Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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          <p>
            <s xml:id="echoid-s4042" xml:space="preserve">
              <pb o="79" file="115" n="116" rhead="Ioan. de Sacro Boſco."/>
            qua uero duo latera A D, C E, parallelogrammi A D C E, (propteree quòd
              <lb/>
            opponuntur minoribus angulis, nempe acutis, in triangulis A D B, A C E)
              <lb/>
              <note position="right" xlink:label="note-115-01" xlink:href="note-115-01a" xml:space="preserve">19. primi.</note>
            minora ſunt reliquis duobus lateribus A B, A C, trianguli A B C, quòd hęc
              <lb/>
            in eiſdem triangulis opponantur maioribus angulis, nempe rectis: </s>
            <s xml:id="echoid-s4043" xml:space="preserve">erit ambi-
              <lb/>
            tus parallelogrammi A D C E, minor ambitu trianguli A B C. </s>
            <s xml:id="echoid-s4044" xml:space="preserve">Quamobrem,
              <lb/>
            ut ambitus parallelogrammi fiat æqualis ambitui trianguli, producenda e-
              <lb/>
            runt latera D A, C E, ad ęqualita@em laterum A B, A C. </s>
            <s xml:id="echoid-s4045" xml:space="preserve">Sit igitur recta
              <lb/>
            D A G, æqualis lateri A B, & </s>
            <s xml:id="echoid-s4046" xml:space="preserve">recta C E F, ęqualis lateri A C, dicaturq́ue re-
              <lb/>
            cta F G. </s>
            <s xml:id="echoid-s4047" xml:space="preserve">Ex quibus efficitur, parallelo grammum C F G D, & </s>
            <s xml:id="echoid-s4048" xml:space="preserve">triangulum
              <lb/>
            A B C, eſſe iſoperimetra. </s>
            <s xml:id="echoid-s4049" xml:space="preserve">Quoniam uero parallelogramum C F G D, ſu-
              <lb/>
            perat parallelo grammum A D C E, quantitate A E F G, oſtenſumq́ue eſt pa-
              <lb/>
            rallelo grammum A D C E, triangulo A B C, ęquale, maius quoque erit pa-
              <lb/>
            rallelo grammum idem C F G D, quam triangulum A B C, eadem quantita-
              <lb/>
            te A E F G. </s>
            <s xml:id="echoid-s4050" xml:space="preserve">Quapropter conſtat, figuram quadrilateram capaciorem eſſe fi-
              <lb/>
            gura triangulari ſibi iſoperimetra, quod erat oſtendendum. </s>
            <s xml:id="echoid-s4051" xml:space="preserve">Cum igitur ea-
              <lb/>
            dem eſſe uideatur ratio in alijs figuris rectilineis plurium laterum, iſoperi-
              <lb/>
            metris tamen; </s>
            <s xml:id="echoid-s4052" xml:space="preserve">Quo enim plures habet angulos figura, eo pluribus in locis
              <lb/>
            latera eius recedunt à centro, & </s>
            <s xml:id="echoid-s4053" xml:space="preserve">medio, ac propterea capacior exiſtit: </s>
            <s xml:id="echoid-s4054" xml:space="preserve">Perſpi-
              <lb/>
            cuum eſt circulum, quòd infinitos quodammodo includat angulos, & </s>
            <s xml:id="echoid-s4055" xml:space="preserve">latera,
              <lb/>
            omnibusq́ue punctis ęqualiter recedat à centro, omnium figurarum iſoperime
              <lb/>
            trarum eſſe capaciſſimum. </s>
            <s xml:id="echoid-s4056" xml:space="preserve">Idem quoque dicendum erit de ſphęra, ſi cum alijs
              <lb/>
            corporibus ſibi iſoperimetris comparetur.</s>
            <s xml:id="echoid-s4057" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Inter figu-
            <lb/>
          ras Iſoperi-
            <lb/>
          metras ca--
            <lb/>
          pacior eſt,
            <lb/>
          quę æquila-
            <lb/>
          tera eſt, &
            <lb/>
          æquiangu@ -
            <lb/>
          la, poſito æ-
            <lb/>
          quali nume
            <lb/>
          ro laterum
            <lb/>
          in utraque,
            <lb/>
          ac proinde
            <lb/>
          circulus ca-
            <lb/>
          paciffimus
            <lb/>
          eſt.</note>
          <p>
            <s xml:id="echoid-s4058" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            Iſoperimetrarum figurarum rectilinearum latera numero ę-
              <lb/>
            qualia habentium, maior eſt illa, quę & </s>
            <s xml:id="echoid-s4059" xml:space="preserve">latera habet æqualia, & </s>
            <s xml:id="echoid-s4060" xml:space="preserve">angulos æ-
              <lb/>
            quales. </s>
            <s xml:id="echoid-s4061" xml:space="preserve">Eſto enim quadratum aliquod habens in quolibet latere 9. </s>
            <s xml:id="echoid-s4062" xml:space="preserve">ita ut to-
              <lb/>
            tus eius ambitus contineat 24. </s>
            <s xml:id="echoid-s4063" xml:space="preserve">Erit area huius quadrati, iuxta pręcepta A-
              <lb/>
            rithmeticorum, 36. </s>
            <s xml:id="echoid-s4064" xml:space="preserve">Ita enim uides, quadratum totum diuiſum eſſe in 36. </s>
            <s xml:id="echoid-s4065" xml:space="preserve">qua
              <lb/>
              <figure xlink:label="fig-115-01" xlink:href="fig-115-01a" number="16">
                <image file="115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/115-01"/>
              </figure>
            drata paruula. </s>
            <s xml:id="echoid-s4066" xml:space="preserve">Eſto quoque aliquod parallelo grammum rectangulum habens
              <lb/>
            unumquodque duorum laterum oppoſitorum 10. </s>
            <s xml:id="echoid-s4067" xml:space="preserve">reliquorum uero duorum
              <lb/>
            quodlibet 2. </s>
            <s xml:id="echoid-s4068" xml:space="preserve">ut ſit ambitui illius ęqualis ambitus quadrati. </s>
            <s xml:id="echoid-s4069" xml:space="preserve">Quo poſito, area
              <lb/>
            huius parallelogrammi comprehendet tantummodo 20. </s>
            <s xml:id="echoid-s4070" xml:space="preserve">quadrata paruula ex
              <lb/>
            illis 36. </s>
            <s xml:id="echoid-s4071" xml:space="preserve">quę quadratum in ſe continet. </s>
            <s xml:id="echoid-s4072" xml:space="preserve">Hoc autem ideo euenit, quoniam pa-
              <lb/>
            rallelo grammum non eſt æquilaterum, ſed altera parte longius, quamuis </s>
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