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-s19046" xml:space="preserve">
              <pb o="274" file="0280" n="280" rhead="ALHAZEN"/>
            aut non erit ibi differentia ſenſibilis in poſitione.</s>
            <s xml:id="echoid-s19047" xml:space="preserve"> Poſitio ergo g o, reſpectu a eſt, ſicut poſitio b c, re-
              <lb/>
            ſpectu a:</s>
            <s xml:id="echoid-s19048" xml:space="preserve"> & inter diſtantias g o, b c reſpectu a, non eſt diuerſitas ſenſibilis.</s>
            <s xml:id="echoid-s19049" xml:space="preserve"> Quapropter g o uidebi-
              <lb/>
            tur maior quàm b c:</s>
            <s xml:id="echoid-s19050" xml:space="preserve"> ſed g o eſt imago b c.</s>
            <s xml:id="echoid-s19051" xml:space="preserve"> Ergo b c uidetur maior quàm ſit.</s>
            <s xml:id="echoid-s19052" xml:space="preserve"> Et hoc eſt quod uo-
              <lb/>
            luimus.</s>
            <s xml:id="echoid-s19053" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div614" type="section" level="0" n="0">
          <head xml:id="echoid-head528" xml:space="preserve" style="it">43. Si tota imago refracti uiſibilis à refractiuo plano, uideatur maior uiſibili: uidebitur &
            <lb/>
          pars imaginis maior parte uiſibilis proportionali. 35 p 10.</head>
          <p>
            <s xml:id="echoid-s19054" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s19055" xml:space="preserve"> iteremus figuram primam huius capituli:</s>
            <s xml:id="echoid-s19056" xml:space="preserve"> [39 n] & ſit perpẽdicularis, ſecans lineam l k, a m
              <lb/>
            o z:</s>
            <s xml:id="echoid-s19057" xml:space="preserve"> erit ergo l o medietas l k:</s>
            <s xml:id="echoid-s19058" xml:space="preserve"> & punctum z uidebitur in o:</s>
            <s xml:id="echoid-s19059" xml:space="preserve"> quia uidetur in perpendiculari z m:</s>
            <s xml:id="echoid-s19060" xml:space="preserve"> er
              <lb/>
            go b c uidebitur in linea l k:</s>
            <s xml:id="echoid-s19061" xml:space="preserve"> & b z eſt medietas b c:</s>
            <s xml:id="echoid-s19062" xml:space="preserve"> & l o eſt medietas l k:</s>
            <s xml:id="echoid-s19063" xml:space="preserve"> & l k uidetur maior quã
              <lb/>
            b c.</s>
            <s xml:id="echoid-s19064" xml:space="preserve"> ergo l o uidebitur maior quàm b z.</s>
            <s xml:id="echoid-s19065" xml:space="preserve"> Cauſſa autem magnitudinis b c eſt refractio:</s>
            <s xml:id="echoid-s19066" xml:space="preserve"> ergo cauſſa ma-
              <lb/>
            gnitudinis b z eſt refractio.</s>
            <s xml:id="echoid-s19067" xml:space="preserve"> a autem eſt in perpendiculari a z, quæ exit ab extremitate b z ſuper ſu-
              <lb/>
            perficiem corporis diaphani.</s>
            <s xml:id="echoid-s19068" xml:space="preserve"> Et hoc idem ſequitur in tribus figuris ſequentibus primam, ſcilicet in
              <lb/>
            ſecunda, in tertia, & quarta huius capituli:</s>
            <s xml:id="echoid-s19069" xml:space="preserve"> ſcilicet quòd
              <lb/>
              <figure xlink:label="fig-0280-01" xlink:href="fig-0280-01a" number="239">
                <variables xml:id="echoid-variables226" xml:space="preserve">a d p m h e ſ g o k b n z c</variables>
              </figure>
            uiſus comprehendit medietates uiſibilium maiores,
              <lb/>
            quàm ſint:</s>
            <s xml:id="echoid-s19070" xml:space="preserve"> & uiſus eſt in perpendiculari exeunte ab ex-
              <lb/>
            tremitate medietatis ſuper ſuperficiem corporis diapha
              <lb/>
            ni, aut ſuper ſuperficiem tranſeuntem per extremitatem
              <lb/>
