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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        <div xml:id="echoid-div247" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s6951" xml:space="preserve">
              <pb o="118" file="0124" n="124" rhead="ALHAZEN"/>
            cõmunis ſuperficiei columnæ & ſuperficiei reflexionis, erit linea recta, ſcilicet latus columnæ:</s>
            <s xml:id="echoid-s6952" xml:space="preserve"> cum
              <lb/>
            in ſuperficie reflexionis ſit diameter columnæ.</s>
            <s xml:id="echoid-s6953" xml:space="preserve"> Et planum hoc eſt, quoniam columnæ compoſitio
              <lb/>
            eſt ex motu ſuperficiei æquidiſtantium laterum ſuper unum latus immotum [per 21 d 11.</s>
            <s xml:id="echoid-s6954" xml:space="preserve">] Vnde ſu-
              <lb/>
            perficiei columnam ſecanti, in qua ſit axis, id eſt latus immotum, & ſuperficiei columnę communis
              <lb/>
            linea, erit latus motum.</s>
            <s xml:id="echoid-s6955" xml:space="preserve"> Et dico, quòd ex omnibus reflexionis ſuperficiebus una ſola eſt, cui & co-
              <lb/>
            lumnæ ſuperficiei ſit linea communis recta.</s>
            <s xml:id="echoid-s6956" xml:space="preserve"> Quoniã unica poteſt intelligi ſuperficies, in qua ſit axis
              <lb/>
            columnæ & centrum uiſus:</s>
            <s xml:id="echoid-s6957" xml:space="preserve"> & non plures.</s>
            <s xml:id="echoid-s6958" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div248" type="section" level="0" n="0">
          <head xml:id="echoid-head277" xml:space="preserve" style="it">30. Si uiſ{us} ſit extrá ſuperficiem ſpeculi cylindracei cõuexi, in planò uiſibilis ad axem recto:
            <lb/>
          communis ſectio ſuperficierum reflexionis & ſpeculi, erit circul{us}: & unic{us} tantùm eſt in ea-
            <lb/>
          dem conſpicuà ſuperficie, à quo ad uiſum reflexio fieri poteſt. 9.17 p 7.</head>
          <p>
            <s xml:id="echoid-s6959" xml:space="preserve">SI uerò ſuperficies reflexionis ſit æquidiſtans baſibus columnæ:</s>
            <s xml:id="echoid-s6960" xml:space="preserve"> erit linea communis circulus
              <lb/>
            [per 5 th Sereni de ſectione cylindri] & hæc ſola eſt ſuperficies, quæ cum columnæ ſuperficie
              <lb/>
            lineam communem habeat circularem.</s>
            <s xml:id="echoid-s6961" xml:space="preserve"> Quoniam in omni reflexione, perpendicularis ſuper
              <lb/>
            ſuperficiem, contingẽtem punctum reflexionis, eſt diameter circuli, baſibus columnæ æquidiſtan-
              <lb/>
            tis:</s>
            <s xml:id="echoid-s6962" xml:space="preserve"> & non poteſt eſſe in columnæ ſuperficie, niſi unus circulus æquidiſtans baſibus, qui cum cen-
              <lb/>
            tro uiſus ſit in eadem ſuperficie.</s>
            <s xml:id="echoid-s6963" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div249" type="section" level="0" n="0">
          <head xml:id="echoid-head278" xml:space="preserve" style="it">31. Si uiſ{us} ſit extra ſuperficiem ſpeculi cylindracei conuexi, in plano uiſibilis ad axem obli-
            <lb/>
          quo: communis ſectio ſuperficierum reflexionis & ſpeculi erit ellipſis: & plures in eadem conſpi-
            <lb/>
          cua ſuperficie eſſe poſſunt, à quib{us} ad eundem uiſum reflexio fiat. 10. 18 p 7.</head>
          <p>
            <s xml:id="echoid-s6964" xml:space="preserve">OMnes autẽ aliæ ſuperficies reflexionis, ſecant columnã & axẽ columnæ:</s>
            <s xml:id="echoid-s6965" xml:space="preserve"> quoniã perpendi-
              <lb/>
            cularis ducta à pũcto reflexionis ſecat axẽ columnæ:</s>
            <s xml:id="echoid-s6966" xml:space="preserve"> & lineæ cõmunes his ſuperficiebus &
              <lb/>
            ſuperficiebus columnę, ſunt ſectiones, quas in colũnis & pyramidibus aſsignãt geometræ.</s>
            <s xml:id="echoid-s6967" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div250" type="section" level="0" n="0">
          <head xml:id="echoid-head279" xml:space="preserve" style="it">32. Si communis ſectio ſuperficierum reflexionis & ſpeculi cylindr acei conuexi, fuerit lat{us}
            <lb/>
          cylindri, uel cιrcul{us}: reflexio à quocun communis ſectionis puncto facta, in eadem ſuperficie
            <lb/>
          ſemper fiet. 19. 20 p 7.</head>
          <p>
            <s xml:id="echoid-s6968" xml:space="preserve">CVm ſuperficiebus columnæ & reflexionis linea recta fuerit cõmunis, quodcunq;</s>
            <s xml:id="echoid-s6969" xml:space="preserve"> punctum
              <lb/>
            illius lineæ intueatur uiſus:</s>
            <s xml:id="echoid-s6970" xml:space="preserve"> fiet reflexio in ſuperficie eadem, in qua eſt axis.</s>
            <s xml:id="echoid-s6971" xml:space="preserve"> Quoniam eſt ſu-
