Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div773" type="section" level="1" n="267">
          <pb o="270" file="300" n="300" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s12433" xml:space="preserve"> Cum ergo hiſce quatuor rectis proportionales ſint quatuor rectæ AH,
              <note symbol="a" position="left" xlink:label="note-300-01" xlink:href="note-300-01a" xml:space="preserve">4. ſexti.</note>
            HO, HI; </s>
            <s xml:id="echoid-s12434" xml:space="preserve">erunt hæ quoque continuè proportionales. </s>
            <s xml:id="echoid-s12435" xml:space="preserve">quod eſt propoſirum.</s>
            <s xml:id="echoid-s12436" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div778" type="section" level="1" n="268">
          <head xml:id="echoid-head293" xml:space="preserve">MODVS NICOMEDIS IN
            <lb/>
          libro de lineis Conchoidibus.</head>
          <p>
            <s xml:id="echoid-s12437" xml:space="preserve">
              <emph style="sc">Nicomedes</emph>
            conſtruit prius inſtrumentum quoddam, quo lineaminfle-
              <lb/>
            xam deſcribit, quam Conchilem, vel Conchoideos appellat. </s>
            <s xml:id="echoid-s12438" xml:space="preserve">Sed nos omiſſo eo
              <lb/>
            inſtrumento, eandem, (quod ad noſtrum inſtitutum ſatis eſt) per puncta deli-
              <lb/>
            neabimus, hac ratione. </s>
            <s xml:id="echoid-s12439" xml:space="preserve">Sit recta linea A B, & </s>
            <s xml:id="echoid-s12440" xml:space="preserve">ad eam perpendicularis C D, in
              <lb/>
            puncto E. </s>
            <s xml:id="echoid-s12441" xml:space="preserve">Sumatur deinde infra E, punctum D, pro polo lineæ deſcribendæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s12442" xml:space="preserve">ſupra E, aliud punctum C, vt libet. </s>
            <s xml:id="echoid-s12443" xml:space="preserve">In vſu lineæ deſcriptæ conſtabit, quan-
              <lb/>
            tum tam punctum D, quam punctum C, à puncto E, abeſſe debeat. </s>
            <s xml:id="echoid-s12444" xml:space="preserve">Si igitur ex
              <lb/>
            D, ducantur plurimæ lineæ occultę parum inter ſe diſtantes, & </s>
            <s xml:id="echoid-s12445" xml:space="preserve">ex ſingulis ab-
              <lb/>
              <figure xlink:label="fig-300-01" xlink:href="fig-300-01a" number="205">
                <image file="300-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/300-01"/>
              </figure>
            ſcindantur portiones rectæ E C, æquales, initio ſemper facto à recta AB; </s>
            <s xml:id="echoid-s12446" xml:space="preserve">ex-
              <lb/>
            trema autem harum portionum puncta per lineam inflexam coniungantur de-
              <lb/>
            ſcripta erit linea conchilis. </s>
            <s xml:id="echoid-s12447" xml:space="preserve">Exemplum habes in quatuor lineis D H, D G, D F,
              <lb/>
            DN, in quibus ſumptæ ſunt L H, K G, SF, BN, ipſi EC, æquales, per quarum ex-
              <lb/>
            trema puncta H, G, F, N, inflexa linea incedit. </s>
            <s xml:id="echoid-s12448" xml:space="preserve">Et quo plures lineæ occultę ex
              <lb/>
            D, educentur, eo crebriora puncta inuenientur, per quæ tranſire debet linea in-
              <lb/>
            flexa.</s>
            <s xml:id="echoid-s12449" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12450" xml:space="preserve">
              <emph style="sc">Seqvitvr</emph>
            ex deſcriptione huius lineæ, eam nunquã poſſe cum recta AB,
              <lb/>
            conuenire, licet vtra que in infinitum producatur: </s>
            <s xml:id="echoid-s12451" xml:space="preserve">quia puncta, per quæ in cedit,
              <lb/>
            ſunt omnia ſupra rectam A B, terminantia nimirum ſegmenta rectarum ex D,
              <lb/>
            prodeuntium ( quæ quidem omnes rectam AB, interſecant) ipſi EC, æqualia.</s>
            <s xml:id="echoid-s12452" xml:space="preserve"/>
          </p>
          <note symbol="b" position="left" xml:space="preserve">pronuncia-
            <lb/>
          tum 11. lib. 1.</note>
          <p>
            <s xml:id="echoid-s12453" xml:space="preserve">
              <emph style="sc">Demonstrat</emph>
            deinde Nicomedes duas proprietates huius lineæ inſignes.
              <lb/>
            </s>
            <s xml:id="echoid-s12454" xml:space="preserve">Prima eſt. </s>
            <s xml:id="echoid-s12455" xml:space="preserve">Quodlibet eius punctum à puncto C, diuerſum minus diſtat à recta
              <lb/>
            AB, quampunctum C: </s>
            <s xml:id="echoid-s12456" xml:space="preserve">Aliorum autem punctorum, quod remotius eſt à C,
              <lb/>
            minus diſtat ab eadem recta A B, quam quod minus remotum eſt. </s>
            <s xml:id="echoid-s12457" xml:space="preserve">Ducta enim
              <lb/>
            recta quacunque D G, demittatur perpendicularis GI. </s>
            <s xml:id="echoid-s12458" xml:space="preserve"> Et quia K G, maior
              <unsure/>
              <note symbol="c" position="left" xlink:label="note-300-03" xlink:href="note-300-03a" xml:space="preserve">19. primi.</note>
            eſt quam GI; </s>
            <s xml:id="echoid-s12459" xml:space="preserve">erit quoque perpendicularis E C, (ipſi K G, æqualis) maior quam
              <lb/>
            perpendicularis IG, hoc eſt, punctum C, magis diſtabit à recta AB, quam pun-
              <lb/>
            ctum G. </s>
            <s xml:id="echoid-s12460" xml:space="preserve">Eademq; </s>
            <s xml:id="echoid-s12461" xml:space="preserve">ratione magis à recta AB, diſtabit punctum C, quam quod-
              <lb/>
            uis aliud. </s>
            <s xml:id="echoid-s12462" xml:space="preserve">Sumatur deinde aliud punctum H, remotius à C, quam punctum G,
              <lb/>
            demittatur que perpendicularis HA. </s>
            <s xml:id="echoid-s12463" xml:space="preserve">Dico punctum H, minus diſtare à recta
              <lb/>
            AB, quampunctum G, hoc eſt, perpendicularem HA, minorem eſſe </s>
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