Clavius, Christoph, Geometria practica

Table of handwritten notes

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            <s xml:id="echoid-s12463" xml:space="preserve">
              <pb o="271" file="301" n="301" rhead="LIBER SEXTVS."/>
            culari G I. </s>
            <s xml:id="echoid-s12464" xml:space="preserve">Ducta namque recta D H, erit angulus DKE, maio@ angulo DLE.</s>
            <s xml:id="echoid-s12465" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-301-01" xlink:href="note-301-01a" xml:space="preserve">16. primi.</note>
            hoc eſt angulus GKI, angulo HLA. </s>
            <s xml:id="echoid-s12466" xml:space="preserve">Cum ergo recti I, A, æquales ſint; </s>
            <s xml:id="echoid-s12467" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-301-02" xlink:href="note-301-02a" xml:space="preserve">15. primi.</note>
            reliquus G, reliquo AHL, minor. </s>
            <s xml:id="echoid-s12468" xml:space="preserve">Siigitur ipſi G, fiat æqualis AHM; </s>
            <s xml:id="echoid-s12469" xml:space="preserve">erunt trian-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-301-03" xlink:href="note-301-03a" xml:space="preserve">32. primi.</note>
            gula KGI, MHA, æquiangula; </s>
            <s xml:id="echoid-s12470" xml:space="preserve"> ideoque erit, vt MH, ad HA, ita KG, ad GI.</s>
            <s xml:id="echoid-s12471" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-301-04" xlink:href="note-301-04a" xml:space="preserve">4. ſexti.</note>
            Et quia L H, maior eſt, quam M H, (quod angulus HML, maior ſit recto
              <note symbol="e" position="right" xlink:label="note-301-05" xlink:href="note-301-05a" xml:space="preserve">19. primi.</note>
            & </s>
            <s xml:id="echoid-s12472" xml:space="preserve">HLM, minor) erit maior proportio LH, ad HA, quam HM, ad HA,
              <note symbol="f" position="right" xlink:label="note-301-06" xlink:href="note-301-06a" xml:space="preserve">16. primi.</note>
            eſt, quam GK, ad GI: </s>
            <s xml:id="echoid-s12473" xml:space="preserve">ac proinde cum GK, HL, æquales ſint, erit quo que ma-
              <lb/>
              <note symbol="g" position="right" xlink:label="note-301-07" xlink:href="note-301-07a" xml:space="preserve">17. primi.</note>
            ior proportio HL, ad HA, quam HL, ad GI; </s>
            <s xml:id="echoid-s12474" xml:space="preserve"> ideo que HA, minor erit
              <note symbol="h" position="right" xlink:label="note-301-08" xlink:href="note-301-08a" xml:space="preserve">8. quinti.</note>
            GI. </s>
            <s xml:id="echoid-s12475" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s12476" xml:space="preserve"/>
          </p>
          <note symbol="i" position="right" xml:space="preserve">10. quinti.</note>
          <p>
            <s xml:id="echoid-s12477" xml:space="preserve">
              <emph style="sc">Altera</emph>
            proprietas eſt. </s>
            <s xml:id="echoid-s12478" xml:space="preserve">Quamuis Conchilis CF, nunquam conueniat cum
              <lb/>
            recta EB, tamen cum qualibet alia recta, etiam ipſi EB, propinquiſsima conue-
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            nit. </s>
            <s xml:id="echoid-s12479" xml:space="preserve">Sit enim primum recta NO, ipſi EB, parallela, ſecans EC, in O. </s>
            <s xml:id="echoid-s12480" xml:space="preserve">Fiatvt EO,
              <lb/>
            ad OD, ita E C, ad P. </s>
            <s xml:id="echoid-s12481" xml:space="preserve">Et quoniam E O, minor eſt quam E C;</s>
            <s xml:id="echoid-s12482" xml:space="preserve">
              <unsure/>
            erit
              <note symbol="k" position="right" xlink:label="note-301-10" xlink:href="note-301-10a" xml:space="preserve">14. quinti.</note>
            OD, minor quam P. </s>
            <s xml:id="echoid-s12483" xml:space="preserve">Si igitur ex D, ad interuallum rectę P, deſcribatur arcus cir-
              <lb/>
            culi, ſecabit is rectam ON, in aliquo puncto, vt in N. </s>
            <s xml:id="echoid-s12484" xml:space="preserve">Dico Conchilem CF, pro-
              <lb/>
            longatam coire cum O N, in N. </s>
            <s xml:id="echoid-s12485" xml:space="preserve">Ducta enim recta D N, ſecante E B, in B, quæ
              <lb/>
            ipſi P, æqualis erit; </s>
            <s xml:id="echoid-s12486" xml:space="preserve"> quoniam eſt vt EO, ad OD, ita BN, ad ND; </s>
            <s xml:id="echoid-s12487" xml:space="preserve">hoc eſt, ad
              <note symbol="l" position="right" xlink:label="note-301-11" xlink:href="note-301-11a" xml:space="preserve">4. ſexti.</note>
            bi æqualem P. </s>
            <s xml:id="echoid-s12488" xml:space="preserve">Fuit autem etiam, vt EO, ad OD, ita EC,
              <unsure/>
            ad P. </s>
            <s xml:id="echoid-s12489" xml:space="preserve">Igitur BN, EC,
              <lb/>
