Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div919" type="section" level="1" n="321">
          <p>
            <s xml:id="echoid-s15141" xml:space="preserve">
              <pb o="323" file="353" n="353" rhead="LIBER SEPTIMVS."/>
            tus DC perueniret. </s>
            <s xml:id="echoid-s15142" xml:space="preserve">Cum ergo rectæ ex centro A, per partes arcus DB, emiſſæ, & </s>
            <s xml:id="echoid-s15143" xml:space="preserve">
              <lb/>
            lineæ parallelæ per partes laterum D A, C B, ductæ abſcindant ſemper ex arcu
              <lb/>
            DB, & </s>
            <s xml:id="echoid-s15144" xml:space="preserve">ex lateribus DA, CB, partes ſimiles, ex conſtructione: </s>
            <s xml:id="echoid-s15145" xml:space="preserve">liquidò conſtat,
              <lb/>
            puncta lineæ inflexæ DE, à nobis Geometricè inuenta, à punctis, quæ à duobus
              <lb/>
            illis motibus reperirentur non differre.</s>
            <s xml:id="echoid-s15146" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15147" xml:space="preserve">
              <emph style="sc">Hæc</emph>
            igitur eſt deſcriptio lineæ Quadratricis Geometrica quo dammodo,
              <lb/>
            quemadmo dum & </s>
            <s xml:id="echoid-s15148" xml:space="preserve">conicarum ſectionum deſcriptiones, quæ per puncta et-
              <lb/>
            iam fiunt, vt ab Apollonio traditur, Geometricæ dicuntur, cum tamen errori
              <lb/>
            magis ſint obnoxiæ, quam noſtra deſcriptio, propterinuentionem plurimarum
              <lb/>
            linearum mediarum proportionalium, quæ ad earum deſcriptiones ſunt neceſ-
              <lb/>
            ſariæ, quibus in Quadratricis deſcriptione opus non eſt. </s>
            <s xml:id="echoid-s15149" xml:space="preserve">Quare niſi quis to-
              <lb/>
            tam conicarum ſectionum do ctrinam, quam tanto ingenij acumine Appollo-
              <lb/>
            nius Pergaeus perſecutus eſt, vt propterea Magnus Geometra appellatus ſit,
              <lb/>
            reiicere velit, tan quam inutilem, & </s>
            <s xml:id="echoid-s15150" xml:space="preserve">non Geometricam, (quod neminem in Geo-
              <lb/>
            metria peritum facturum exiſtimo, cum ſectiones conicas ad demonſtrationes
              <lb/>
            adhibuerint præſtantiſsimi Geometræ. </s>
            <s xml:id="echoid-s15151" xml:space="preserve">Nam Menechmus Hyperbola, ac Pa-
              <lb/>
            rabola vſus eſt in duarum linearum mediarum prop ortionalium inter quaſuis
              <lb/>
            duas rectas inuentione; </s>
            <s xml:id="echoid-s15152" xml:space="preserve">Et Archimedes ipſe multa præclarè de iiſdem ſectioni-
              <lb/>
            bus conicis demonſtrauit: </s>
            <s xml:id="echoid-s15153" xml:space="preserve">ac denique eiuſmodi ſectiones inſignem vſum ha-
              <lb/>
            bẽt in re Gnomonica, vt ex noſtra Gnomonica apparet) admittere omninò co-
              <lb/>
            getur, hanc deſcriptionem noſtram Quadratricis lineæ eſſe quodammodo Geo-
              <lb/>
            metricam. </s>
            <s xml:id="echoid-s15154" xml:space="preserve">Adde quod linea conchilis, qua Nicomedes duas medias lineas
              <lb/>
            proportionales acutiſsimè inueſtigat, per puncta etiam deſcribitur, vt lib. </s>
            <s xml:id="echoid-s15155" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15156" xml:space="preserve">pro-
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            poſ. </s>
            <s xml:id="echoid-s15157" xml:space="preserve">15. </s>
            <s xml:id="echoid-s15158" xml:space="preserve">diximus.</s>
            <s xml:id="echoid-s15159" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15160" xml:space="preserve">
              <emph style="sc">Habet</emph>
            linea hæc quadratrix multas, & </s>
            <s xml:id="echoid-s15161" xml:space="preserve">inſignes vtilitates, quarum nonnul-
              <lb/>
            las ad finem lib. </s>
            <s xml:id="echoid-s15162" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15163" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s15164" xml:space="preserve">demonſtrauimus, quas hoc loco repetere ſuperuaca-
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            neum eſt. </s>
            <s xml:id="echoid-s15165" xml:space="preserve">Solum igitur eius vſum in quadrandis circulis hic exponemus. </s>
            <s xml:id="echoid-s15166" xml:space="preserve">Qua
              <lb/>
            in re indigemus tantummodo vltimo puncto E, in priori figura, etiamſi nullum
              <lb/>
            aliud Quadratricis punctum inuentum eſſet. </s>
            <s xml:id="echoid-s15167" xml:space="preserve">quod quidem vltimum punctum
              <lb/>
            licet Geometricè, ac præcisè non reperiatur: </s>
            <s xml:id="echoid-s15168" xml:space="preserve">tamen ſi artificium poſterioris fi-
              <lb/>
            guræ adhibeatur, non aberrabimus à vero puncto notabiliter, vt ſupra diximus.
              <lb/>
            </s>
            <s xml:id="echoid-s15169" xml:space="preserve">Quando namque deprehenſum fuerit, vltimam perpendicularem A H, æqua-
              <lb/>
            lem eſſe præcedenti vltimæ lineæ translatæ A G, ita vt nulla differentia inter illas
              <lb/>
            per circinum diſcernatur: </s>
            <s xml:id="echoid-s15170" xml:space="preserve">ſumi poterit citra errorem notabilem vltimum illud
              <lb/>
            punctum G, pro puncto extremo Quadratricis: </s>
            <s xml:id="echoid-s15171" xml:space="preserve">Sin minus, ducendæ erunt aliæ
              <lb/>
            perpendiculares eo artificio, quo AF, AH, ductæ ſunt, donecinter vltimam, & </s>
            <s xml:id="echoid-s15172" xml:space="preserve">
              <lb/>
            poſtremo loco inuentam rectam in ſemidiametro AB, nullum appareat diſcri-
              <lb/>
            men. </s>
            <s xml:id="echoid-s15173" xml:space="preserve">cuius quidem rei operatio ipſa optimus erit magiſter.</s>
            <s xml:id="echoid-s15174" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div924" type="section" level="1" n="322">
          <head xml:id="echoid-head349" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s15175" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15176" xml:space="preserve">Ex deſcriptione Quadratricis colligitur, ſi ex centro A, ducatur recta vt-
              <lb/>
            cunque A Q, ſecans arcum Quadrantis in Q, & </s>
            <s xml:id="echoid-s15177" xml:space="preserve">Quadratricem in O; </s>
            <s xml:id="echoid-s15178" xml:space="preserve">ita eſſe
              <lb/>
            arcum BD, ad arcum B Q, vt eſt ſemidiameter A D, ad rectam A R, ducta prius
              <lb/>
            O R, ipſi A B, parallela: </s>
            <s xml:id="echoid-s15179" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s15180" xml:space="preserve">ad rectam, quæ ex O, ad A B, demit-
              <lb/>
            titur perpendicularis. </s>
            <s xml:id="echoid-s15181" xml:space="preserve">Quia enim eadem pars eſt arcus D Q, totius arcus DB, quę
              <lb/>
              <note symbol="a" position="right" xlink:label="note-353-01" xlink:href="note-353-01a" xml:space="preserve">34. primi.</note>
            </s>
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