Clavius, Christoph, Geometria practica

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          <pb o="296" file="326" n="326" rhead="GEOMETR. PRACT."/>
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        <div xml:id="echoid-div853" type="section" level="1" n="296">
          <head xml:id="echoid-head323" xml:space="preserve">THEOR. 6. PROPOS. 6.</head>
          <p>
            <s xml:id="echoid-s14008" xml:space="preserve">ISOPERIMETRARVM figurarum regularium maior eſt illa, quæ
              <lb/>
              <note position="left" xlink:label="note-326-01" xlink:href="note-326-01a" xml:space="preserve">Inter figur{as}
                <lb/>
              Iſoperimetr{as},
                <lb/>
              quæ plur{es} an-
                <lb/>
              gulos, ſeu late-
                <lb/>
              ra continet, il-
                <lb/>
              la maior eſt.</note>
            plures continet angulos, pluraue latera.</s>
            <s xml:id="echoid-s14009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14010" xml:space="preserve">
              <emph style="sc">Sint</emph>
            duæ figuræ regulares iſoperimetræ ABC, DEF, habeatque plura late-
              <lb/>
            ra, ſiue angulos figura ABC, quam DEF. </s>
            <s xml:id="echoid-s14011" xml:space="preserve">Dico ABC, maiorem eſſe, quam DEF.
              <lb/>
            </s>
            <s xml:id="echoid-s14012" xml:space="preserve">
              <figure xlink:label="fig-326-01" xlink:href="fig-326-01a" number="218">
                <image file="326-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/326-01"/>
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            Deſcribatur enim circa figuras circuli, à quorum centris G, H, ducantur ad BC,
              <lb/>
            EF, perpendiculares GI, HK, quæ diuident rectas BC, EF, bifariam. </s>
            <s xml:id="echoid-s14013" xml:space="preserve">
              <note symbol="a" position="left" xlink:label="note-326-02" xlink:href="note-326-02a" xml:space="preserve">3. tertij.</note>
            igitur figura ABC, plura habet latera, quam DEF, ſibi iſoperimetra, efficitur, vt
              <lb/>
            latus BC, ſæpius repetitum metiatur ambitum figuræ ABC, quam latus EF, am-
              <lb/>
            bitum figuræ DEF. </s>
            <s xml:id="echoid-s14014" xml:space="preserve">Quare latus B C, minus erit latere EF, ideo que BI, medietas
              <lb/>
            lateris B C, minor, quàm EK, medietas lateris EF. </s>
            <s xml:id="echoid-s14015" xml:space="preserve">Ponatur KL, ęqualis ipſi BI, & </s>
            <s xml:id="echoid-s14016" xml:space="preserve">
              <lb/>
            ducantur rectæ LH, HE, HF, GB, GC. </s>
            <s xml:id="echoid-s14017" xml:space="preserve"> Et quia omnes arcus circuli D E F,
              <note symbol="b" position="left" xlink:label="note-326-03" xlink:href="note-326-03a" xml:space="preserve">28. tertij.</note>
            æquales, quòd & </s>
            <s xml:id="echoid-s14018" xml:space="preserve">rectæ ſubtenſę æquales ponantur; </s>
            <s xml:id="echoid-s14019" xml:space="preserve">erit recta E F, ita ſubmul-
              <lb/>
            tiplex ambitus figuræ D E F, vt arcus E F, ſubmultiplex eſt circumferen-
              <lb/>
            tiæ circuli D E F: </s>
            <s xml:id="echoid-s14020" xml:space="preserve">Eademque ratione ita multiplex ambitus figuræ A B C,
              <lb/>
            rectæ B C, ſicut multiplex eſt circumferentia A B C, arcus B C. </s>
            <s xml:id="echoid-s14021" xml:space="preserve"> Vt
              <note symbol="c" position="left" xlink:label="note-326-04" xlink:href="note-326-04a" xml:space="preserve">2. coroll. 33.
