Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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        <div xml:id="echoid-div205" type="section" level="1" n="67">
          <p>
            <s xml:id="echoid-s4117" xml:space="preserve">
              <pb o="81" file="117" n="118" rhead="Ioan. de Sacro Boſco."/>
            ra, & </s>
            <s xml:id="echoid-s4118" xml:space="preserve">æquiangula exiſtit, omnium eſſe maximam: </s>
            <s xml:id="echoid-s4119" xml:space="preserve">Eadem enim eſt ratio haben-
              <lb/>
            da de figuris Iſoperimetris, quæ plura latera, pluresq́ue angulos continent.
              <lb/>
            </s>
            <s xml:id="echoid-s4120" xml:space="preserve">Quamobrem, cum circulus infinita propemodum latera æqualia, infinitos
              <lb/>
            quoque angulos quodammodo æquales comprehendat, eo quòd eius circun-
              <lb/>
            ferentia ſemper curuetur æqualiter, efficitur, ut ſit inter omnes figuras Iſope-
              <lb/>
            rimetras capaciſſimus. </s>
            <s xml:id="echoid-s4121" xml:space="preserve">Atque hiſce potiſſimum rationibus nituntur nonnullĩ
              <unsure/>
              <lb/>
            auctores confirmare, circulum eſſe maxime capacem: </s>
            <s xml:id="echoid-s4122" xml:space="preserve">Ex quibus manifeſtum ar
              <lb/>
            bitror relinqui, quidnam ſibi uelit auctor noſter in ſecunda hac ratione de-
              <lb/>
            ſumpta à commoditate, in qua mentionem ſecit figurarum Iſoperimetrarum.</s>
            <s xml:id="echoid-s4123" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4124" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            quoniam prædictæ rationes coniecturæ potius, quàm demonſtra-
              <lb/>
            tiones ſunt appellandæ: </s>
            <s xml:id="echoid-s4125" xml:space="preserve">Neque enim circulus angulos ullos, aut latera conti
              <lb/>
            net, ex quibus componatur, quemadmodum in præfatis rationibus aſſumeba-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s4126" xml:space="preserve">Immo vero, etiamſi & </s>
            <s xml:id="echoid-s4127" xml:space="preserve">angulos, & </s>
            <s xml:id="echoid-s4128" xml:space="preserve">latera haberet propemodum infinita, nõ
              <lb/>
            eſt tamen in uniuerſum demonſtratione confirmatum, eam ſemper figurã, quę
              <lb/>
            plures habet angulos, ſiue latera, atque adeo eam, quæ & </s>
            <s xml:id="echoid-s4129" xml:space="preserve">latera & </s>
            <s xml:id="echoid-s4130" xml:space="preserve">angulos ha-
              <lb/>
            bet æquales, inter iſoperimetras figuras eſſe capaciſſimam; </s>
            <s xml:id="echoid-s4131" xml:space="preserve">ſed hoc tantum oſtẽ
              <lb/>
            ſum eſt in triangulo Iſoſcele, vel Æquilatero, ſi cum parallelogrãmo confe-
              <lb/>
            ratur, & </s>
            <s xml:id="echoid-s4132" xml:space="preserve">in parallelogrammis; </s>
            <s xml:id="echoid-s4133" xml:space="preserve">non autem in figuris, quæ plura continent late-
              <lb/>
            ra. </s>
            <s xml:id="echoid-s4134" xml:space="preserve">Idcirco non abs re me facturum iudicaui, ſi hoc loco interponam tractatio
              <lb/>
            nem perbreuem de figuris Iſoperimetris, in qua euidentiſſime demonſtratur,
              <lb/>
            circulum inter figuras planas iſoperimetras eſſe capaciſſimum; </s>
            <s xml:id="echoid-s4135" xml:space="preserve">Itemq́; </s>
            <s xml:id="echoid-s4136" xml:space="preserve">ſphæ-
              <lb/>
            ram maiorem eſſe omnibus aliis figuris ſolidis ſibi iſoperimetris. </s>
            <s xml:id="echoid-s4137" xml:space="preserve">Quamuis. </s>
            <s xml:id="echoid-s4138" xml:space="preserve">n.
              <lb/>
            </s>
            <s xml:id="echoid-s4139" xml:space="preserve">hæc omnia à Theone quoque in commentarijs, quos in Ptolemæi Almageſtũ
              <lb/>
            compoſuit, Geometrice ſint confir
              <unsure/>
            mata; </s>
            <s xml:id="echoid-s4140" xml:space="preserve">tamen quia non omnibus in promptu
              <lb/>
            habentur eius demonſtrationes, (Græcus enim tantum codex reperitur) & </s>
            <s xml:id="echoid-s4141" xml:space="preserve">
              <lb/>
            obſcure admodum, atque ſuccincte ab eo omnia demonſtrantur; </s>
            <s xml:id="echoid-s4142" xml:space="preserve">deo cona-
              <lb/>
            bor, quoad eius fieri poterit, aliquam lucem hiſce demonſtrationibus afferre,
              <lb/>
            vt uel illis ſatisfeciſſe videamur, qui plurimum demonſtrationibus Geometri-
              <lb/>
            cis delectantur. </s>
            <s xml:id="echoid-s4143" xml:space="preserve">Cæterum licet in hoctractatu ſolum demonſt@etur, ſphæram
              <lb/>
            eſſe maiorem corpore quolibet ſibi Iſoperimetro, in quo ſphæra aliqua deſcri-
              <lb/>
            bi poſſit, & </s>
            <s xml:id="echoid-s4144" xml:space="preserve">quod contineatur uel ſuperficiebus planis, uel conicis, ut ſuo loco
              <lb/>
            apparebit: </s>
            <s xml:id="echoid-s4145" xml:space="preserve">Pappus tamen idem de omnicorpore demonſtrauit 70. </s>
            <s xml:id="echoid-s4146" xml:space="preserve">propoſitio-
              <lb/>
            nibus, quas hoc loco apponere ſuperuacaneum duximus, cum breui, ut ſpero,
              <lb/>
            Pappus ipſe in latinam linguam conuerſus in lucem ſit proditurus.</s>
            <s xml:id="echoid-s4147" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div211" type="section" level="1" n="68">
          <head xml:id="echoid-head72" xml:space="preserve">DE FIGVRIS ISOPERIMETRIS.
            <lb/>
          DEFINITIONES.
            <lb/>
          I.</head>
          <p style="it">
            <s xml:id="echoid-s4148" xml:space="preserve">
              <emph style="sc">TSoperimetrae</emph>
            figurę ſunt, quæ æquales ambitus
              <lb/>
              <note position="right" xlink:label="note-117-01" xlink:href="note-117-01a" xml:space="preserve">Definitio-
                <lb/>
              nes ad tra
                <lb/>
              ctationem-
                <lb/>
              Iſoperime-
                <lb/>
              trarum fi-
                <lb/>
              gurarũ per
                <lb/>
              tinentes.</note>
            continent.</s>
            <s xml:id="echoid-s4149" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div213" type="section" level="1" n="69">
          <head xml:id="echoid-head73" xml:space="preserve">II.</head>
          <p style="it">
            <s xml:id="echoid-s4150" xml:space="preserve">
              <emph style="sc">Regvlaris</emph>
            figura dicitur ea, quæ & </s>
            <s xml:id="echoid-s4151" xml:space="preserve">æquilatera, & </s>
            <s xml:id="echoid-s4152" xml:space="preserve">
              <lb/>
            æquiangula eſt.</s>
            <s xml:id="echoid-s4153" xml:space="preserve"/>
          </p>
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