Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s15085" xml:space="preserve">
              <pb o="322" file="352" n="352" rhead="GEOMETR. PRACT."/>
            Rectæ namque GL, AB, MN, ſi parum inter ſe diſtent, in circulo omnino æqua-
              <lb/>
            les iudicabuntur, quamuis verè AB, aliquanto maior ſit. </s>
            <s xml:id="echoid-s15086" xml:space="preserve">Itaque ſi res illæ rectæ
              <lb/>
            GH, AE, MP, perexiguam habeant diſtantiam inter ſe, dubitari non poteſt, pun-
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            ctum E, in quo quadratrix linea ſemidiametrum AB, ſecat, ab eo, quod verè in
              <lb/>
            Quadratriceibi exiſtit, non differre notabiliter: </s>
            <s xml:id="echoid-s15087" xml:space="preserve">dummodo puncta H, P, exqui-
              <lb/>
            ſitè & </s>
            <s xml:id="echoid-s15088" xml:space="preserve">ſumma adhibita diligentia, inuenta ſint.</s>
            <s xml:id="echoid-s15089" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15090" xml:space="preserve">
              <emph style="sc">Rectam</emph>
            porrò AD, vocamus latus Quadratricis: </s>
            <s xml:id="echoid-s15091" xml:space="preserve">& </s>
            <s xml:id="echoid-s15092" xml:space="preserve">rectam AE, eiuſdem
              <lb/>
              <note position="left" xlink:label="note-352-01" xlink:href="note-352-01a" xml:space="preserve">Lat{us} baſis &
                <lb/>
              @entrũ Qua-
                <lb/>
              dratricis.</note>
            baſem: </s>
            <s xml:id="echoid-s15093" xml:space="preserve">ac denique punctum A, centrum eiuſdem.</s>
            <s xml:id="echoid-s15094" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15095" xml:space="preserve">7. </s>
            <s xml:id="echoid-s15096" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            puncta Quadratricis prope baſem certius inueniemus (ſine in-
              <lb/>
            terſectionibus linearum, quæ ibi valdè obliquæ ſunt) per lineas perpendicula-
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            res: </s>
            <s xml:id="echoid-s15097" xml:space="preserve">hocmodo. </s>
            <s xml:id="echoid-s15098" xml:space="preserve">Ducta chorda Quadrantis B Q, ſecetur in D, bifariam. </s>
            <s xml:id="echoid-s15099" xml:space="preserve">quod
              <lb/>
            fiet, ſi ex A, ad C, punctum medium Quadrantis recta ducatur. </s>
            <s xml:id="echoid-s15100" xml:space="preserve"> Hæc enim
              <note symbol="a" position="left" xlink:label="note-352-02" xlink:href="note-352-02a" xml:space="preserve">ſchol. 27.
                <lb/>
              tertii.</note>
            ctam BQ, ſecabit bifariam. </s>
            <s xml:id="echoid-s15101" xml:space="preserve">Deinde rectæ AD, ſumatur æqualis AE; </s>
            <s xml:id="echoid-s15102" xml:space="preserve">iuncta que
              <lb/>
            recta D E, ſecetur bifariam in F. </s>
            <s xml:id="echoid-s15103" xml:space="preserve">quod etiam fiet, ſi ex A, ad I, punctum medium
              <lb/>
              <note symbol="b" position="left" xlink:label="note-352-03" xlink:href="note-352-03a" xml:space="preserve">ſchol. 27.
                <lb/>
              tertii.</note>
            arcus B C, ducatur AI. </s>
            <s xml:id="echoid-s15104" xml:space="preserve"> Hæc enim chordam B
              <figure xlink:label="fig-352-01" xlink:href="fig-352-01a" number="242">
                <image file="352-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/352-01"/>
              </figure>
            (ſi duceretur) ſecaret bifariam: </s>
            <s xml:id="echoid-s15105" xml:space="preserve"> ac proinde &</s>
            <s xml:id="echoid-s15106" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-352-04" xlink:href="note-352-04a" xml:space="preserve">ſchol. 4. ſe-
                <lb/>
              xti.</note>
            rectam DE, quæ chordæ BC, eſt parallela: </s>
            <s xml:id="echoid-s15107" xml:space="preserve">pro- pterea quod latera A B, A C, in triangulo A B C,
              <lb/>
              <note symbol="d" position="left" xlink:label="note-352-05" xlink:href="note-352-05a" xml:space="preserve">2. ſexti.</note>
            proportionaliter ſecantur, in D, E: </s>
            <s xml:id="echoid-s15108" xml:space="preserve">quippe cum
              <lb/>
            tam AB, AC, quam AE, AD, æquales ſint. </s>
            <s xml:id="echoid-s15109" xml:space="preserve">Rurſus
              <lb/>
            rectæ AF, capiatur æqualis AG, iunctaque FG, ſe-
              <lb/>
            cetur bifariam in H. </s>
            <s xml:id="echoid-s15110" xml:space="preserve">quod etiam fiet per rectam
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            AK, ductam ad K, punctum medium arcus BI. </s>
            <s xml:id="echoid-s15111" xml:space="preserve">At-
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            que hoc modo, ſi rectæ A H, æqualis accipiatur,
              <lb/>
            & </s>
            <s xml:id="echoid-s15112" xml:space="preserve">reliqua fiant, vt prius, inuenietur aliud punctum
              <lb/>
            inter H, & </s>
            <s xml:id="echoid-s15113" xml:space="preserve">G. </s>
            <s xml:id="echoid-s15114" xml:space="preserve">Et ſic deinceps quotuis alia puncta reperiemus viciniora ipſi
              <lb/>
            A B, per lineas perpendiculares, non autem per obliquas ſectiones, vt in prio-
              <lb/>
              <note symbol="e" position="left" xlink:label="note-352-06" xlink:href="note-352-06a" xml:space="preserve">3. tertii.</note>
            rifigura. </s>
            <s xml:id="echoid-s15115" xml:space="preserve"> Eſt enim A D, ad D B, perpendicularis, & </s>
            <s xml:id="echoid-s15116" xml:space="preserve">A F, ad DE, & </s>
            <s xml:id="echoid-s15117" xml:space="preserve">DH,
              <note symbol="f" position="left" xlink:label="note-352-07" xlink:href="note-352-07a" xml:space="preserve">ſchol. 26.
