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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            <s xml:id="echoid-s18451" xml:space="preserve">
              <pb o="265" file="0271" n="271" rhead="OPTICAE LIBER VII."/>
            minor, quàm diminutio anguli g h a ab angulo g m a:</s>
            <s xml:id="echoid-s18452" xml:space="preserve"> eſt ergo minor, quàm diminutio anguli h g m
              <lb/>
            ab angulo h a m:</s>
            <s xml:id="echoid-s18453" xml:space="preserve"> ergo diminutio anguli c h a ab angulo
              <lb/>
              <figure xlink:label="fig-0271-01" xlink:href="fig-0271-01a" number="234">
                <variables xml:id="echoid-variables221" xml:space="preserve">a k r q c n g h l m d p z b</variables>
              </figure>
            n m a eſt minor, quàm angulus g m a:</s>
            <s xml:id="echoid-s18454" xml:space="preserve"> Sed diminutio an-
              <lb/>
            guli c h a ab angulo n m a, eſt exceſſus anguli b h a ſu-
              <lb/>
            per angulum b m a [per 13 p 1,] qui ſunt duo anguli h a m,
              <lb/>
            h b m [ut patuit 27 n.</s>
            <s xml:id="echoid-s18455" xml:space="preserve">] Ergo iſti duo anguli ſimul ſunt mi
              <lb/>
            nores angulo h a m:</s>
            <s xml:id="echoid-s18456" xml:space="preserve"> qđ eſt impoſsibile.</s>
            <s xml:id="echoid-s18457" xml:space="preserve"> Si uerò a fuerit
              <lb/>
            extra lineã k d ad partem k:</s>
            <s xml:id="echoid-s18458" xml:space="preserve"> & corpus, in quo eſt a, fuerit
              <lb/>
            cõtinuũ uſq;</s>
            <s xml:id="echoid-s18459" xml:space="preserve"> ad a:</s>
            <s xml:id="echoid-s18460" xml:space="preserve"> cõtinuabimus duas lineas a h, a m:</s>
            <s xml:id="echoid-s18461" xml:space="preserve"> &
              <lb/>
            ſecabũt circumferentiã in q & in r.</s>
            <s xml:id="echoid-s18462" xml:space="preserve"> Et ſi angulus c h g fue
              <lb/>
            rit æqualis angulo n m g:</s>
            <s xml:id="echoid-s18463" xml:space="preserve"> tunc [per 12 n] angulus b h a
              <lb/>
            erit æqualis angulo b m a:</s>
            <s xml:id="echoid-s18464" xml:space="preserve"> quod eſt impoſsibile [ut ſu-
              <lb/>
            prà.</s>
            <s xml:id="echoid-s18465" xml:space="preserve">] Et ſi fuerit maior:</s>
            <s xml:id="echoid-s18466" xml:space="preserve"> tunc angulus c h a erit maior an-
              <lb/>
            gulo n m a:</s>
            <s xml:id="echoid-s18467" xml:space="preserve"> & ſic [per 13 p 1] angulus b h a erit minor
              <lb/>
            angulo b m a:</s>
            <s xml:id="echoid-s18468" xml:space="preserve"> quod eſt impoſsibile.</s>
            <s xml:id="echoid-s18469" xml:space="preserve"> Si uerò fuerit mi-
              <lb/>
            nor:</s>
            <s xml:id="echoid-s18470" xml:space="preserve"> tunc angulus c h a erit minor angulo n m a:</s>
            <s xml:id="echoid-s18471" xml:space="preserve"> & to-
              <lb/>
            tus angulus g h a erit minor toto angulo g m a.</s>
            <s xml:id="echoid-s18472" xml:space="preserve"> Ergo an-
              <lb/>
            gulus h g m erit minor angulo h a m [ut ſuprà:</s>
            <s xml:id="echoid-s18473" xml:space="preserve">] ſed an-
              <lb/>
            gulus h g m eſt ille, quem reſpicit apud circumferẽtiam
              <lb/>
            arcus h m duplicatus:</s>
            <s xml:id="echoid-s18474" xml:space="preserve"> & angulus h a m eſt ille, quem re-
              <lb/>
            ſpicit in circumferentia exceſſus arcus h m ſupra arcum
              <lb/>
            r q [per 25 n.</s>
            <s xml:id="echoid-s18475" xml:space="preserve">] Ergo arcus h m duplicatus eſt minor
              <lb/>
            exceſſu arcus h m, ſupra arcum r q:</s>
            <s xml:id="echoid-s18476" xml:space="preserve"> quod eſt impoſsibi-
              <lb/>
            le [& contra 9 ax.</s>
            <s xml:id="echoid-s18477" xml:space="preserve">] Ergo ſi punctum b fuerit extra lineã
              <lb/>
            a k g:</s>
            <s xml:id="echoid-s18478" xml:space="preserve"> tunc forma eius non refringetur ad a, niſi ex uno
              <lb/>
            puncto tantùm.</s>
            <s xml:id="echoid-s18479" xml:space="preserve"> Quapropter non habebit, niſi unami-
              <lb/>
            maginem:</s>
            <s xml:id="echoid-s18480" xml:space="preserve"> quæ imago aut erit ante uiſum, aut retro,
              <lb/>
            aut in loco refractionis, ut in præcedentibus declaraui-
              <lb/>
            mus.</s>
            <s xml:id="echoid-s18481" xml:space="preserve"> Et hoc eſt quod uoluimus declarare.</s>
            <s xml:id="echoid-s18482" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div600" type="section" level="0" n="0">
