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-s6829" xml:space="preserve">
              <pb o="116" file="0122" n="122" rhead="ALHAZEN"/>
            circuli diſtet à ſuo polo quadrante peripheriæ maximi circuli:</s>
            <s xml:id="echoid-s6830" xml:space="preserve"> erit peripheria, conuerſione radij ab
              <lb/>
            uno uiſu ſphæram tangentis, in ſphærica ſuperficie deſcripta, minor maximi circuli peripheria.</s>
            <s xml:id="echoid-s6831" xml:space="preserve">]</s>
          </p>
        </div>
        <div xml:id="echoid-div241" type="section" level="0" n="0">
          <head xml:id="echoid-head272" xml:space="preserve" style="it">25. Si duarum rectarum linearum à uiſu, alter a ſpeculum ſphæricum conuexum tangat, re-
            <lb/>
          liqua per centrum ſecet: tangens circa ſecantem fixam cõuerſa, definiet ſegmentum ſuperficiei
            <lb/>
          ſpeculι: à cui{us} puncto quolibet poteſt ad uiſum fieri reflexio. Et centra uiſ{us} & ſpeculi, puncta
            <lb/>
          reflexionis & uiſibilis ſunt in reflexionis ſuperficie. 2.5.6 p 6.</head>
          <p>
            <s xml:id="echoid-s6832" xml:space="preserve">DIco igitur, quòd à quolibet puncto huius portionis poterit fieri reflexio.</s>
            <s xml:id="echoid-s6833" xml:space="preserve"> Quoniã ſumpto ali-
              <lb/>
            quo eius puncto:</s>
            <s xml:id="echoid-s6834" xml:space="preserve"> diameter ſphæræ ab illo puncto intellecta, erit perpẽdicularis ſuper ſuper-
              <lb/>
            ficiem planam tangentem ſphæram in puncto illo [per 4 th.</s>
            <s xml:id="echoid-s6835" xml:space="preserve"> 1 ſphæ.</s>
            <s xml:id="echoid-s6836" xml:space="preserve">] Et huius rei probatio
              <lb/>
            eſt.</s>
            <s xml:id="echoid-s6837" xml:space="preserve"> Intellectis duabus ſuperficiebus ſphæram ſuper diametrum à puncto ſumptam, intellectam ſe-
              <lb/>
            cantibus:</s>
            <s xml:id="echoid-s6838" xml:space="preserve"> lineæ communes ſuperficiei ſphæræ & his ſuperficiebus ſunt circuli ſphæræ tranſeuntes
              <lb/>
            per punctum ſumptum [per 1 th.</s>
            <s xml:id="echoid-s6839" xml:space="preserve"> 1 ſphæ:</s>
            <s xml:id="echoid-s6840" xml:space="preserve">] & intellectis duabus lineis, tangentibus hos circulos in
              <lb/>
            puncto ſumpto:</s>
            <s xml:id="echoid-s6841" xml:space="preserve"> erit diameter perpendicularis ſuper utramq;</s>
            <s xml:id="echoid-s6842" xml:space="preserve"> lineam [per 18 p 3.</s>
            <s xml:id="echoid-s6843" xml:space="preserve">] Quare ſuper ſu-
              <lb/>
            perficiem, in qua ſunt illæ lineæ [per 4 p 11.</s>
            <s xml:id="echoid-s6844" xml:space="preserve">] Et cum deſcenderit radius ſuper punctum
              <gap/>
            ſumptum:</s>
            <s xml:id="echoid-s6845" xml:space="preserve">
              <lb/>
            eritin eadem ſuperficie cũ diametro ſphæræ, cuius terminus punctum eſt ſumptum [per 2 p 11] &
              <lb/>
            linea à centro uiſus ad centrũ ſphæræ intellecta:</s>
            <s xml:id="echoid-s6846" xml:space="preserve"> quæ quidẽ tranſit per polum circuli (& eſt radius
              <lb/>
            orthogonaliter cadens ſuper ſuperficiem ſphęræ) [quia per 4 th.</s>
            <s xml:id="echoid-s6847" xml:space="preserve"> 1 ſphær.</s>
            <s xml:id="echoid-s6848" xml:space="preserve"> eſt perpendicularis plano
              <lb/>
            ſphæram in puncto d tangenti] eſt ſimiliter in eadem ſuperficie [per 2 p 11:</s>
            <s xml:id="echoid-s6849" xml:space="preserve">] & exhis tribus lineis
              <lb/>