                <lb/>
              primi.</note>
            FG, &</s>
            <s xml:id="echoid-s15118" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15119" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15120" xml:space="preserve">
              <emph style="sc">Omnia</emph>
            verò hæc puncta inuenta D, F, H, &</s>
            <s xml:id="echoid-s15121" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15122" xml:space="preserve">eſſe in Quadratrice, ita oſten-
              <lb/>
              <note symbol="g" position="left" xlink:label="note-352-08" xlink:href="note-352-08a" xml:space="preserve">2. ſexti.</note>
            do. </s>
            <s xml:id="echoid-s15123" xml:space="preserve">Ductis DL, FM, NH, ipſi AB, parallelis ſecantibus BD, in O, P; </s>
            <s xml:id="echoid-s15124" xml:space="preserve"> erit vt BD, ad D Q, ita AL, ad L Q, ideoque & </s>
            <s xml:id="echoid-s15125" xml:space="preserve">A Q, ſectaerit in L, bifariam. </s>
            <s xml:id="echoid-s15126" xml:space="preserve">Sectus autem
              <lb/>
            eſt & </s>
            <s xml:id="echoid-s15127" xml:space="preserve">arcus B Q, in bifariam. </s>
            <s xml:id="echoid-s15128" xml:space="preserve">Igitur, vt oſtenſum eſt, punctum D, eſt in Qua-
              <lb/>
              <note symbol="h" position="left" xlink:label="note-352-09" xlink:href="note-352-09a" xml:space="preserve">2. ſexti.</note>
            dratrice. </s>
            <s xml:id="echoid-s15129" xml:space="preserve">Rurſus quia D E, ſecta eſt bifariam in F, erit quoque DB, ſecta
              <note symbol="i" position="left" xlink:label="note-352-10" xlink:href="note-352-10a" xml:space="preserve">2. ſexti.</note>
            riam in O, ideoque erit vt EF, ad FD, ita BO, ad OD. </s>
            <s xml:id="echoid-s15130" xml:space="preserve">Sed vt BO, ad OD; </s>
            <s xml:id="echoid-s15131" xml:space="preserve">ita eſt AM, ad ML, & </s>
            <s xml:id="echoid-s15132" xml:space="preserve">vt EF, ad FD, ita arcus BI, ad IC. </s>
            <s xml:id="echoid-s15133" xml:space="preserve">Ergo vt oſten dimus, ſeca-
              <lb/>
            bunt ſeſe AI, MO, in puncto Quadratricis. </s>
            <s xml:id="echoid-s15134" xml:space="preserve">Eademque ratio eſt de aliis punctis
              <lb/>
            hac arte inuentis.</s>
            <s xml:id="echoid-s15135" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15136" xml:space="preserve">8. </s>
            <s xml:id="echoid-s15137" xml:space="preserve">
              <emph style="sc">Esse</emph>
            porrò lineam hanc inflexam DE, à nobis Geometricè deſcriptam,
              <lb/>
            eandem, quam Dinoſtratus, & </s>
            <s xml:id="echoid-s15138" xml:space="preserve">Nicomedes per duos illos motus imaginarios
              <lb/>
            deſcribi concipiebant, perſpicuũ eſt. </s>
            <s xml:id="echoid-s15139" xml:space="preserve">Nam ſi ſemidiameter A D, in priori figura
              <lb/>
            circa centrum A, per arcum D B, eodem tempore moueatur motu vniformi,
              <lb/>
            quo latus DC, deorſum fertur motu quo que vniformi: </s>
            <s xml:id="echoid-s15140" xml:space="preserve">fit vt quando ſemidia-
              <lb/>
            meter AD, pertranſiuit quamcunque partem arcus DB, tunc latus DC, ſimilem
              <lb/>
            partem laterum DA, CB, percurrerit. </s>
            <s xml:id="echoid-s15141" xml:space="preserve">Alias aut duo illi motus non eſſent vni-
              <lb/>
            formes, aut non eodem tempore ad latus A B, tam ſemidiameter AD, quam </s>
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