            medietatis perpendicularis ſuper ſuperficiem corporis.</s>
            <s xml:id="echoid-s19071" xml:space="preserve">
              <lb/>
            Nam punctum, quod eſt medium imaginis, eſt in perpen
              <lb/>
            diculari exeunte à medio rei uiſæ, ſiue res uiſa ſit ęquidi-
              <lb/>
            ſtans ſuperficiei corporis diaphani, ſiue non.</s>
            <s xml:id="echoid-s19072" xml:space="preserve"> Item b n ſit
              <lb/>
            quædam pars lineę b z:</s>
            <s xml:id="echoid-s19073" xml:space="preserve"> & extrahamus perpendicularem
              <lb/>
            n g:</s>
            <s xml:id="echoid-s19074" xml:space="preserve"> imago ergo n erit in linea n g:</s>
            <s xml:id="echoid-s19075" xml:space="preserve"> [per 19 n] ſit ergo gi-
              <lb/>
            mago n:</s>
            <s xml:id="echoid-s19076" xml:space="preserve"> g ergo aut erit in linea l g, aut prope illam.</s>
            <s xml:id="echoid-s19077" xml:space="preserve"> Qua-
              <lb/>
            propter l g aut erit æqualis lineæ b n, aut ferè.</s>
            <s xml:id="echoid-s19078" xml:space="preserve"> Sed in pri-
              <lb/>
            ma figura huius capituli [39 n] declarauimus, quòd b c
              <lb/>
            comprehenditur maior, quàm ſit.</s>
            <s xml:id="echoid-s19079" xml:space="preserve"> Et cauſſa huius eſt re-
              <lb/>
            fractio:</s>
            <s xml:id="echoid-s19080" xml:space="preserve"> & refractiones formarum, quæ remotiores ſunt
              <lb/>
            â perpendiculari, cadente à centro uiſus ſuper ſuperfi-
              <lb/>
            ciem corporis diaphani, ſunt maiores refractionibus for
              <lb/>
            marum, quæ ſunt propinquiores perpendiculari:</s>
            <s xml:id="echoid-s19081" xml:space="preserve"> refra-
              <lb/>
            ctio ergo formæ b n ad a eſt maior quàm refractio formę
              <lb/>
            partis z n ad a.</s>
            <s xml:id="echoid-s19082" xml:space="preserve"> Cauſſa ergo, quæ facit imaginem b z ui-
              <lb/>
            deri maiorem, facit, ut b n habeat maiorem proportio-
              <lb/>
            nem ad ipſam, quàm illa, quam habet b z ad b n:</s>
            <s xml:id="echoid-s19083" xml:space="preserve"> ergo l g
              <lb/>
            (quæ eſt imago b n) comprehenditur maior, quàm b n.</s>
            <s xml:id="echoid-s19084" xml:space="preserve">
              <lb/>
            Item ſi a non comprehenderit imaginem b n maiorem,
              <lb/>
            quàm ipſam b n:</s>
            <s xml:id="echoid-s19085" xml:space="preserve"> non comprehendet imagines cætera-
              <lb/>
            rum partium lineæ b n, quæ ſunt propinquiores a d z, ma
              <lb/>
            iores ipſis partibus.</s>
            <s xml:id="echoid-s19086" xml:space="preserve"> Nam formæ cæterarum partium ſunt minoris refractionis, quàm forma b z:</s>
            <s xml:id="echoid-s19087" xml:space="preserve">
              <lb/>
            ſed refractio eſt cauſſa magnitudinis imaginis:</s>
            <s xml:id="echoid-s19088" xml:space="preserve"> ergo a non comprehenderet l o maiorem, quàm b z:</s>
            <s xml:id="echoid-s19089" xml:space="preserve">
              <lb/>
            a ergo comprehendet maiorem b n, quàm ſit.</s>
            <s xml:id="echoid-s19090" xml:space="preserve"> Et idem accidit, ſi a extra perpendicularem eſt exe-
              <lb/>
            untem ex b z ſuper ſuperficiem corporis diaphani, & linea, quæ exit ex a ad mediũ b z, non eſt per-
              <lb/>
            pendicularis ſuper b z.</s>
            <s xml:id="echoid-s19091" xml:space="preserve"> Et hoc idem ſequitur in tribus figuris, in ſecunda ſcilicet, tertia & quarta
              <lb/>
            huius capituli:</s>