            erit triangulum:</s>
            <s xml:id="echoid-s6850" xml:space="preserve"> & radius ſuper punctũ ſumptũ incidẽs;</s>
            <s xml:id="echoid-s6851" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="26">
                <variables xml:id="echoid-variables16" xml:space="preserve">a k f s d m b g c h</variables>
              </figure>
            tenet acutũ angulũ cũ diametro ſphæræ ab exteriori par
              <lb/>
            te:</s>
            <s xml:id="echoid-s6852" xml:space="preserve"> quoniã cũ elatior ſit iſte radius radio ſphæram cõtin-
              <lb/>
            gente:</s>
            <s xml:id="echoid-s6853" xml:space="preserve"> ſecabit ſphęram cũ producta intelligitur:</s>
            <s xml:id="echoid-s6854" xml:space="preserve"> & ſuper-
              <lb/>
            ficies tangẽs ſphærã in pũcto ſumpto demiſsior erit hoe
              <lb/>
            radio:</s>
            <s xml:id="echoid-s6855" xml:space="preserve"> & ſecabit inter ſphærã & uiſum, uiſam diametrũ,
              <lb/>
            id eſt lineã à cẽtro uiſus ad centrũ ſphæræ intellectã, per
              <lb/>
            polum circuli tranſeuntem:</s>
            <s xml:id="echoid-s6856" xml:space="preserve"> unde cũ diameter ſphęræ ſit
              <lb/>
            orthogonalis in ſuperficie punctũ tangente:</s>
            <s xml:id="echoid-s6857" xml:space="preserve"> tenebit an-
              <lb/>
            gulũ recto maiorẽ ex parte interiori cũ radio in punctũ
              <lb/>
            deſcendente:</s>
            <s xml:id="echoid-s6858" xml:space="preserve"> unde [per 13 p 1] in exteriori parte tenebit
              <lb/>
            cum eo angulũ minorẽ recto:</s>
            <s xml:id="echoid-s6859" xml:space="preserve"> & producta, orthogonalis
              <lb/>
            erit ſuper ſuperficiẽ cõtingentẽ exterius [ք 4 th.</s>
            <s xml:id="echoid-s6860" xml:space="preserve"> 1 ſphæ.</s>
            <s xml:id="echoid-s6861" xml:space="preserve">]
              <lb/>
            Quare ex angulo recto, quẽ tenebit cũ ſuperficie ex alia
              <lb/>
            radij parte, poterit abſcindi acutus æqualis ei, quẽ inclu-
              <lb/>
            dit radius cũ illa diametro:</s>
            <s xml:id="echoid-s6862" xml:space="preserve"> & erũt lineę tres hos angulos
              <lb/>
            duos includêtes in eadẽ ſuperficie [per 6.</s>
            <s xml:id="echoid-s6863" xml:space="preserve"> 13 n.</s>
            <s xml:id="echoid-s6864" xml:space="preserve">] Quare à
              <lb/>
            puncto portionis ſumpto poteſt produci linea in eadem
              <lb/>
            ſuperficie cum radio, in punctũ illud cadẽte, & linea or-
              <lb/>
            thogonali in ſuperficie punctũ contingẽte, & ad parita-
              <lb/>
            tem angulorum cũ perpẽdiculari illa:</s>
            <s xml:id="echoid-s6865" xml:space="preserve"> & illi lineæ occur-
              <lb/>
            rer forma puncti mota ad ſuperficiẽ ſpeculi per radium
              <lb/>
            illum.</s>
            <s xml:id="echoid-s6866" xml:space="preserve"> Igitur eiuſdem eſt ſitus cum linea, quæ poterit re-
              <lb/>
            flecti [per 12 uel 18 n.</s>
            <s xml:id="echoid-s6867" xml:space="preserve">] Et erit ſuperficies, in qua ſunt hæ
              <lb/>
            lineæ, orthogonalis ſuper ſuperficiem, ſphærã in puncto
              <lb/>
            contingentẽ [per 13 n.</s>
            <s xml:id="echoid-s6868" xml:space="preserve">] Et ita in quolibet portionis pun-
              <lb/>
            cto intelligendum.</s>
            <s xml:id="echoid-s6869" xml:space="preserve"> Ergo in omni ſuperficie reflexionis
              <lb/>
