Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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            <s xml:id="echoid-s4292" xml:space="preserve">
              <pb o="87" file="123" n="124" rhead="Ioan. de Sacro Boſco."/>
            ſiguræ A B C, quam latus E F, ambitum figuræ D E F. </s>
            <s xml:id="echoid-s4293" xml:space="preserve">Quare latus B C, mi-
              <lb/>
            nus erit latere E F, ideoq, B I, medietas lateris B C, minor, quàm E K, medie
              <lb/>
            tas lateris E F. </s>
            <s xml:id="echoid-s4294" xml:space="preserve">Ponatur K L, æqualis ipſi B I, & </s>
            <s xml:id="echoid-s4295" xml:space="preserve">ducantur rectæ L H, H E,
              <lb/>
              <note position="right" xlink:label="note-123-01" xlink:href="note-123-01a" xml:space="preserve">28. tertij.</note>
            H F, G B, G C. </s>
            <s xml:id="echoid-s4296" xml:space="preserve">Et quia omnes arcus circuli D E F, ſunt æquales, quòd & </s>
            <s xml:id="echoid-s4297" xml:space="preserve">re-
              <lb/>
            ctæ ſubtenſæ æquales ponantur; </s>
            <s xml:id="echoid-s4298" xml:space="preserve">erit recta E F, ita ſubmultiplex ambitus ſigu-
              <lb/>
            ræ D E F, ut arcus E F, ſubmultiplex eſt circunferentiæ circuli D E F: </s>
            <s xml:id="echoid-s4299" xml:space="preserve">Ea-
              <lb/>
            demq́ue ratione ita multiplex ambitus figuræ A B C, rectæ B C, ficut multi-
              <lb/>
            plex eſt circunferentia A B C, arcus B C: </s>
            <s xml:id="echoid-s4300" xml:space="preserve">Vt autem arcus E F, ad circunferen
              <lb/>
            tiam circuli D E F, ita eſt (ex coroll. </s>
            <s xml:id="echoid-s4301" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4302" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4303" xml:space="preserve">33. </s>
            <s xml:id="echoid-s4304" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4306" xml:space="preserve">Eucl.) </s>
            <s xml:id="echoid-s4307" xml:space="preserve">angulus E H F,
              <lb/>
            ad quatuor rectos. </s>
            <s xml:id="echoid-s4308" xml:space="preserve">Igitur erit quoque, ut recta E F, ad ambitum figuræ D E F,
              <lb/>
            hoc eſt, ad ambitum ſiguræ A B C, illi æqualem, ita angulus E H F, ad qua-
              <lb/>
            tuor rectos; </s>
            <s xml:id="echoid-s4309" xml:space="preserve">Vt autem ambitus figuræ A B C, ad rectam B C, ita eſt circunferẽ
              <lb/>
            tia circuli A B C, ad aroum B C, hoc eſt, ita quatuor recti (ex eodem coroll.
              <lb/>
            </s>
            <s xml:id="echoid-s4310" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4311" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4312" xml:space="preserve">33. </s>
            <s xml:id="echoid-s4313" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">Eucl.) </s>
            <s xml:id="echoid-s4316" xml:space="preserve">ad angulum B G C. </s>
            <s xml:id="echoid-s4317" xml:space="preserve">Ex æquo igitur ut recta E F, ad
              <lb/>
            rectam B C, hoc eſt, ut recta E K, ad rectam B I, hoc eſt, ad rectam K L, ita an-
              <lb/>
            gulus E H F, ad angulum B G C, hoc eſt, ita angulus E H K, ad angulum
              <lb/>
              <note position="right" xlink:label="note-123-02" xlink:href="note-123-02a" xml:space="preserve">15. quinti.</note>
            B G I. </s>
            <s xml:id="echoid-s4318" xml:space="preserve">Eſ
              <unsure/>
            t autem maior proportio rectæ E K, ad rectam K L, (per 5. </s>
            <s xml:id="echoid-s4319" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s4320" xml:space="preserve">
              <note position="right" xlink:label="note-123-03" xlink:href="note-123-03a" xml:space="preserve">15. quinti.</note>
            huius) quàm anguli E H K, ad angulum K H L. </s>
            <s xml:id="echoid-s4321" xml:space="preserve">Quare maior erit proportio
              <lb/>
            quoque anguli E H K, ad angulum B G I, quàm eiuſdem anguli E H K, ad
              <lb/>
              <note position="right" xlink:label="note-123-04" xlink:href="note-123-04a" xml:space="preserve">13. quinti.</note>
            angulum K H L; </s>
            <s xml:id="echoid-s4322" xml:space="preserve">ideoq́ue maior erit angulus K H L, quàm angulus B G L. </s>
            <s xml:id="echoid-s4323" xml:space="preserve">Cũ
              <lb/>
              <note position="right" xlink:label="note-123-05" xlink:href="note-123-05a" xml:space="preserve">10. quinti.</note>
            igitur anguli H K L, G I B, ſint æquales, vtpote recti, erit reliquus an
              <unsure/>
            gulus
              <lb/>
            H L K, minor reliquo angulo G B I. </s>
            <s xml:id="echoid-s4324" xml:space="preserve">Fiat igitur angulus K L M, æqualis an-
              <lb/>
              <note position="right" xlink:label="note-123-06" xlink:href="note-123-06a" xml:space="preserve">32. primi.</note>
            gulo G B I; </s>
            <s xml:id="echoid-s4325" xml:space="preserve">cadetq́ue L M, extra L H; </s>
            <s xml:id="echoid-s4326" xml:space="preserve">conuenietq́ue cum K H, producta ul-
              <lb/>
            tra H, in puncto M. </s>
            <s xml:id="echoid-s4327" xml:space="preserve">Quoniam igitur duo anguli B, I, trianguli G B I, æqua
              <lb/>
            les ſunt duobus angulis L, K, trianguli M L K, & </s>
            <s xml:id="echoid-s4328" xml:space="preserve">latera B I, L K, ęqualia,
              <lb/>
            erunt rectæ G I, M K, æquales. </s>
            <s xml:id="echoid-s4329" xml:space="preserve">Recta ergo G I, maior eſt, quàm recta H K.