            <s xml:id="echoid-s19092" xml:space="preserve"> [40.</s>
            <s xml:id="echoid-s19093" xml:space="preserve"> 41.</s>
            <s xml:id="echoid-s19094" xml:space="preserve"> 42 numeris.</s>
            <s xml:id="echoid-s19095" xml:space="preserve">] Omne ergo, quod comprehenditur à uiſu ultra corpus
              <lb/>
            diaphanum groſsius aere, cuius ſuperficies fuerit plana, comprehenditur maius, quàm ſit, ſiue ſit
              <lb/>
            uiſus in aliqua perpendiculari exeunte exillo uiſu ſuper ſuperficiem corporis, ſiue ſit extra:</s>
            <s xml:id="echoid-s19096" xml:space="preserve"> & in-
              <lb/>
            differenter, ſiue diameter rei uiſæ fuerit æquidiſtans ſuperficiei corporis, ſiue non æquidiſtans.</s>
            <s xml:id="echoid-s19097" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div616" type="section" level="0" n="0">
          <head xml:id="echoid-head529" xml:space="preserve" style="it">44. Si uiſ{us} ſit in continuat a diametro circuli (qui eſt communis ſectio ſuperficierum, re-
            <lb/>
          fractionis & refractiui conuexi denſioris) uiſibile uerò inter ipſi{us} centrum & uiſum, ab eodem
            <lb/>
          centro æquabiliter diſtet: imago uidebitur maior uiſibili. 36 p 10.</head>
          <p>
            <s xml:id="echoid-s19098" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s19099" xml:space="preserve"> ſit ſuperficies corporis ſphærica, cuius conuexum ſit ex parte uiſus, & groſsius aere:</s>
            <s xml:id="echoid-s19100" xml:space="preserve"> & ſit
              <lb/>
            uiſus a:</s>
            <s xml:id="echoid-s19101" xml:space="preserve"> & res uiſa b c:</s>
            <s xml:id="echoid-s19102" xml:space="preserve"> & ſit centrum ſphæræ ultra b c, in reſpectu uiſus:</s>
            <s xml:id="echoid-s19103" xml:space="preserve"> & ſit centrum d:</s>
            <s xml:id="echoid-s19104" xml:space="preserve"> z me-
              <lb/>
            dium b c:</s>
            <s xml:id="echoid-s19105" xml:space="preserve"> & continuemus d b, d z, d c:</s>
            <s xml:id="echoid-s19106" xml:space="preserve"> & extrahamus has lineas, quouſq;</s>
            <s xml:id="echoid-s19107" xml:space="preserve"> concurrant cũ ſuperfi-
              <lb/>
            cie ſphæræ a d e, m, n:</s>
            <s xml:id="echoid-s19108" xml:space="preserve"> & extrahamus z m in parte m:</s>
            <s xml:id="echoid-s19109" xml:space="preserve"> & primò ſit uiſus in linea z m:</s>
            <s xml:id="echoid-s19110" xml:space="preserve"> erit ergo a m z
              <lb/>
            linea recta:</s>
            <s xml:id="echoid-s19111" xml:space="preserve"> & primò ſit b d æqualis c d:</s>
            <s xml:id="echoid-s19112" xml:space="preserve"> Sic ergo [per 8 p 1.</s>
            <s xml:id="echoid-s19113" xml:space="preserve"> 10 d 1] erit a z perpẽdicularis ſuper b c.</s>
            <s xml:id="echoid-s19114" xml:space="preserve"> Po
              <lb/>
            ſitio ergo b, reſpectu a, erit ſimilis poſitioni c reſpectu a.</s>
            <s xml:id="echoid-s19115" xml:space="preserve"> Et extrahamus ſuperficiem, in qua ſunt de,
              <lb/>
            d n, d m:</s>
            <s xml:id="echoid-s19116" xml:space="preserve"> faciet ergo [per 1 th.</s>
            <s xml:id="echoid-s19117" xml:space="preserve"> 1 ſphęricorum] in ſuperficie ſphęrica arcũ circuli magni:</s>
            <s xml:id="echoid-s19118" xml:space="preserve"> ſit ergo arcus
              <lb/>
            e m n:</s>
            <s xml:id="echoid-s19119" xml:space="preserve"> & hæc ſuperficies eſt perpẽdicularis ſuք ſuperficiem ſphæricã [per 9 n:</s>
            <s xml:id="echoid-s19120" xml:space="preserve"> quia eſt ſuperficies re
              <lb/>
            </s>
          </p>
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