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-s6019" xml:space="preserve">
              <pb o="104" file="0110" n="110" rhead="ALHAZEN"/>
            huius albi à corpore colorato, in quod cadit lux foraminis, eadem cum elongatione albi, quod eſt
              <lb/>
            in concauo ab eodem, & cum elongatione ſpeculi ab codem:</s>
            <s xml:id="echoid-s6020" xml:space="preserve"> tunc comprehendetur color debilior
              <lb/>
            in albo, quod eſt intra concauum, quàm in eo, quod eſt extra:</s>
            <s xml:id="echoid-s6021" xml:space="preserve"> licet æquidiſtent ab ortu ſuo, id eſt à
              <lb/>
            corpore colorato.</s>
            <s xml:id="echoid-s6022" xml:space="preserve"> Et in cauſſa eſt reflexio colorem debilitans.</s>
            <s xml:id="echoid-s6023" xml:space="preserve"> Amplius:</s>
            <s xml:id="echoid-s6024" xml:space="preserve"> lux reflexa fortior eſt lu-
              <lb/>
            ceſecundaria:</s>
            <s xml:id="echoid-s6025" xml:space="preserve"> licet eiuſdem ſint elongationis ab origine ſua.</s>
            <s xml:id="echoid-s6026" xml:space="preserve"> Luce enim reflexa cadente in cor-
              <lb/>
            pus aliquod:</s>
            <s xml:id="echoid-s6027" xml:space="preserve"> ſi aliud eiuſmodi corpus ponatur extra locum reflexionis:</s>
            <s xml:id="echoid-s6028" xml:space="preserve"> & ſit cum eo eiuſdem e-
              <lb/>
            longationis à ſpeculo:</s>
            <s xml:id="echoid-s6029" xml:space="preserve"> uidebitur ſuper ipſum lux minor, quàm in illo.</s>
            <s xml:id="echoid-s6030" xml:space="preserve"> Idem etiam planum erit in
              <lb/>
            domo:</s>
            <s xml:id="echoid-s6031" xml:space="preserve"> ſi deponatur in terram, in directo foraminis ſpeculum, quod accipiat totam foramin is lu-
              <lb/>
            cem:</s>
            <s xml:id="echoid-s6032" xml:space="preserve"> erit lux fortior ſuper corpus in loco reflexionis poſitum, quàm ſuper aliud eiuſdem modi
              <lb/>
            extra hunc locum, tantundem elongatum à ſpeculo.</s>
            <s xml:id="echoid-s6033" xml:space="preserve"> Eodem modo ſi excedat lux foraminis quan-
              <lb/>
            titatem ſpeculi:</s>
            <s xml:id="echoid-s6034" xml:space="preserve"> & cadat circa ſpeculum lux in terram, aut corpus album, à quo aliud corpus tan-
              <lb/>
            tùm elongatur, quantùm corpus reflexionis à ſpeculo:</s>
            <s xml:id="echoid-s6035" xml:space="preserve"> debilior apparebit in eo lux, quàm ſuper
              <lb/>
            reflexionis corpus.</s>
            <s xml:id="echoid-s6036" xml:space="preserve"> Similiter accidit in colore, ſi corpus aliquod tantùm diſtet à ſpeculo extra ſi-
              <lb/>
            tum reflexionis, quantùm aliud ei ſimile, quod eſt in ſitu reflexionis:</s>
            <s xml:id="echoid-s6037" xml:space="preserve"> apparebit quidem ſuper cor-
              <lb/>
            pus, quod eſt in ſitu reflexionis, color reflexus:</s>
            <s xml:id="echoid-s6038" xml:space="preserve"> ſuper aliud forſitan nullus.</s>
            <s xml:id="echoid-s6039" xml:space="preserve"> Si enim ferreum fuerit
              <lb/>
            ſpeculum:</s>
            <s xml:id="echoid-s6040" xml:space="preserve"> aut modicus uidebitur, aut omnino nullus.</s>
            <s xml:id="echoid-s6041" xml:space="preserve"> Si uerò argenteum fuerit ſpeculum:</s>
            <s xml:id="echoid-s6042" xml:space="preserve"> appa-
              <lb/>
            rebit ſuper ipſum color aliquis, ſed ualde debilis, & longè debilior, quàm in corpore, quod eſt in
              <lb/>
            ſitu reflexionis.</s>
            <s xml:id="echoid-s6043" xml:space="preserve"> Et iã igitur planũ, quòd formæ luciũ & colorũ ex corporibus politis reflectuntur,
              <lb/>
            & in reflexione debilitantur:</s>
            <s xml:id="echoid-s6044" xml:space="preserve"> & erit forma directa fortior reflexa, cũ eadẽ fuerit earũ origo, & æqua
