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-s12089" xml:space="preserve">
              <pb o="180" file="0186" n="186" rhead="ALHAZEN"/>
            quem facient [qui ſit at b] erit minorangulo [b g d] quem una diameter facit cum alia, exparte c
              <gap/>
            -
              <lb/>
            tri:</s>
            <s xml:id="echoid-s12090" xml:space="preserve"> [Nam ſi à puncto f, in quo g t ſecat peripheriam
              <lb/>
              <figure xlink:label="fig-0186-01" xlink:href="fig-0186-01a" number="138">
                <variables xml:id="echoid-variables128" xml:space="preserve">m t h
                  <gap/>
                f b p a g d n</variables>
              </figure>
            circuli a b g, ducantur rectæ f a, f b:</s>
            <s xml:id="echoid-s12091" xml:space="preserve"> ęquabuntur angu
              <lb/>
            li ad f & g duobus rectis per 22 p 3:</s>
            <s xml:id="echoid-s12092" xml:space="preserve"> quibus etiam æ-
              <lb/>
            quantur anguli ad g deinceps per 13 p 1:</s>
            <s xml:id="echoid-s12093" xml:space="preserve"> quare per 3
              <lb/>
            ax.</s>
            <s xml:id="echoid-s12094" xml:space="preserve"> b g d ęquatur a f b:</s>
            <s xml:id="echoid-s12095" xml:space="preserve"> qui per 21 p 1 maior eſt angulo
              <lb/>
            a t b.</s>
            <s xml:id="echoid-s12096" xml:space="preserve"> Angulus igitur a t b minor eſt angulo b g d.</s>
            <s xml:id="echoid-s12097" xml:space="preserve">] Et
              <lb/>
            quilibet angulus ſic factus ſuper arcum oppoſitum
              <lb/>
            [l m] minor erit illo angulo.</s>
            <s xml:id="echoid-s12098" xml:space="preserve"> Quoniam angulus fa-
              <lb/>
            ctus in interiore circulo, per lineas à punctis ad ar-
              <lb/>
            cum eius interiacentem ductas, erιt æqualis illi an-
              <lb/>
            gulo:</s>
            <s xml:id="echoid-s12099" xml:space="preserve"> quoniam cum angulo diametrorum ſuper cen
              <lb/>
            trũ ualet duos angulos rectos [per 22 p 3.</s>
            <s xml:id="echoid-s12100" xml:space="preserve">] Sed [per
              <lb/>
            21 p 1] angulus arcus minoris circuli [angulus nem-
              <lb/>
            pe in ipſius peripheria] maior eſt angulo arcus ſpe-
              <lb/>
            culi [eo nempe, qui fit in peripheria circuli:</s>
            <s xml:id="echoid-s12101" xml:space="preserve"> qui eſt
              <lb/>
            communis ſectio ſuperficierum, reflexionis & ſpe-
              <lb/>
            culi.</s>
            <s xml:id="echoid-s12102" xml:space="preserve">] Igitur in arcu ſpeculi nõ fiet reflexio, niſiab u-
              <lb/>
            no puncto:</s>
            <s xml:id="echoid-s12103" xml:space="preserve"> cum iam dictum ſit [80 n] quòd non eſt
              <lb/>
            poſsibile reflexionem à duobus punctis fieri, ut ſit uterque angulus, conſtans ex angulo incidentiæ
              <lb/>
            & reflexionis, minor angulo diametrorum ex alia parte centri.</s>
            <s xml:id="echoid-s12104" xml:space="preserve"> Siuerò circulus ille contingat intrin
              <lb/>
            ſecus circulum ſpeculi:</s>
            <s xml:id="echoid-s12105" xml:space="preserve"> angulus factus à lineis, ab il-
              <lb/>
              <figure xlink:label="fig-0186-02" xlink:href="fig-0186-02a" number="139">
                <variables xml:id="echoid-variables129" xml:space="preserve">m t h
                  <gap/>
                b
                  <gap/>
                a g d n</variables>
              </figure>
            lis punctis ad punctum contactus ductis, erit æqua-
              <lb/>
            lis angulo diametrorum ex alia parte centri [angu-
              <lb/>
            li enim ad h & g æquantur duobus rectis per 22 p 3:</s>
            <s xml:id="echoid-s12106" xml:space="preserve">
              <lb/>
            quibus etiam æquantur anguli ad g deinceps per 13
              <lb/>
            p 1:</s>
            <s xml:id="echoid-s12107" xml:space="preserve"> angulus igitur a h d æquatur angulo b g d per 13
              <lb/>
            ax.</s>
            <s xml:id="echoid-s12108" xml:space="preserve">] Quare ab illo puncto contactus non fiet refle-
              <lb/>
            xio [per 79 n.</s>
            <s xml:id="echoid-s12109" xml:space="preserve">].</s>
            <s xml:id="echoid-s12110" xml:space="preserve"> Et angulus factus ſuper quodcunq;</s>
            <s xml:id="echoid-s12111" xml:space="preserve">
              <lb/>
            punctum aliud maioris circuli, erit minorillo [ut ſi
              <lb/>
            angulus fiat ſuper pũctum t:</s>
            <s xml:id="echoid-s12112" xml:space="preserve"> erit a f b maior a t b per
              <lb/>
            21 p 1:</s>
            <s xml:id="echoid-s12113" xml:space="preserve"> ſed a f b æquatur a h b per 21 p 3:</s>
            <s xml:id="echoid-s12114" xml:space="preserve"> quare a h b ma
              <lb/>
            ior eſt a t b:</s>
            <s xml:id="echoid-s12115" xml:space="preserve"> eodemq́;</s>
