Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div910" type="section" level="1" n="320">
          <pb o="320" file="350" n="350" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s15011" xml:space="preserve">
              <emph style="sc">Colligitvr</emph>
            ergo ex hac ratione Hippocratis, quadraturam circuli eſſe
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            poſsibilem, cum ſicut Lunula A G B F, quadrata eſt, ita quo que Lunulam
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            HNKM, quadrari poſſe, nihil obſtet, quamuis adhuc non ſit à quo quam qua-
              <lb/>
            drata. </s>
            <s xml:id="echoid-s15012" xml:space="preserve">Et certè, vt quidam rectè affirmat, quod hic oſtenditur ab Hippocrate
              <lb/>
            de Lunula AGBF, quæ pars eſt circuli AFBE, nihil idem prohibet de circulo to-
              <lb/>
            to ſciri poſſe, etiam non inueſtigata quantitate peripheriæ circuli, cum ſolum
              <lb/>
            deſit ars quadrandi Lunulam HNKM. </s>
            <s xml:id="echoid-s15013" xml:space="preserve">Immo plus aliquando dubitationis in-
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            ferretinuentio quadraturæ Lunulæ AGBF, non cognita, quam circuli.</s>
            <s xml:id="echoid-s15014" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15015" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15016" xml:space="preserve">
              <emph style="sc">Mvlta</emph>
            quoque hic dicenda eſſent de falſis aliorum quadraturis, ſed
              <lb/>
              <note position="left" xlink:label="note-350-01" xlink:href="note-350-01a" xml:space="preserve">Cur defalſis
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              aliorum qua-
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              draturis hic
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              nihil dicatur.</note>
            quia hæ vel ſe ipſas produnt, cum in progreſſu earum facilè appareat, aliquid
              <lb/>
            deeſſe ad conſtituendum circulo æquale quadratum, cuiuſmo di eſt quadratura
              <lb/>
            Iacobi Falconis Equitis Hiſpani, qui ſine inuẽtione lineæ rectæ, quæ peripheriæ
              <lb/>
            ſit æqualis, circulum quadrare conatur: </s>
            <s xml:id="echoid-s15017" xml:space="preserve">vel ab aliis iam dudum ſunt confuta-
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            tæ, nimirum Nicolai Cuſani Cardinalis quadratura à Ioanne Regiomontano, ac
              <lb/>
            Ioanne Buteone, & </s>
            <s xml:id="echoid-s15018" xml:space="preserve">Orontij Finaei Tetragoniſmus tum ab eodem Buteone,
              <lb/>
            tum à Petro Nonio Luſitano in libello de Erratis Orontij: </s>
            <s xml:id="echoid-s15019" xml:space="preserve">quorum vterque
              <lb/>
            variis viis lineam rectam circumferentiæ æqualem ſeinueniſſe putauit, nihil o-
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            mniò dicendum mihi eſſe ſtatuo, ne fruſtra tempus terere inutiliter videar.
              <lb/>
            </s>
            <s xml:id="echoid-s15020" xml:space="preserve">Quamobrem ſolum hoc loco eam quadraturam ſubiiciam, & </s>
            <s xml:id="echoid-s15021" xml:space="preserve">plenius aliquan-
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            to exponam, quam ad finem libr. </s>
            <s xml:id="echoid-s15022" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15023" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s15024" xml:space="preserve">conſcripſi, quæ videlicet per li-
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              <note position="left" xlink:label="note-350-02" xlink:href="note-350-02a" xml:space="preserve">Quæ nõ qua-
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              dratura per
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              line{as} hic ex-
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              plicetur.</note>
            neam Quadratricem (ſic enim eam appellare lubet, lineam rectam inuenit cir-
              <lb/>
            culari æqualem. </s>
            <s xml:id="echoid-s15025" xml:space="preserve">Hæc enim via licet ad Geometricè inueniendum punctum
              <lb/>
            quoddam, nonnihil in ea deſideretur, accuratior tamen eſt omnibus aliis, quas
              <lb/>
            hactenus videre potui; </s>
            <s xml:id="echoid-s15026" xml:space="preserve">ita vt practicè à ſcopo aberrare non poſsimus. </s>
            <s xml:id="echoid-s15027" xml:space="preserve">Vt au-
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            tem clarè atque ordinatè procedam, abſoluam totum negotium paucis quibuſ-
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            dam propoſitionibus.</s>
            <s xml:id="echoid-s15028" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div919" type="section" level="1" n="321">
          <head xml:id="echoid-head348" xml:space="preserve">I.
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          QVADRA TRICEM lineam deſcribere.</head>
          <p>
            <s xml:id="echoid-s15029" xml:space="preserve">
              <emph style="sc">Dinostratvs</emph>
            , & </s>
            <s xml:id="echoid-s15030" xml:space="preserve">Nicomedes, vt auctor eſt Pappus Alexandrinus in
              <lb/>
            4. </s>
            <s xml:id="echoid-s15031" xml:space="preserve">libr. </s>
            <s xml:id="echoid-s15032" xml:space="preserve">Mathematicarum collectionum, lineam quandam inflexam excogita-
              <lb/>
            runt ad circuli quadraturam, ideo que ab officio {τε}{τρ}α{γο}νίζ{ου}{σα} ab iiſdem eſt ap-
              <lb/>
            pellata; </s>
            <s xml:id="echoid-s15033" xml:space="preserve">à nobis verò eadem de cauſa quadratrix dicetur. </s>
            <s xml:id="echoid-s15034" xml:space="preserve">Quanquam autem
              <lb/>
            prædicti auctores conentur huiuſmodi lineam deſcribere per duos motus ima-
              <lb/>
            ginarios duarum rectarum ſeſe interſecantium, qua in re principium (vt philo-
              <lb/>
            ſophilo quuntur) petunt, vt propterea à Pappo reiiciatur, tanquam inutilis, & </s>
            <s xml:id="echoid-s15035" xml:space="preserve">
              <lb/>
            quæ deſcribi non poſsit: </s>
            <s xml:id="echoid-s15036" xml:space="preserve">nostamen eam ſineillis motibus Geometricè delinea-
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            bimus per inuentionem quotuis punctorum, per quæ duci debeat; </s>
            <s xml:id="echoid-s15037" xml:space="preserve">quemadmo-
              <lb/>
            dum in deſcriptionibus conicarum ſectio
              <unsure/>
            num fieri ſolet.</s>
            <s xml:id="echoid-s15038" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15039" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15040" xml:space="preserve">
              <emph style="sc">Sit</emph>
            ergo in quadrato ABCD, deſcriptus Quadrans BD. </s>
            <s xml:id="echoid-s15041" xml:space="preserve">Si igitur, vt vo-
              <lb/>
              <note position="left" xlink:label="note-350-03" xlink:href="note-350-03a" xml:space="preserve">Quadratricis
                <lb/>
              deſcriptio.</note>
            lunt inuentores lineæ Quadratricis, tam ſemidiameter A D, æquabiliter ferri in-
              <lb/>
            telligatur circa centrum A, quam latus quadrati ſupremum CD, deorſum verſus
              <lb/>
            æquabiliter quo que: </s>
            <s xml:id="echoid-s15042" xml:space="preserve">ita vt quo tempore punctum D, circumferentiam DB, vni-
              <lb/>
            formi ſemper motu percurrit, eodemrecta DC, vniformi etiam motu deſcendens
              <lb/>
            adlatus AB, perueniat, ſic tamen, vt perpetuo ſit lateri AB, parallela. </s>
            <s xml:id="echoid-s15043" xml:space="preserve">& </s>
            <s xml:id="echoid-s15044" xml:space="preserve"/>
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