Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1035" type="section" level="1" n="372">
          <p>
            <s xml:id="echoid-s16724" xml:space="preserve">
              <pb o="358" file="386" n="386" rhead="GEOMETR. PRACT."/>
            quam EG, quod perpendicularis remotior à centro minor ſemper ſit, quam pro-
              <lb/>
            pinquior. </s>
            <s xml:id="echoid-s16725" xml:space="preserve">Ducta igitur recta ED, ſecabit lineam axis in B. </s>
            <s xml:id="echoid-s16726" xml:space="preserve">Secta autem A B, bi-
              <lb/>
            fariam in H, deſcribatur ex H, circa AB, ſemicirculus AKB. </s>
            <s xml:id="echoid-s16727" xml:space="preserve">Diuiſa quoque F G,
              <lb/>
            inter ductas perpendiculares bifariam in I, ducatur IK, ad AB, perpendicularis
              <lb/>
            ſecans circumferentiam in K, & </s>
            <s xml:id="echoid-s16728" xml:space="preserve">rectam B E, in L. </s>
            <s xml:id="echoid-s16729" xml:space="preserve">Ducta quoque recta B K, ſe-
              <lb/>
              <figure xlink:label="fig-386-01" xlink:href="fig-386-01a" number="278">
                <image file="386-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/386-01"/>
              </figure>
            cante perpendiculares DF, EG, in M, N, iungantur re-
              <lb/>
            ctæ AM, AK, AN. </s>
            <s xml:id="echoid-s16730" xml:space="preserve"> Et quoniam eſt, vt FI, ad IG,
              <note symbol="a" position="left" xlink:label="note-386-01" xlink:href="note-386-01a" xml:space="preserve">2. ſexti.</note>
            lem, ita MK, ad KN, erit quoque MK, ipſi KN, æqua-
              <lb/>
            lis. </s>
            <s xml:id="echoid-s16731" xml:space="preserve">Igitur duo latera AK, KM, duobus lateribus AK,
              <lb/>
            KN, æqualia erunt. </s>
            <s xml:id="echoid-s16732" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s16733" xml:space="preserve">angulos æquales
              <lb/>
            comprehendant, vtpoterectos, quod angulus
              <note symbol="b" position="left" xlink:label="note-386-02" xlink:href="note-386-02a" xml:space="preserve">31. tertii.</note>
            in ſemicirculo rectus ſit; </s>
            <s xml:id="echoid-s16734" xml:space="preserve"> erunt baſes AM, AN,
              <note symbol="c" position="left" xlink:label="note-386-03" xlink:href="note-386-03a" xml:space="preserve">4. primi.</note>
            les. </s>
            <s xml:id="echoid-s16735" xml:space="preserve">Circulus igitur ex A, per N, deſcriptus tranſibit
              <lb/>
            per M, ſecabitque BC, in O, & </s>
            <s xml:id="echoid-s16736" xml:space="preserve">C. </s>
            <s xml:id="echoid-s16737" xml:space="preserve">Dico OC, eſſe axem
              <lb/>
            Ellipſis maiorem. </s>
            <s xml:id="echoid-s16738" xml:space="preserve"> Cum enim ſit, vt MD, ad DF,
              <note symbol="d" position="left" xlink:label="note-386-04" xlink:href="note-386-04a" xml:space="preserve">ſchol 4.</note>
            NE, ad EG, tranſibit neceſſariò Ellipſis, quæ per O, D,
              <lb/>
            C, deſcribitur, (poſſe autem Ellipſim deſcribi circa
              <lb/>
            O C, tanquam axem maiorem, per punctum D, con-
              <lb/>
            ſtat ex iis, quæ ad finem ſcholij propoſ. </s>
            <s xml:id="echoid-s16739" xml:space="preserve">8. </s>
            <s xml:id="echoid-s16740" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16741" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16742" xml:space="preserve">Gno-
              <lb/>
            monices, & </s>
            <s xml:id="echoid-s16743" xml:space="preserve">in ſcholio Lemmatis 50. </s>
            <s xml:id="echoid-s16744" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16745" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16746" xml:space="preserve">Aſtrolabij
              <lb/>
            ſcripſimus) per punctum E, ex ſcholio Lemmatis 51.