                <lb/>
              ſexti.</note>
            arcus EF, ad circumferentiam circuli DEF, ita eſt angulus EHF, ad quatuor re-
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            ctos; </s>
            <s xml:id="echoid-s14022" xml:space="preserve">Igitur erit quoque vt recta EF, ad ambitum figuræ DEF, hoc eſt, ad ambi-
              <lb/>
            tum figuræ ABC, illi æqualem, ita angulus EHF, ad quatuor rectos: </s>
            <s xml:id="echoid-s14023" xml:space="preserve">Vt autem
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            ambitus figuræ ABC, ad rectam BC, ita eſt circumferentia circuli ABC, ad arcum
              <lb/>
            BC, hoc eſt, ita quatuor rectiad angulum B G C. </s>
            <s xml:id="echoid-s14024" xml:space="preserve">Ex æquo igitur, vt recta E
              <note symbol="d" position="left" xlink:label="note-326-05" xlink:href="note-326-05a" xml:space="preserve">2. coroll. 33.
                <lb/>
              ſexti.</note>
            ad rectam BC, hoc eſt, vt recta EK, ad rectam BI, hoc eſt, ad rectam KL, ita an- gulus EHF, ad angulum BGC, hoc eſt, ita angulus EHK, ad angulum B G I. </s>
            <s xml:id="echoid-s14025" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-326-06" xlink:href="note-326-06a" xml:space="preserve">15. quinti.</note>
            Eſt autem maior proportio rectæ EK, ad rectam KL, quam anguli EHK, ad an-
              <lb/>
              <note symbol="f" position="left" xlink:label="note-326-07" xlink:href="note-326-07a" xml:space="preserve">15. quinti.</note>
            gulum KHL. </s>
            <s xml:id="echoid-s14026" xml:space="preserve"> Quare maior erit proportio quoque anguli EHK, ad
              <note symbol="g" position="left" xlink:label="note-326-08" xlink:href="note-326-08a" xml:space="preserve">5. hui{us}.</note>
            BGI, quam eiuſdem anguli EHK, ad angulum KHL; </s>
            <s xml:id="echoid-s14027" xml:space="preserve"> ideoq; </s>
            <s xml:id="echoid-s14028" xml:space="preserve">maior erit
              <note symbol="h" position="left" xlink:label="note-326-09" xlink:href="note-326-09a" xml:space="preserve">13. quinti.</note>
            lus KHL, quam angulus B G I. </s>
            <s xml:id="echoid-s14029" xml:space="preserve">Cumigitur anguli H K L, G I B, ſint ęquales, vt
              <lb/>
              <note symbol="i" position="left" xlink:label="note-326-10" xlink:href="note-326-10a" xml:space="preserve">10. quinti.</note>
            pote recti; </s>
            <s xml:id="echoid-s14030" xml:space="preserve"> erit reliquus angulus HLK, minor reliquo angulo GBI. </s>
            <s xml:id="echoid-s14031" xml:space="preserve">
              <note symbol="k" position="left" xlink:label="note-326-11" xlink:href="note-326-11a" xml:space="preserve">32. primi.</note>
            angulus K L M, æqualis angulo G B I; </s>
            <s xml:id="echoid-s14032" xml:space="preserve">cadetque LM, extra L H; </s>
            <s xml:id="echoid-s14033" xml:space="preserve">conuenietque
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            cum KH, producta vltra H, in puncto M. </s>
            <s xml:id="echoid-s14034" xml:space="preserve">Quoniam igitur duo anguli B, I, trian-
              <lb/>
            guli GBI, ęquales ſunt duobus angulis L, K, trianguli MLK, & </s>
            <s xml:id="echoid-s14035" xml:space="preserve">latera BI, LK, æ-
              <lb/>
            qualia, erunt rectæ GI, MK, ęquales. </s>
            <s xml:id="echoid-s14036" xml:space="preserve">Recta ergo GI, maior eſt, quam recta HK.</s>
            <s xml:id="echoid-s14037" xml:space="preserve">
              <note symbol="l" position="left" xlink:label="note-326-12" xlink:href="note-326-12a" xml:space="preserve">26. primi.</note>
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