna cum quadrato ex A K,
              <lb/>
            quadrato ex K F, ęquale eſt; </s>
            <s xml:id="echoid-s12324" xml:space="preserve">addito communi
              <lb/>
            quadrato ex E K, eritrectangulum ſub D F, A F,
              <lb/>
            vna cum quadratis ex A K, E K, hoc eſt,
              <note symbol="d" position="right" xlink:label="note-297-04" xlink:href="note-297-04a" xml:space="preserve">47. primi.</note>
            cũ quadrato ex EA, ęquale quadratis ex KF, EF, hoceſt, quadrato ex EF,
              <note symbol="e" position="right" xlink:label="note-297-05" xlink:href="note-297-05a" xml:space="preserve">47. primi.</note>
            eſt, quadrato ex EG, quę ipſi EF, eſt æqualis. </s>
            <s xml:id="echoid-s12325" xml:space="preserve">Eademratione oſtendemus, re-
              <lb/>
            ctangulum ſub DG, GC, vna cum quadrato ex CE, id eſt, ex EA, ęquale eſſe ei-
              <lb/>
            dem quadrato ex E G. </s>
            <s xml:id="echoid-s12326" xml:space="preserve">Igitur rectangulum ſub D F, A F, vna cum quadrato
              <lb/>
            ex EA, ęquale erit rectangulo ſub DG, GC, vna cum quadrato ex EA: </s>
            <s xml:id="echoid-s12327" xml:space="preserve">dempto-
              <lb/>
            que communi quadrato EA; </s>
            <s xml:id="echoid-s12328" xml:space="preserve">remanebitrectangulum ſub DG, GC, rectangu-
              <lb/>
            lo ſub DF, AF, ęquale. </s>
            <s xml:id="echoid-s12329" xml:space="preserve"> Quo circa erit DG, ad DF, vt AF, ad CG: </s>
            <s xml:id="echoid-s12330" xml:space="preserve"> Vt
              <note symbol="f" position="right" xlink:label="note-297-06" xlink:href="note-297-06a" xml:space="preserve">16. ſexti.</note>
            DG, ad DF, ita eſt AB, ad AF. </s>
            <s xml:id="echoid-s12331" xml:space="preserve">Ergo erit vt AB, ad AF, ita A F, ad C G: </s>
            <s xml:id="echoid-s12332" xml:space="preserve">hoc eſt,
              <lb/>
              <note symbol="g" position="right" xlink:label="note-297-07" xlink:href="note-297-07a" xml:space="preserve">4. ſexti.</note>
            tres AB, AF, CG, continuè proportionales erunt. </s>
            <s xml:id="echoid-s12333" xml:space="preserve"> Sed rurſuseſt, vt D G,
              <note symbol="h" position="right" xlink:label="note-297-08" xlink:href="note-297-08a" xml:space="preserve">4. ſexti.</note>
            DF, ita CG, ad CB. </s>
            <s xml:id="echoid-s12334" xml:space="preserve">Igitur erit quoque CG, ad CB, vt AB, ad A F; </s>
            <s xml:id="echoid-s12335" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s12336" xml:space="preserve">vt AF
              <lb/>
            ad CG. </s>
            <s xml:id="echoid-s12337" xml:space="preserve">Quare erunt quatuor AB, AF, CG, CB, continuè proportionales. </s>
            <s xml:id="echoid-s12338" xml:space="preserve">quod
              <lb/>
            erat demonſtrandum.</s>
            <s xml:id="echoid-s12339" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div771" type="section" level="1" n="266">
          <head xml:id="echoid-head291" xml:space="preserve">MODVS PHILONIS BYSANTII,
            <lb/>
          qui Philoppono quoque tribuitur.</head>
          <p>
            <s xml:id="echoid-s12340" xml:space="preserve">
              <emph style="sc">Sint</emph>
            rurſus in eadem figura inter rectas A B, B C, inueniendę duę medię
              <lb/>
            proportionales. </s>
            <s xml:id="echoid-s12341" xml:space="preserve">Conſtituto rectangulo ABCD, vna cum diametro CA, produ-
              <lb/>
            ctiſq; </s>
            <s xml:id="echoid-s12342" xml:space="preserve">lateribus D A, D C, vt ſupra; </s>
            <s xml:id="echoid-s12343" xml:space="preserve">deſcribatur ex E, medio puncto diametricir-
              <lb/>
            culus CBA, ad interuallum E C, vel EA, qui neceſſario per angulum rectum
              <note symbol="i" position="right" xlink:label="note-297-09" xlink:href="note-297-09a" xml:space="preserve">ſchol. 31.
                <lb/>
              tertij.</note>
            tranſibit. </s>
            <s xml:id="echoid-s12344" xml:space="preserve">Deinde circa punctum B, regula hincinde moueatur, ſecans DA, DC,
              <lb/>
            protractas in F, & </s>
            <s xml:id="echoid-s12345" xml:space="preserve">G, & </s>
            <s xml:id="echoid-s12346" xml:space="preserve">circumferentiamin O, donec B G, O F, ęquales ſint.
              <lb/>
            </s>
            <s xml:id="echoid-s12347" xml:space="preserve">Quod fiet, ſi per B, plurimę lineę occultę ducantur. </s>
            <s xml:id="echoid-s12348" xml:space="preserve">Vna enim earum habebit
              <lb/>
            ſegmentum inter rectam DG, & </s>
            <s xml:id="echoid-s12349" xml:space="preserve">circulum æquale ſegmento inter DF, & </s>
            <s xml:id="echoid-s12350" xml:space="preserve"/>
          </p>
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