Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of figures

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          <pb o="97" file="133" n="134" rhead="Ioan. de Sacro Boſco."/>
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        <div xml:id="echoid-div254" type="section" level="1" n="87">
          <head xml:id="echoid-head91" style="it" xml:space="preserve">THEOR. 11. PROPOS. 13.</head>
          <p style="it">
            <s xml:id="echoid-s4710" xml:space="preserve">
              <emph style="sc">IRCVLVS</emph>
            omnibus figuris rectilineis regularibus ſibi iſoperime-
              <lb/>
              <note position="right" xlink:label="note-133-01" xlink:href="note-133-01a" xml:space="preserve">Circulus
                <lb/>
              omnium
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              figurarũ re
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              cti linearũ
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              regulariũ
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              ſibi iſoperi
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              metrarum
                <lb/>
              maximus
                <lb/>
              eſt.</note>
            tris eſt.</s>
            <s xml:id="echoid-s4711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4712" xml:space="preserve">
              <emph style="sc">Esto</emph>
            circulus A B C, figura autem regularis quotcunque laterum ei iſo-
              <lb/>
            perimetra D E F. </s>
            <s xml:id="echoid-s4713" xml:space="preserve">Dico circulum A B C, eſſe maiorem figura D E F. </s>
            <s xml:id="echoid-s4714" xml:space="preserve">Sit enim G,
              <lb/>
            centrum circuli A B C; </s>
            <s xml:id="echoid-s4715" xml:space="preserve">& </s>
            <s xml:id="echoid-s4716" xml:space="preserve">H, centrum figuræ D E F; </s>
            <s xml:id="echoid-s4717" xml:space="preserve">Deſcribaturq́. </s>
            <s xml:id="echoid-s4718" xml:space="preserve">circa cir-
              <lb/>
            culum A B C, figura B I K C, tot laterum, & </s>
            <s xml:id="echoid-s4719" xml:space="preserve">angulorum ęqualium, quot con-
              <lb/>
            tinet figura D E F, id eſt, ſimilis figurę D E F, per ea, quæ ex Campano docui-
              <lb/>
            mus in ſcholio 1. </s>
            <s xml:id="echoid-s4720" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4721" xml:space="preserve">16. </s>
            <s xml:id="echoid-s4722" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4723" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4724" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4725" xml:space="preserve">Deinde ex puncto contactus A, ad cen
              <lb/>
            trum G, ducatur recta A G, quæ perpendicularis erit ad I K. </s>
            <s xml:id="echoid-s4726" xml:space="preserve">Ducatur rur-
              <lb/>
              <note position="right" xlink:label="note-133-02" xlink:href="note-133-02a" xml:space="preserve">18. tertij.</note>
            ſus H D, ad L M, perpendicularis; </s>
            <s xml:id="echoid-s4727" xml:space="preserve">Diuidentq́. </s>
            <s xml:id="echoid-s4728" xml:space="preserve">rectæ G A, H D, rectas I K, L M,
              <lb/>
              <note position="right" xlink:label="note-133-03" xlink:href="note-133-03a" xml:space="preserve">3. tertij.</note>
            bifariam, ut conſtat, ſi figuris B I K C, D E F, circunſcribantur circuli. </s>
            <s xml:id="echoid-s4729" xml:space="preserve">Du-
              <lb/>
            cantur quoque recte G I, H L, quæ diuident angulos I, & </s>
            <s xml:id="echoid-s4730" xml:space="preserve">L, bifariam, ut ma-
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            nifeſtum eſt ex demonſtratione propoſ. </s>
            <s xml:id="echoid-s4731" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4732" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4733" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4734" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4735" xml:space="preserve">Quoniam igitur toti
              <lb/>
            anguli I, & </s>
            <s xml:id="echoid-s4736" xml:space="preserve">L, ſunt æquales, propter ſimilitudinem figurarum, erunt etia@
              <lb/>
              <figure xlink:label="fig-133-01" xlink:href="fig-133-01a" number="35">
                <image file="133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/133-01"/>
              </figure>
            ipſorum dimidia, uidelicet anguli A I G, D L H, ęqualia. </s>
            <s xml:id="echoid-s4737" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s4738" xml:space="preserve">an-
              <lb/>
              <note position="right" xlink:label="note-133-04" xlink:href="note-133-04a" xml:space="preserve">32. primi.</note>
            guli I A G, L D H, ſint ęquales, vtpote recti, erunt triangula A I G, D L H,
              <lb/>
            ęquiangula. </s>
            <s xml:id="echoid-s4739" xml:space="preserve">Quia uero ambitus figuræ B I K C, maior eſt (per 1. </s>
            <s xml:id="echoid-s4740" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4741" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4742" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s4743" xml:space="preserve">Archimedis de ſphæra, & </s>
            <s xml:id="echoid-s4744" xml:space="preserve">cylindro) ambitu circuli A B C; </s>
            <s xml:id="echoid-s4745" xml:space="preserve">Ambitus autem cir-
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            culi æqualis ponitur ambitui figuræ D E F; </s>
            <s xml:id="echoid-s4746" xml:space="preserve">erit quoq. </s>
            <s xml:id="echoid-s4747" xml:space="preserve">ambitus figurę B I K C. </s>
            <s xml:id="echoid-s4748" xml:space="preserve">
              <lb/>
            maior ambitu figurę D E F. </s>
            <s xml:id="echoid-s4749" xml:space="preserve">Cum igitur figuræ ſint regulares, & </s>
            <s xml:id="echoid-s4750" xml:space="preserve">ſimiles, erit
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            etiam latus I K, latere L M, maius, & </s>
            <s xml:id="echoid-s4751" xml:space="preserve">ideo I A, dimidium lateris I K, maius,
              <lb/>
              <note position="right" xlink:label="note-133-05" xlink:href="note-133-05a" xml:space="preserve">4. ſexti.</note>
            quàm L D, dimidium lateris L M. </s>
            <s xml:id="echoid-s4752" xml:space="preserve">Rurſus, quoniam eſt, vt I A, ad A G, ita L D,
              <lb/>
              <note position="right" xlink:label="note-133-06" xlink:href="note-133-06a" xml:space="preserve">14. quinti.</note>
            ad D H; </s>
            <s xml:id="echoid-s4753" xml:space="preserve">Et eſt I A, maior quàm L D, erit quoq. </s>
            <s xml:id="echoid-s4754" xml:space="preserve">A G, maior, quàm D H. </s>
            <s xml:id="echoid-s4755" xml:space="preserve">Quam
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            obrem rectangulum contentum ſub A G, & </s>
            <s xml:id="echoid-s4756" xml:space="preserve">dimidio ambitu circu li A B G,
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            quod (per 4. </s>
            <s xml:id="echoid-s4757" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4758" xml:space="preserve">huius) circulo A B C, eſt æquale, maius eſt, quàm rectangu
              <lb/>
            lum contentum ſub D H, & </s>
            <s xml:id="echoid-s4759" xml:space="preserve">dimidio ambitu figurę D E F, hoc eſt, (per 2. </s>
            <s xml:id="echoid-s4760" xml:space="preserve">pro-
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            poſ. </s>
            <s xml:id="echoid-s4761" xml:space="preserve">huius) quàm area figurę D E F. </s>
            <s xml:id="echoid-s4762" xml:space="preserve">Circulus igitur omnibus figuris rectilineis
              <lb/>
            regularibus ſibi iſoperimetris maior eſt, quod oſtendendum erat.</s>
            <s xml:id="echoid-s4763" xml:space="preserve"/>
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