              <lb/>
            lis ab ea origine elongatio:</s>
            <s xml:id="echoid-s6045" xml:space="preserve"> & reflexa fortior ſecũdaria, cũ eſt idẽ uel æqualis ortus, & par elõgatio.</s>
            <s xml:id="echoid-s6046" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div217" type="section" level="0" n="0">
          <head xml:id="echoid-head250" xml:space="preserve">DE MODO REFLEXIONIS FORMARVM À
            <unsure/>
          POLI-
            <lb/>
          tis corporibus. Cap. III.</head>
          <head xml:id="echoid-head251" xml:space="preserve" style="it">6. Lenitatis: politæ ſuperficiei: & perpendicularis incidentiæ definitiones. In def. 5 libr.</head>
          <p>
            <s xml:id="echoid-s6047" xml:space="preserve">POlitum eſt læue multùm in ſuperficie:</s>
            <s xml:id="echoid-s6048" xml:space="preserve"> Et læuitas eſt, ut ſint partes ſuperficiei continuæ, ſine
              <lb/>
            pororum multitudine.</s>
            <s xml:id="echoid-s6049" xml:space="preserve"> Læuitas intenſa eſt, ubi eſt multa partium ſuperficiei continuitas, &
              <lb/>
            pororum paruitas & paucitas:</s>
            <s xml:id="echoid-s6050" xml:space="preserve"> & finis læuitatis eſt priuatio pororũ, & priuatio diuiſionis par
              <lb/>
            tium.</s>
            <s xml:id="echoid-s6051" xml:space="preserve"> Itaq;</s>
            <s xml:id="echoid-s6052" xml:space="preserve"> politio eſt politiua cõtinuitas partium ſuperficiei, cum poris raris & exiguis:</s>
            <s xml:id="echoid-s6053" xml:space="preserve"> & finis po-
              <lb/>
            litionis eſt uera continuitas partium, & priuatio pororum.</s>
            <s xml:id="echoid-s6054" xml:space="preserve"> In omnibus politis ſuperficiebus, licet
              <lb/>
            diuerſis ſubiaceant figuris, accidet reflexio:</s>
            <s xml:id="echoid-s6055" xml:space="preserve"> & idem reflexionis modus & eadem proprietas eſt.</s>
            <s xml:id="echoid-s6056" xml:space="preserve"> Et
              <lb/>
            eſt, quòd ab omni politi ſuperficie & quolibet eius puncto fit reflexio.</s>
            <s xml:id="echoid-s6057" xml:space="preserve"> Et ſumpto quocunq;</s>
            <s xml:id="echoid-s6058" xml:space="preserve"> pũcto
              <lb/>
            in ſuperficie, à qua fit reflexio:</s>
            <s xml:id="echoid-s6059" xml:space="preserve"> linea acceſſus formæ ad illud punctum, & linea reflexionis in eadẽ
              <lb/>
            ſuperficie erunt cum linea perpendiculari ſuper illud punctum erecta:</s>
            <s xml:id="echoid-s6060" xml:space="preserve"> & tenebunthę lineæ eundẽ
              <lb/>
            ſitum reſpectu perpendicularis, & æqualitatem angulorum.</s>
            <s xml:id="echoid-s6061" xml:space="preserve"> Et uolo dicere perpendicularem:</s>
            <s xml:id="echoid-s6062" xml:space="preserve"> quæ
              <lb/>
            ſit perpendicularis ſuper ſuperficiẽ, tangentem corpus politum in illo puncto.</s>
            <s xml:id="echoid-s6063" xml:space="preserve"> Et duę lineę cũ per-
              <lb/>
            pendiculari ſunt in eadem ſuperficie orthogonaliter cadente ſuper ſuperficiem, corpus politum in
              <lb/>
            puncto, à quo fit reflexio, tangentem.</s>
            <s xml:id="echoid-s6064" xml:space="preserve"> Si autem linea, per quam accedit ad ſpeculũ forma, cadat per-
              <lb/>
            pendiculariter ſuper illud:</s>
            <s xml:id="echoid-s6065" xml:space="preserve"> fiet reflexio formæ per ipſam, non per aliam.</s>
            <s xml:id="echoid-s6066" xml:space="preserve"> Et hoc eſt propriũ in omni
              <lb/>
            reflexione, in omni polito corpore.</s>
            <s xml:id="echoid-s6067" xml:space="preserve"> Si igitur corpus politum fuerit planum:</s>
            <s xml:id="echoid-s6068" xml:space="preserve"> ſuperficies tangẽs pun
              <lb/>
            ctũ reflexionis, erit una & eadem cũ ſuperficie corporis.</s>