            erũt centrũ uiſus:</s>
            <s xml:id="echoid-s6870" xml:space="preserve"> centrũ ſphæræ:</s>
            <s xml:id="echoid-s6871" xml:space="preserve"> punctũ reflexionis:</s>
            <s xml:id="echoid-s6872" xml:space="preserve"> & punctũ reflexũ.</s>
            <s xml:id="echoid-s6873" xml:space="preserve"> Et oẽs hæ ſuքficies ſecabũt
              <lb/>
            ſe ſuք lineã à cẽtro uiſus ad cẽtrũ ſphęræ ptractã:</s>
            <s xml:id="echoid-s6874" xml:space="preserve"> & cuilibet reflexiõis ſuքficiei & ſuքficiei ſphæræ,
              <lb/>
            cõmunis linea erit circulus ſphęræ [ք 1th.</s>
            <s xml:id="echoid-s6875" xml:space="preserve"> 1 ſphæ:</s>
            <s xml:id="echoid-s6876" xml:space="preserve">] & oẽs circuli ſecabũt ſe ſuք pũctũ ſphęræ, in qđ
              <lb/>
            cadit diameter uiſus:</s>
            <s xml:id="echoid-s6877" xml:space="preserve"> & eſt ſuք circuli portiõis polũ.</s>
            <s xml:id="echoid-s6878" xml:space="preserve"> Cũ aũt radius ceciderit in ſpeculũ orthogona-
              <lb/>
            liter ſuք ſuքficiẽ, in pũcto, in qđ radius cadit, ſphærã tãgentẽ (& eſt radius ille, diameter uiſus ք po-
              <lb/>
            lũ circuli portiõis ad cẽtrũ ſphęræ) fiet reflexio ad uiſum ք eũdẽ radiũ ad motus radij ortũ [ք 11 n.</s>
            <s xml:id="echoid-s6879" xml:space="preserve">]</s>
          </p>
        </div>
        <div xml:id="echoid-div243" type="section" level="0" n="0">
          <head xml:id="echoid-head273" xml:space="preserve" style="it">26. Siduo plana à cẽtro uiſiis, ducãtur ք later a cõſpicuam ſpeculi cylindracei cõuexi ſuperficiẽ
            <lb/>
          terminãtia: tangẽt ſpeculũ: & facient in uiſu cõmunem ſectionẽ par allelã axiſpeculi. 2.3 p 7.</head>
          <p>
            <s xml:id="echoid-s6880" xml:space="preserve">IN ſpeculis autẽ columnaribus patebit, quod diximus.</s>
            <s xml:id="echoid-s6881" xml:space="preserve"> Opponatur ſpeculũ columnare exterius
              <lb/>
            politum oculo:</s>
            <s xml:id="echoid-s6882" xml:space="preserve"> (& eſt oppoſitio, ut non ſit uiſus in ſuperficie columnæ, aut ſuperficie ei conti-
              <lb/>
            nua) & intelligamus ſuperficiem à centro uiſus ad columnæ ſuperficiem, ſecantem columnam
              <lb/>
            ſuper circulum æquidiſtantẽ baſibus columnæ:</s>
            <s xml:id="echoid-s6883" xml:space="preserve"> & in hac ſuperficie ſumantur duæ lineæ, tangentes
              <lb/>
            circulũ ſectionis in duobus punctis oppoſitis:</s>
            <s xml:id="echoid-s6884" xml:space="preserve"> ab utroq;</s>
            <s xml:id="echoid-s6885" xml:space="preserve"> illorũ punctorum producatur linea ſecun-
              <lb/>
            dum longitudinem columnæ:</s>
            <s xml:id="echoid-s6886" xml:space="preserve"> & intelligãtur duæ ſuperficies, in quibus ſint hæ duæ lineæ longitu-
              <lb/>
            dinis, & duæ lineæ à centro uiſus ductæ, contin gentes circulũ ſectionis.</s>
            <s xml:id="echoid-s6887" xml:space="preserve"> Dico, quòd hæ ſuperficies
              <lb/>
            tangent columnã.</s>
            <s xml:id="echoid-s6888" xml:space="preserve"> Si enim dicatur, quòd altera ſecat illã:</s>
            <s xml:id="echoid-s6889" xml:space="preserve"> planũ eſt, quòd ſectio eſt ſuper lineã longi-
              <lb/>
            tudinis colũnæ, in quã ſuperficies cadit:</s>
            <s xml:id="echoid-s6890" xml:space="preserve"> [per 21 def.</s>
            <s xml:id="echoid-s6891" xml:space="preserve"> 11] & ſimiliter erit ſectio ſuper lineã lõgitudinis
              <lb/>
            </s>
          </p>
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