Ibn-al-Haitam, al-Hasan Ibn-al-Hasan; Witelo; Risner, Friedrich, Opticae thesavrvs Alhazeni Arabis libri septem, nunc primùm editi. Eivsdem liber De Crepvscvlis & Nubium ascensionibus. Item Vitellonis Thuvringopoloni Libri X. Omnes instaurati, figuris illustrati & aucti, adiectis etiam in Alhazenum commentarijs, a Federico Risnero, 1572

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          <p>
            <s xml:id="echoid-s41598" xml:space="preserve">
              <pb o="333" file="0635" n="635" rhead="LIBER OCTAVVS."/>
            lis angulo f b e trigoni fe b:</s>
            <s xml:id="echoid-s41599" xml:space="preserve"> & angulus k e b per 20 th.</s>
            <s xml:id="echoid-s41600" xml:space="preserve"> 5 huius eſt æqualis angulo f e b, linea uerò
              <lb/>
            e b eſt latus commune:</s>
            <s xml:id="echoid-s41601" xml:space="preserve"> ergo per 26 p 1 illa trigona f b e & k b e ſunt æ qualia:</s>
            <s xml:id="echoid-s41602" xml:space="preserve"> & erit linea b f æ qualis
              <lb/>
            lineæ k b:</s>
            <s xml:id="echoid-s41603" xml:space="preserve"> ſed linea a k æ qualis eſt lineæ f t ex hypotheſi:</s>
            <s xml:id="echoid-s41604" xml:space="preserve"> ergo per 4 p 1 in trigonis b t f & b k a erit
              <lb/>
            linea b t æ qualis lineæ b a:</s>
            <s xml:id="echoid-s41605" xml:space="preserve"> & angulus a b k æqualis angulo f b t:</s>
            <s xml:id="echoid-s41606" xml:space="preserve"> addito ergo utrobiq;</s>
            <s xml:id="echoid-s41607" xml:space="preserve"> communi an-
              <lb/>
            gulo f b a, erit angulus k b f æ qualis angulo a b t:</s>
            <s xml:id="echoid-s41608" xml:space="preserve"> ſed duo anguli k b f & fe a ualent duos rectos per
              <lb/>
            32 p 1, quia in quadrilatero k b ſ e alij duo anguli (qui ſunt b f e & b k e) ſunt recti:</s>
            <s xml:id="echoid-s41609" xml:space="preserve"> ergo duo angulit
              <lb/>
            b a & t e a ualent duos rectos:</s>
            <s xml:id="echoid-s41610" xml:space="preserve"> ſed per 13 p 1 angulus t b g cum angulo t b a ualet duos rectos:</s>
            <s xml:id="echoid-s41611" xml:space="preserve"> ergo
              <lb/>
            angulus t b g æqualis eſt angulo t e a, quieſt angulus conſtans ex angulo incidentiæ & angulo refle
              <lb/>
            xionis.</s>
            <s xml:id="echoid-s41612" xml:space="preserve"> Si igitur à centro ſpeculi, quod eſt b, ad lineam t e ducatur linea ultra punctum t, faciet an-
              <lb/>
              <figure xlink:label="fig-0635-01" xlink:href="fig-0635-01a" number="756">
                <variables xml:id="echoid-variables733" xml:space="preserve">e o f t p d a b g k</variables>
              </figure>
              <figure xlink:label="fig-0635-02" xlink:href="fig-0635-02a" number="757">
                <variables xml:id="echoid-variables734" xml:space="preserve">e o f l p k d a b g</variables>
              </figure>
            gulum cum diametro b g ex parte puncti g minorem angulo t e a:</s>
            <s xml:id="echoid-s41613" xml:space="preserve"> quoniam faciet minorem angulo
              <lb/>
            t b g, qui eſt æ qualis angulo t e a:</s>
            <s xml:id="echoid-s41614" xml:space="preserve"> & erit illa linea maior quàm linea a b:</s>
            <s xml:id="echoid-s41615" xml:space="preserve"> quia erit per 19 p 1 maior
              <lb/>
            quàm linea b t, quæ eſt æ qualis lineæ a b.</s>
            <s xml:id="echoid-s41616" xml:space="preserve"> Quælibet uerò linea ducta ab aliquo puncto lineæ t e ad
              <lb/>
            centrum ſpeculi, quod eſt b, faciet angulum cum diametro b g maiorem angulo t b g:</s>
            <s xml:id="echoid-s41617" xml:space="preserve"> ergo & maio-
              <lb/>
            rem angulo t e a:</s>
            <s xml:id="echoid-s41618" xml:space="preserve"> & erit quælibet illarum linearum minor quàm linea b t:</s>