            <s xml:id="echoid-s6069" xml:space="preserve"> Si uerò fuerit columnare ſpeculũ interius
              <lb/>
            aut exterius politũ:</s>
            <s xml:id="echoid-s6070" xml:space="preserve"> erunt contactus ſuperficiei ſpeculi & ſuperficiei contingentis linea tantùm, ſe-
              <lb/>
            cundum longitudinem ſpeculi intellecta.</s>
            <s xml:id="echoid-s6071" xml:space="preserve"> Idẽ in ſpeculo pyramidali intus uel extrà polito.</s>
            <s xml:id="echoid-s6072" xml:space="preserve"> In ſphæ-
              <lb/>
            rico ſiue interius ſiue exterius polito, contingens ſuperficies tangit in ſolo puncto.</s>
            <s xml:id="echoid-s6073" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div218" type="section" level="0" n="0">
          <head xml:id="echoid-head252" xml:space="preserve" style="it">7. Fabricatio & uſus organi reflexionis. 9 p 5.</head>
          <p>
            <s xml:id="echoid-s6074" xml:space="preserve">QVomodo autem etiam ad oculum pateat hic modus reflexionis in ſpeculis omnibus, expla
              <lb/>
            nabimus.</s>
            <s xml:id="echoid-s6075" xml:space="preserve"> Accipe tabulam æneam ſpiſſam, ut firmior ſit:</s>
            <s xml:id="echoid-s6076" xml:space="preserve"> eius longitudo ſit non minor duo-
              <lb/>
            decim digitis:</s>
            <s xml:id="echoid-s6077" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s6078" xml:space="preserve"> latitudo ſex digitorum, & fiat linea æquidiſtans extremitati longitudi-
              <lb/>
            nis:</s>
            <s xml:id="echoid-s6079" xml:space="preserve"> & circa illam extremitatẽ, & ſuper pũctũ
              <lb/>
              <figure xlink:label="fig-0110-01" xlink:href="fig-0110-01a" number="19">
                <variables xml:id="echoid-variables12" xml:space="preserve">n m l b h i k e p t r o s u q a f d g c</variables>
              </figure>
            huius lineæ mediũ ponatur pes circini, & fiat
              <lb/>
            ſemicirculus, cuius ſemidiameter ſit latitudo
              <lb/>
            tabulæ & [per 11 p 1] extrahatur à puncto,
              <lb/>
            quod eſt centrũ, linea orthogonaliter ſuper
              <lb/>
            diametrũ iã factã:</s>
            <s xml:id="echoid-s6080" xml:space="preserve"> & erit linea illa ſemidiame-
              <lb/>
            ter diuidens ſemicirculum per æqualia [per
              <lb/>
            33 p 6.</s>
            <s xml:id="echoid-s6081" xml:space="preserve">] Et in hac ſemidiametro ſumatur men
              <lb/>
            ſura unius digiti, & poſito pede circini ſuper
              <lb/>
            centrũ, fiat ſemicirculus ſecundũ quantitatẽ
              <lb/>
            partis reſiduæ ſemidiametri, ſecundum ſemi-
              <lb/>
            diametrũ quinq;</s>
            <s xml:id="echoid-s6082" xml:space="preserve"> digitorũ.</s>
            <s xml:id="echoid-s6083" xml:space="preserve"> Et diuidiantur ſe-
              <lb/>
            micirculi primi medietates, in quot libuerit, partes, ita ut ſibi reſpondeant in æ qualitate, prima ſcili
              <lb/>
            cet primæ, ſecũda ſecundæ, & ſic de alijs:</s>
            <s xml:id="echoid-s6084" xml:space="preserve"> & protrahantur lineę à centro ad pũcta diuiſionum.</s>
            <s xml:id="echoid-s6085" xml:space="preserve"> De-
              <lb/>
            inceps in ſemidiametro menſura digiti ſignetur:</s>
            <s xml:id="echoid-s6086" xml:space="preserve"> & ex parte centri & ſuper punctum ſignatum pro-
              <lb/>
            trahatur linea, æquidiſtans diametro ſemicirculi, ſiue tabulæ extremitati [per 31 p 1:</s>
            <s xml:id="echoid-s6087" xml:space="preserve">] & ſecetur è
              <lb/>
            tabula, quod interiacet hanc lineam & ſemidiametrũ, uſq;</s>
            <s xml:id="echoid-s6088" xml:space="preserve"> ad centrum & lineas primas, ad diuiſio-
              <lb/>
            </s>
          </p>
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