Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.002029">
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              patet ex 48. 10. Vitellionis; vt in figura, in qua ſydus B, oculus A, nubes
                <lb/>
              C D F, radij viſuales tres refracti in nube ſint B C A, B D A, B E A, facien­
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              tes conſimilem refractionem, ideſt angulos refractos B C A, B D A, B E A,
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              æquales in punctis C, D, F:
                <expan abbr="atq;">atque</expan>
              hoc eſt conſimilem facere refractionem.
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              </s>
              <s id="s.002030">Supponit ſecundò lineas à ſydere ad nubem, vſque extenſas eſſe æquales, vt
                <lb/>
              ſunt B C, B D, B F: ſimiliter reliquas tres à nube ad viſum A. pares eſſe C A,
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              D A, F A. his ſuppoſitis, ſi deinde protrahatur recta A B, ab oculo ad ſydus,
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              exurgunt tria triangula omninò æqualia, & ſimilia, cum duo latera vnius
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              ſint æqualia duobus alterius
                <expan abbr="vtrunq;">vtrunque</expan>
              vtrique, & angulus angulo, & præterea
                <lb/>
              baſis ſit communis; ideò per quartam primi ſunt omninò æqualia. </s>
              <s id="s.002031">ducan­
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              tur nunc ex angulis C, D, F, tres perpendiculares ad rectam A B, quæ ſint
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              C E, D E, F E, in figura; quæ tres neceſſariò erunt æquales, cum ſint ductæ
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              ab angulis æqualibus æqualium triangulorum ad communem baſim, & di­
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              uident neceſſariò baſim in eodem puncto E, cum diuidant triangula æqua­
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              lia proportionaliter;
                <expan abbr="eruntq́">eruntque</expan>
              ; propterea hæ tres rectæ in eodem plano, quod
                <lb/>
              in nube concipitur ex 5. 11. Quare ſi concipiamus ſuperficiem, ſiue planum
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              delineari circa E, ad interuallum linearum æqualium C E, D E, F E, de­
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              ſcriptus erit circulus per 9. tertij, cuius circumferentia C D F. </s>
              <s id="s.002032">Ex quibus
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              patet tria illa puncta C, D, E, per quæ Sol tranſparet eſſe in orbem diſpoſi­
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              ta. </s>
              <s id="s.002033">cauſa igitur rotunditatis Areæ, eſt ſimilitudo angulorum refractionis,
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              quibus Sol tranſparet: vel ideo rotunda eſt, quia ſimiles anguli neceſſariò
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              in orbem conſtituuntur, vt oſtenſum eſt. </s>
              <s id="s.002034">Eadem ratione omnia alia puncta
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              eiuſdem
                <expan abbr="circũferentiæ">circunferentiæ</expan>
              ſunt puncta, per quæ Sol videtur refractè; & hoc mo­
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              do ad ſimilitudinem trium linearum A C B, A D B, A F B, refractarum, in­
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              finitæ
                <expan abbr="vndiq;">vndique</expan>
              intelligendæ ſunt, quarum aliæ refrangantur in circunferentia
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              prædicta, aliæ verò in alia periphæria maiori, aliæ etiam in minori, ita vt
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              ex tota nube fiant refractiones circulares plurimæ, ex quibus in nube area
                <lb/>
              conſtituatur. </s>
              <s id="s.002035">
                <expan abbr="Atq;">Atque</expan>
              hæc cur Halonis figura orbicularis videatur, rationem
                <lb/>
              reddunt,
                <expan abbr="vnaq́">vnaque</expan>
              ; textui lucem afferunt.</s>
            </p>
            <p type="head">
              <s id="s.002036">
                <emph type="italics"/>
              Summæ 2. cap. 4. De Iridis figura.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.002037">
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            <p type="margin">
              <s id="s.002038">
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              162</s>
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            <p type="main">
              <s id="s.002039">
                <emph type="italics"/>
              Qvod autem
                <expan abbr="neq;">neque</expan>
              circulum poſſibile ſit fieri Iridis,
                <expan abbr="neq;">neque</expan>
              maiorem ſemicir­
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              culo portionem, & de alijs accidentibus circa ipſam, ex deſcriptione
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              erit conſiderantibus manifeſtum)
                <emph.end type="italics"/>
              In Logicis ſæpius monui Ariſt. per
                <lb/>
              deſcriptiones intelligere geometricas demonſtrationes, quod
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              etiam hoc loco confirmatur, vbi Geometrica demonſtratione quam deſcri­
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              ptionem appellat, Iridis figuræ accidentia oſtendit; nimirum cur ſit quidem
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              circularis, nunquam tamen circulus integer, imò
                <expan abbr="neq;">neque</expan>
              ſemicirculo vnquam
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              maior, ſed tamen ſemicirculo minor.</s>
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            <p type="main">
              <s id="s.002040">
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            <p type="margin">
              <s id="s.002041">
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              163</s>
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            <p type="main">
              <s id="s.002042">Ibidem
                <emph type="italics"/>
              (Hemiſphærio enim exiſtente ſuper horizontis circulum in quo A. cen­
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              tro autem K, alio autem quodam oriente puncto, in quo G, ſi lineæ, quæ à K, ſecun­
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              dum conum excidentes faciant velut axem lineam in qua G K, & à K. ad M, co­
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              pulatæ refrangantur ab hemiſphærio ad G, ſuper maiorem angulum, circuli circun­
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              ferentiam incident lineæ, quæ à K, & ſi quidem in ortu, aut in occaſu aſtri reflexio
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              fiat, ſemicirculus ab
                <expan abbr="horizõte">horizonte</expan>
              aſſumetur ſuper terram factus. </s>
              <s id="s.002043">ſi autem ſupra, minor
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
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