              <lb/>
            </s>
            <s xml:id="echoid-s16747" xml:space="preserve">Aſtrolabij: </s>
            <s xml:id="echoid-s16748" xml:space="preserve">Acproinde Ellipſis per data puncta D, E,
              <lb/>
            circa centrum A, deſcripta tranſibit per O, C, ita vt ab Ellipſi per O, D, C, deſcri-
              <lb/>
            pta non differat. </s>
            <s xml:id="echoid-s16749" xml:space="preserve">Alioquin Ellipſis Ellipſim in 8. </s>
            <s xml:id="echoid-s16750" xml:space="preserve">punctis ſecaret, nimirum in D,
              <lb/>
            E, & </s>
            <s xml:id="echoid-s16751" xml:space="preserve">aliis duobus reſpondentibus ex altera parte axis: </s>
            <s xml:id="echoid-s16752" xml:space="preserve">deinde in aliis 4. </s>
            <s xml:id="echoid-s16753" xml:space="preserve">infra
              <lb/>
            centrum reſpondentibus. </s>
            <s xml:id="echoid-s16754" xml:space="preserve">quod eſt abſurdum quippe cum Ellipſis Ellipſim in 4. </s>
            <s xml:id="echoid-s16755" xml:space="preserve">tantum punctis ſecet.</s>
            <s xml:id="echoid-s16756" xml:space="preserve"/>
          </p>
          <note symbol="e" position="left" xml:space="preserve">25. quinti
            <lb/>
          Apollonii.</note>
        </div>
        <div xml:id="echoid-div1037" type="section" level="1" n="373">
          <head xml:id="echoid-head400" xml:space="preserve">THEOR. 10. PROPOS. 28.</head>
          <p>
            <s xml:id="echoid-s16757" xml:space="preserve">SI in circuli diametro producta punctum ſumatur, ab eoque recta cir-
              <lb/>
            culum tangens ducatur; </s>
            <s xml:id="echoid-s16758" xml:space="preserve">à puncto autem contactus chorda ducatur
              <lb/>
            ad diametrum perpendicularis: </s>
            <s xml:id="echoid-s16759" xml:space="preserve">Recta ex eodem contactus puncto
              <lb/>
            ad vtrumlibet extremum diametri ducta diuidet angulum à tangen-
              <lb/>
            te, & </s>
            <s xml:id="echoid-s16760" xml:space="preserve">prædicta chorda perpendiculari comprehenſum bifariam.
              <lb/>
            </s>
            <s xml:id="echoid-s16761" xml:space="preserve">Item ſi ab eodem puncto in diametro producta aſſumpto recta du-
              <lb/>
            catur circulum ſecans, & </s>
            <s xml:id="echoid-s16762" xml:space="preserve">ab alterutro ſectionis puncto ad interſectio-
              <lb/>
            nem diametri cum prædicta chorda perpendiculari recta iungatur: </s>
            <s xml:id="echoid-s16763" xml:space="preserve">
              <lb/>
            Recta ex eodem ſectionis puncto ad vtrumlibet diametri extremum
              <lb/>
            ducta ſecabit quoque angulum à linea ſecante, & </s>
            <s xml:id="echoid-s16764" xml:space="preserve">illa alia, quæ per in-
              <lb/>
            terſectionem diametri cum prædicta chorda perpendiculari ducitur,
              <lb/>
            bifariam.</s>
            <s xml:id="echoid-s16765" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16766" xml:space="preserve">
              <emph style="sc">In</emph>
            circulo ABCD, cuius centrum E, pro ducta ſit diameter AC, & </s>
            <s xml:id="echoid-s16767" xml:space="preserve">ex F, duca-
              <lb/>
            tur primum recta FH, tangens circulum in B, atque ex B, ducatur chorda B </s>
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