          <head xml:id="echoid-head515" xml:space="preserve" style="it">32. Si communis ſectio ſuperficierum, refractionis & refractiui cauirarioris, fuerit peri-
            <lb/>
          pheria: uiſibile extra perpendicularem à uiſu ſuper refractiuum ductam, ab uno puncto refrin
            <lb/>
          getur, unam́ habebit imaginem, uariè pro uaria uiſ{us} uel uiſibilis poſitione ſitam. 28 p 10.</head>
          <p>
            <s xml:id="echoid-s18483" xml:space="preserve">SI uerò corpus diaphanum groſsius fuerit ex parte uiſus, & ſubtilius ex parte rei uiſæ, ijſdem
              <lb/>
            manentibus figuris:</s>
            <s xml:id="echoid-s18484" xml:space="preserve"> tunc etiam res uiſa non habebit niſi unam imaginem ſolam:</s>
            <s xml:id="echoid-s18485" xml:space="preserve"> & hoc decla-
              <lb/>
            rabitur, ut in conuerſa ſeptimæ figuræ [quæ fuit 27.</s>
            <s xml:id="echoid-s18486" xml:space="preserve"> 28 n.</s>
            <s xml:id="echoid-s18487" xml:space="preserve">] Et omnia, quæ declarauimus in re-
              <lb/>
            fractionibus à conuexo & concauo circuli:</s>
            <s xml:id="echoid-s18488" xml:space="preserve"> ſequũtur in ſuperficiebus ſphæricis & columnaribus:</s>
            <s xml:id="echoid-s18489" xml:space="preserve">
              <lb/>
            præter refractionem circularem, à circumferentia circuli, quæ non fit, niſi in ſuperficiebus ſphæri-
              <lb/>
            cis tantùm.</s>
            <s xml:id="echoid-s18490" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div601" type="section" level="0" n="0">
          <head xml:id="echoid-head516" xml:space="preserve" style="it">33. Viſibile refractum à refractiuo uariæ uel figuræ uel perſpicuitatis, uel ſimul utriuſ:
            <lb/>
          uari{as} & monſtrific{as} uarijs in locis imagines habet. 29. 30 p 10.</head>
          <p>
            <s xml:id="echoid-s18491" xml:space="preserve">HÆc autem, quæ diximus, ſunt imagines uiſibilium, quæ comprehenduntur à uiſu ultra
              <lb/>
            corpora diaphana ſimplicia, quæ ſunt unius ſubſtantiæ, & quorum figura, quæ eſt ex par-
              <lb/>
            te uiſus, eſt una figura.</s>
            <s xml:id="echoid-s18492" xml:space="preserve"> Si uerò corpus diaphanum fuerit diuerſum, aut non conſimilis dia-
              <lb/>
            phanitatis:</s>
            <s xml:id="echoid-s18493" xml:space="preserve"> tunc imagines rei uiſæ diuerſantur.</s>
            <s xml:id="echoid-s18494" xml:space="preserve"> Et ſi ſuperficies corporis diaphani, quæ eſt ex par-
              <lb/>
            te uiſus, fuerit diuerſa:</s>
            <s xml:id="echoid-s18495" xml:space="preserve"> tunc loca etiam imaginum rei uiſæ diuerſantur, cum formę refractionum ex
              <lb/>
            ſuperficie corporis diaphani diuerſentur etiam.</s>
            <s xml:id="echoid-s18496" xml:space="preserve"> Et ſi aliquis reſpexerit ad paruam ſphæram, aut ali
              <lb/>
            quod corpus rotundum paruum, aut columnare uitri aut cryſtalli, ultra quod corpus fuerit ali-
              <lb/>
            quod uiſibile:</s>
            <s xml:id="echoid-s18497" xml:space="preserve"> inueniet imaginem illius alio modo, quàm ſit res uiſa in ſe:</s>
            <s xml:id="echoid-s18498" xml:space="preserve"> & fortè inueniet rei ui-
              <lb/>
            ſæ imaginem aliam:</s>
            <s xml:id="echoid-s18499" xml:space="preserve"> & ſic dubitabitur ſuper ea.</s>
            <s xml:id="echoid-s18500" xml:space="preserve"> Sed huiuſmodi refractio non eſt una, ſed duæ:</s>
            <s xml:id="echoid-s18501" xml:space="preserve"> for-
              <lb/>
            ma enim rei uiſæ extenditur à re uiſa ad ſphæram, aut ad aliud corpus rotundum columnare, &
              <lb/>
            refringitur à conuexo ſphæræ aut columnæ ad interius corporis, & extenditur intra corpus, quo-
              <lb/>
            uſque perueniat ad ſuperficiem eius:</s>
            <s xml:id="echoid-s18502" xml:space="preserve"> & deinde refringitur à ſphæra aut columna apud concaui-
              <lb/>
            tatem aeris contingentis ſphæram aut columnam.</s>
            <s xml:id="echoid-s18503" xml:space="preserve"> Et ſic comprehenſio huiuſmodi rerum erit dua-
              <lb/>
            bus diuerſis refractionibus.</s>
            <s xml:id="echoid-s18504" xml:space="preserve"> Quapropter imago eius erit diuerſa ab imagine eius, quod compre-
              <lb/>
            henditur una refractione.</s>
            <s xml:id="echoid-s18505" xml:space="preserve"> Nos autem loquemur de hoc parum, quando tracta-
              <lb/>
            bimus de deceptionibus uiſus, quæ fiunt per
              <lb/>
            refractionem.</s>
            <s xml:id="echoid-s18506" xml:space="preserve"/>
          </p>
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