              <lb/>
            </s>
            <s xml:id="echoid-s4330" xml:space="preserve">
              <note position="right" xlink:label="note-123-07" xlink:href="note-123-07a" xml:space="preserve">26. primi.</note>
            Quamobrem rectangulum ſub G I, & </s>
            <s xml:id="echoid-s4331" xml:space="preserve">dimidio ambitu ſiguræ A B C, conten
              <lb/>
            tum maius erit rectangulo contento ſub H K, & </s>
            <s xml:id="echoid-s4332" xml:space="preserve">dimidio ambitu figuræ
              <lb/>
            D E C, qui æqualis ponitur dimidio ambitus figuræ A B C. </s>
            <s xml:id="echoid-s4333" xml:space="preserve">Quocirca cum
              <lb/>
            illud rectangulum oſtenſum ſit, in 2. </s>
            <s xml:id="echoid-s4334" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4335" xml:space="preserve">huius, æquale figuræ A B C,
              <lb/>
            hoc autem figuræ D E F, æquale; </s>
            <s xml:id="echoid-s4336" xml:space="preserve">maior quoque erit figura A B C, quàm fi-
              <lb/>
            gura D E F. </s>
            <s xml:id="echoid-s4337" xml:space="preserve">Iſoperimetrarum ergo ſigurarum regularium maior eſt illa, &</s>
            <s xml:id="echoid-s4338" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4339" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s4340" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div232" type="section" level="1" n="79">
          <head xml:id="echoid-head83" style="it" xml:space="preserve">THEOR. 1. PROPOS. 7.</head>
          <note position="right" xml:space="preserve">Qua arte
            <lb/>
          triangulũ
            <lb/>
          Iſoſceles cõ
            <lb/>
          ſtituatur
            <lb/>
          Iſoperime-
            <lb/>
          trũ cuiuis
            <lb/>
          triangulo
            <lb/>
          non Iſoſce-
            <lb/>
          li.</note>
          <p style="it">
            <s xml:id="echoid-s4341" xml:space="preserve">
              <emph style="sc">Proposito</emph>
            triangulo, cuius duo latera ſint inæqualia, ſupra
              <lb/>
            reliquum latus triangulum priori Iſoperimetrum, ac duo habens latera
              <lb/>
            æqu alia, deſcribere.</s>
            <s xml:id="echoid-s4342" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4343" xml:space="preserve">
              <emph style="sc">Sit</emph>
            triangulum A B C, cuius duo latera A B, B C, ſint inæqualia, nempe
              <lb/>
            A B, maius, quàm B C; </s>
            <s xml:id="echoid-s4344" xml:space="preserve">oporreatq́ue ſupra A C, conſtruere triangulum Iſo-
              <lb/>
            ſceles, atque iſoperimetrum triangulo A B C. </s>
            <s xml:id="echoid-s4345" xml:space="preserve">Sumatur recta D E, æqualis
              <lb/>
            duobus lateribus A B, B C, ſimul, diuidaturq́ue bifariam in F. </s>
            <s xml:id="echoid-s4346" xml:space="preserve">Et quoniam
              <lb/>
              <note position="right" xlink:label="note-123-09" xlink:href="note-123-09a" xml:space="preserve">10. primi.</note>
            latera A B, B C, ſimul maiora ſunt latere A G, erit quoque dimidium illo-
              <lb/>
            rum, nempe D F, vel F E, maius, quàm dimidium lateris A C: </s>
            <s xml:id="echoid-s4347" xml:space="preserve">Atque ob </s>
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