            <s xml:id="echoid-s41619" xml:space="preserve"> ergo erit minor quàm li-
              <lb/>
            nea b a.</s>
            <s xml:id="echoid-s41620" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s41621" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1655" type="section" level="0" n="0">
          <head xml:id="echoid-head1243" xml:space="preserve" style="it">33. Centro uiſus & puncto rei uiſæ in diuerſis diametris circuli (qui eſt communis ſectio ſu-
            <lb/>
          perficiei reflexionis & ſpeculi ſphærici concaui) exiſtentibus, & inæqualiter diſtantibus à cen-
            <lb/>
          tro ſpeculi: ſi ab aliquo puncto circumferentiæ circuli fiat reflexio, impoßibile eſt diametrum, in
            <lb/>
          qua eſt punctus rei uiſæ cumdiametro, in qua eſt centrum uiſus, angulum extrinſecum æqua-
            <lb/>
          lem conſtituere angulo conſtanti ex angulis incidentiæ & reflexionis. Alhazen 79 n 5.</head>
          <p>
            <s xml:id="echoid-s41622" xml:space="preserve">Sit b centrum uiſus:</s>
            <s xml:id="echoid-s41623" xml:space="preserve"> & centrum ſpeculi ſphærici concaui ſit g:</s>
            <s xml:id="echoid-s41624" xml:space="preserve"> & ducatur diameter per pun-
              <lb/>
            cta b & g:</s>
            <s xml:id="echoid-s41625" xml:space="preserve"> quæ ſit z d:</s>
            <s xml:id="echoid-s41626" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s41627" xml:space="preserve"> a punctus rei uiſæ:</s>
            <s xml:id="echoid-s41628" xml:space="preserve"> & eſto, ut aliqua ſuperficies plana ſecet ſphæram ſpecu
              <lb/>
            li ſuper circulum z e d per 69 th.</s>
            <s xml:id="echoid-s41629" xml:space="preserve"> 1 huius.</s>
            <s xml:id="echoid-s41630" xml:space="preserve"> Dico (ſi forma puncti a exiſtentis in diametro h g e reflecti
              <lb/>
            tur ad uiſum exiſtentem in puncto b ab aliquo puncto cir-
              <lb/>
            culi z e d:</s>
            <s xml:id="echoid-s41631" xml:space="preserve"> & ſi in-
              <lb/>
              <figure xlink:label="fig-0635-03" xlink:href="fig-0635-03a" number="758">
                <variables xml:id="echoid-variables735" xml:space="preserve">t z e b a g h d</variables>
              </figure>
              <figure xlink:label="fig-0635-04" xlink:href="fig-0635-04a" number="759">
                <variables xml:id="echoid-variables736" xml:space="preserve">t z c b a g h d</variables>
              </figure>
            æqualis eſt di-
              <lb/>
            ſtantia puncto-
              <lb/>
            rum a & b à cen
              <lb/>
            tro ſpeculi, qđ
              <lb/>
            eſt g) quòd dia
              <lb/>
            meter a g cũ dia
              <lb/>
            metro b g d ex
              <lb/>
            parte pũcti d fa-
              <lb/>
            eiet angulum a
              <lb/>
            g d, quem im-
              <lb/>
            poſsibile eſt eſſe
              <lb/>
            æqualem angu-
              <lb/>
            lo conſtanti ex
              <lb/>
            angulis inciden
              <lb/>
            tiæ & reflexiõis.</s>
            <s xml:id="echoid-s41632" xml:space="preserve">
              <lb/>
            Si uerò hoc ſit
              <lb/>
            poſsibile, ponatur eſſe:</s>
            <s xml:id="echoid-s41633" xml:space="preserve"> & ſit punctus reflexionis t:</s>
            <s xml:id="echoid-s41634" xml:space="preserve"> ſit q́;</s>
            <s xml:id="echoid-s41635" xml:space="preserve"> linea à g inæqualis lineæ b g:</s>
            <s xml:id="echoid-s41636" xml:space="preserve"> & ducantur
              <lb/>
            lineæ t a, t b, t g, b a:</s>
            <s xml:id="echoid-s41637" xml:space="preserve"> & fiat circulus tranſiens pertria puncta a g b trigoni a b g per 5 p 4:</s>
            <s xml:id="echoid-s41638" xml:space="preserve"> trãſibit ergo
              <lb/>
            </s>
          </p>
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