            <s xml:id="echoid-s12116" xml:space="preserve"> modo de quocunq;</s>
            <s xml:id="echoid-s12117" xml:space="preserve"> angulo de-
              <lb/>
            monſtrabitur.</s>
            <s xml:id="echoid-s12118" xml:space="preserve">] Quare à duobus punctis arcus non
              <lb/>
            fiet reflexio ſecundum prædicta [80 n.</s>
            <s xml:id="echoid-s12119" xml:space="preserve">] Si uerò cir-
              <lb/>
            culus interior ſecet circulum ſpeculi:</s>
            <s xml:id="echoid-s12120" xml:space="preserve"> duo puncta
              <lb/>
            [peripheria enim peripheriam in duobus punctis
              <lb/>
            tantùm ſecat per 10 p 3] aut erunt extra circulũ:</s>
            <s xml:id="echoid-s12121" xml:space="preserve"> aut
              <lb/>
            intra:</s>
            <s xml:id="echoid-s12122" xml:space="preserve"> aut unum intra, aliud extra:</s>
            <s xml:id="echoid-s12123" xml:space="preserve"> aut unum in cir-
              <lb/>
            cumferentia, aliud extra, uel intra.</s>
            <s xml:id="echoid-s12124" xml:space="preserve"> Si fuerint extra:</s>
            <s xml:id="echoid-s12125" xml:space="preserve"> circulus ſecans, non ſecabit arcum circuli ſpecu-
              <lb/>
            li, interiacentem diametros.</s>
            <s xml:id="echoid-s12126" xml:space="preserve"> Et iam probatum eſt in præcedente figura [pręcedentis numeri] quòd
              <lb/>
            hęc puncta ab uno ſolo puncto arcus
              <lb/>
              <figure xlink:label="fig-0186-03" xlink:href="fig-0186-03a" number="140">
                <variables xml:id="echoid-variables130" xml:space="preserve">a b l
                  <unsure/>
                m l
                  <unsure/>
                t a b m g n d n d</variables>
              </figure>
              <figure xlink:label="fig-0186-04" xlink:href="fig-0186-04a" number="141">
                <variables xml:id="echoid-variables131" xml:space="preserve">f e t h k o b m
                  <gap/>
                a g n d</variables>
              </figure>
            interiacentis diametros poterunt re-
              <lb/>
            flecti [quod eſt punctum peripheriæ
              <lb/>
            inter ſemidiametros, extra quas ſunt
              <lb/>
            reflexa puncta, ut patuit pręcedẽte nu
              <lb/>
            mero.</s>
            <s xml:id="echoid-s12127" xml:space="preserve">] Si uerò unum fuerit in circũ-
              <lb/>
            ferentia, aliud extra:</s>
            <s xml:id="echoid-s12128" xml:space="preserve"> circulus ſecans
              <lb/>
            ſecabit arcum circuli ſpeculi, diame-
              <lb/>
            tros interiacentem in unico puncto.</s>
            <s xml:id="echoid-s12129" xml:space="preserve">
              <lb/>
            Et quilibet angulus factus ſuper arcũ
              <lb/>
            illum:</s>
            <s xml:id="echoid-s12130" xml:space="preserve"> erit maior angulo diametrorũ
              <lb/>
            ex alia parte centri:</s>
            <s xml:id="echoid-s12131" xml:space="preserve"> & ſic [per 80 n] ab
              <lb/>
            uno puncto, uel à duobus poteſt fieri
              <lb/>
            reflexio.</s>
            <s xml:id="echoid-s12132" xml:space="preserve"> Si uerò duo pũcta fuerint in-
              <lb/>
            tra:</s>
            <s xml:id="echoid-s12133" xml:space="preserve"> ſecabit circulus interior arcũ in-
              <lb/>
            teriacentem in duobus punctis:</s>
            <s xml:id="echoid-s12134" xml:space="preserve"> & re-
              <lb/>
            ſtabunt ex eo duo arcus ex diuerſis
              <lb/>
            partibus.</s>
            <s xml:id="echoid-s12135" xml:space="preserve"> Et omnes anguli facti ſuper
              <lb/>
            arcum, interiacentem duo puncta ſectionis, erunt maiores angulo diametrorum ex alia parte cen-
              <lb/>
            tri:</s>
            <s xml:id="echoid-s12136" xml:space="preserve"> [ut patet in angulo a e b per 22 p 3.</s>
            <s xml:id="echoid-s12137" xml:space="preserve"> 13.</s>
            <s xml:id="echoid-s12138" xml:space="preserve"> 21 p 1.</s>
            <s xml:id="echoid-s12139" xml:space="preserve">] Etab hoc arcu poſſet fieri reflexio forſitan ab u-
              <lb/>
            no puncto tantùm:</s>
            <s xml:id="echoid-s12140" xml:space="preserve"> forſitan à duobus [per 80 n.</s>
            <s xml:id="echoid-s12141" xml:space="preserve">] Et ſi à duobus arcubus fiat reflexio, quireſtant
              <lb/>
            ex arcu totali, & ex diuerſis partibus:</s>
            <s xml:id="echoid-s12142" xml:space="preserve"> omnes anguli erunt minores angulo diametrorum:</s>
            <s xml:id="echoid-s12143" xml:space="preserve"> [per
              <lb/>
            22 p 3.</s>
            <s xml:id="echoid-s12144" xml:space="preserve"> 13.</s>
            <s xml:id="echoid-s12145" xml:space="preserve"> 21 p 1] & tantùm ab uno eorum puncto fiet reflexio [per 80 n.</s>
            <s xml:id="echoid-s12146" xml:space="preserve">] Et in hoc ſitu poterit
              <lb/>
            </s>
          </p>
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