            ad P, eandem proportionem habebunt: </s>
            <s xml:id="echoid-s12490" xml:space="preserve"> ac proinde inter ſe æquales erunt;</s>
            <s xml:id="echoid-s12491" xml:space="preserve">
              <note symbol="m" position="right" xlink:label="note-301-12" xlink:href="note-301-12a" xml:space="preserve">9. quinti.</note>
            ideoque Conchilis per N, tranſibit.</s>
            <s xml:id="echoid-s12492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12493" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde recta Q F, non parallela ipſi E B, ſed eam ſecet in E, vergatque
              <lb/>
            verſus Conchilem. </s>
            <s xml:id="echoid-s12494" xml:space="preserve">Quia igitur Conchilis cum recta ON, conuenit, conueniet
              <lb/>
            prius cum ipſa QF, in F, vt perſpicuum eſt.</s>
            <s xml:id="echoid-s12495" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12496" xml:space="preserve">
              <emph style="sc">Post</emph>
            hæc Nicomedes diſſoluit huiuſmodi problema. </s>
            <s xml:id="echoid-s12497" xml:space="preserve">Dato quouis angu-
              <lb/>
            lo rectilineo, & </s>
            <s xml:id="echoid-s12498" xml:space="preserve">puncto extra lineas angulum datum comprehendentes: </s>
            <s xml:id="echoid-s12499" xml:space="preserve">Ab
              <lb/>
            illo puncto educere rectam ſecantem rectas datum continentes angulum, ita vt
              <lb/>
            eius portio inter illas rectas intercepta æqualis ſit datæ rectę. </s>
            <s xml:id="echoid-s12500" xml:space="preserve">In eadem nam-
              <lb/>
            que figura rectæ EB, EF, angulum contineant BEF, ducendaque ſit ex D, linea,
              <lb/>
            ita vt eius portio inter E B, E F, æqualis ſit datæ rectæ, R. </s>
            <s xml:id="echoid-s12501" xml:space="preserve">Ex O, ad inferiorem
              <lb/>
            lineam E B, ducatur perpendicularis DE, ſumatur que EC, datæ rectæ R, æqua-
              <lb/>
            lis: </s>
            <s xml:id="echoid-s12502" xml:space="preserve">& </s>
            <s xml:id="echoid-s12503" xml:space="preserve">polo D, interuallo verò EG, Conchilis deſcribatur, quæ per ſecun-
              <lb/>
            dam proprietatem rectam E F, ſecabit in F. </s>
            <s xml:id="echoid-s12504" xml:space="preserve">Ducta ergo recta D F, ſecante
              <lb/>
            E B, in S; </s>
            <s xml:id="echoid-s12505" xml:space="preserve">erit S F, ipſi EC, hoc eſt, ipſi R, æqualis, vt ex deſcriptione Conchi-
              <lb/>
            lis liquet.</s>
            <s xml:id="echoid-s12506" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12507" xml:space="preserve">
              <emph style="sc">His</emph>
            præmiſsis, ſint duæ rectæ AB BC, ad angulum rectum B, coniunctæ, in-
              <lb/>
            ter quas reperiendæ ſint duę lineæ medię proportionales. </s>
            <s xml:id="echoid-s12508" xml:space="preserve">Compleatur rectan-
              <lb/>
            gulum AC, cuius duo latera A D, CD, bifariam ſecentur in F, E. </s>
            <s xml:id="echoid-s12509" xml:space="preserve">Ducta autem
              <lb/>
            ex B, per E, recta ſecante A D, productam in G; </s>
            <s xml:id="echoid-s12510" xml:space="preserve"> erit DG, ipſi CB, hoc eſt,
              <note symbol="n" position="right" xlink:label="note-301-13" xlink:href="note-301-13a" xml:space="preserve">26. primi.</note>
            D A, æqualis; </s>
            <s xml:id="echoid-s12511" xml:space="preserve">propterea quod anguli D, E, trianguli D E G, angulis CE, trian-
              <lb/>
            guli CEB, æquales ſunt, & </s>
            <s xml:id="echoid-s12512" xml:space="preserve">latera quoque DE, CE, quibus adiacent, æqualia.
              <lb/>
            </s>
            <s xml:id="echoid-s12513" xml:space="preserve">Rurſus ductam perpendicularem FH, ſecet AH, ipſi CE, æqualis, quod fiet, ſi ex
              <lb/>
            A, ad interuallum C E, arcus delineetur ſecans F H, in H. </s>
            <s xml:id="echoid-s12514" xml:space="preserve">Deinde iuncta recta
              <lb/>
            GH, ducatur ei parallela AI: </s>
            <s xml:id="echoid-s12515" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s12516" xml:space="preserve">producta DA; </s>
            <s xml:id="echoid-s12517" xml:space="preserve">ex H, per problema præcedens,
              <lb/>
            ducatur recta HK, vtramque AI, AK, ita ſecans, vt inter cepta IK, ipſi AH, vel
              <lb/>
            CE, æqualis ſit. </s>
            <s xml:id="echoid-s12518" xml:space="preserve">quod fiet, ſi ex H, plurimæ rectæ ducentur occultæ, donec v-
              <lb/>
            nius portio inter cepta æqualis ſit ipſi AH, vel CE. </s>
            <s xml:id="echoid-s12519" xml:space="preserve">Poſtremò ex K, per B, </s>
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