              <lb/>
            perficies unica, contingens columnam in linea illa longitudinis:</s>
            <s xml:id="echoid-s6972" xml:space="preserve"> & quocunq;</s>
            <s xml:id="echoid-s6973" xml:space="preserve"> puncto huius
              <lb/>
            lineæ ſumpto:</s>
            <s xml:id="echoid-s6974" xml:space="preserve"> perpendicularis ab eo ad axem ducta, erit in eadem ſuperficie cum axe:</s>
            <s xml:id="echoid-s6975" xml:space="preserve"> & hæc linea
              <lb/>
            erit orthogonalis ſuper ſuperficiem, contingentem ſuperficiem columnæ [Nam quia per 21 d 11 la-
              <lb/>
            tus cylindri eſt parallelum axi:</s>
            <s xml:id="echoid-s6976" xml:space="preserve"> erit recta linea perpendicularis axi:</s>
            <s xml:id="echoid-s6977" xml:space="preserve"> perpendicularis tum lateri per
              <lb/>
            29 p 1, tum rectæ circulum per idem lateris punctum deſcriptum, tangenti, per 18 p 3.</s>
            <s xml:id="echoid-s6978" xml:space="preserve"> Quare per
              <lb/>
            4 p 11 erit perpendicularis plano ſpeculum tangenti.</s>
            <s xml:id="echoid-s6979" xml:space="preserve">] Sed centrum uiſus eſt in ſuperficie orthogo-
              <lb/>
            nali ſuper eandem ſuperficiem:</s>
            <s xml:id="echoid-s6980" xml:space="preserve"> quia in una ſuperficie eſt centrum uiſus & linea communis & axis
              <lb/>
            columnæ [per 6.</s>
            <s xml:id="echoid-s6981" xml:space="preserve"> 13 n] & una ſola eſt ſuperficies orthogonalis ſuper illam ſuperficiem [per 13 p 11.</s>
            <s xml:id="echoid-s6982" xml:space="preserve">]
              <lb/>
            Quare omnes reflexiones à punctis huius lineæ factæ, ſunt in eadem reflexionis ſuperficie.</s>
            <s xml:id="echoid-s6983" xml:space="preserve"> Verùm
              <lb/>
            cum linea cõmunis ſuperficiei reflexionis & columnæ fuerit circulus, quo cunq;</s>
            <s xml:id="echoid-s6984" xml:space="preserve"> puncto illius cir-
              <lb/>
            culi uiſo:</s>
            <s xml:id="echoid-s6985" xml:space="preserve"> fiet in una & eadem ſuperficie reflexio.</s>
            <s xml:id="echoid-s6986" xml:space="preserve"> Quoniam quæcunq;</s>
            <s xml:id="echoid-s6987" xml:space="preserve"> perpendicularis à puncto re-
              <lb/>
            flexionis ducta:</s>
            <s xml:id="echoid-s6988" xml:space="preserve"> erit diameter huius circuli:</s>
            <s xml:id="echoid-s6989" xml:space="preserve"> quare in ſuperficie huius circuli eſt:</s>
            <s xml:id="echoid-s6990" xml:space="preserve"> & punctum uiſus
              <lb/>
            ſimiliter:</s>
            <s xml:id="echoid-s6991" xml:space="preserve"> & ſuperficies hæc orthogonalis eſt ſuper ſuperficiẽ, quodcunq;</s>
            <s xml:id="echoid-s6992" xml:space="preserve"> punctũ huius circuli ſum-
              <lb/>
            ptum contingentem.</s>
            <s xml:id="echoid-s6993" xml:space="preserve"> Quare in hac ſola ſuperficie erit cuiuslibet puncti, prædicti circuli reflexio.</s>
            <s xml:id="echoid-s6994" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div251" type="section" level="0" n="0">
          <head xml:id="echoid-head280" xml:space="preserve" style="it">33. Ab uno cõmunis ſectionis ſuperficierum reflexionis & ſpeculi cylindr acei conuexi pun-
            <lb/>
          cto, unum uiſibilis punctum ad unum uiſum in eadem ſuperficie reflectitur. 22 p 7.</head>
          <p>
            <s xml:id="echoid-s6995" xml:space="preserve">QVacunq;</s>
            <s xml:id="echoid-s6996" xml:space="preserve"> uerò alia linea communi ſumpta:</s>
            <s xml:id="echoid-s6997" xml:space="preserve"> nõ fiet in eadem reflexionis ſuperficie reflexio,
              <lb/>
            niſi ex uno tantùm huius lineæ puncto.</s>
            <s xml:id="echoid-s6998" xml:space="preserve"> Quoniam perpẽdicularis ducta à puncto reflexio-
              <lb/>
            nis, orthogonalis eſt ſuper lineam longitudinis columnæ per punctũ illud tranſeuntis [per
              <lb/>
            3 d 11] quare & ſuper axem [per 29 p 1] & perpendicularis illa, eſt diameter circuli, æquidiſtantis
              <lb/>
            baſibus columnæ:</s>
            <s xml:id="echoid-s6999" xml:space="preserve"> & ſuperficies reflexionis & circulus ille ſecant ſe:</s>
            <s xml:id="echoid-s7000" xml:space="preserve"> & linea ijs communis, eſt dia-
              <lb/>
            meter illius circuli:</s>
            <s xml:id="echoid-s7001" xml:space="preserve"> & eſt illa diameter perpendicularis ſuper ſuperficiem, columnam in illo puncto
              <lb/>
            contingentem, & ſuperficies reflexionis ſecat illam lineam longitudinis columnæ ſuper quam fit
              <lb/>
            contingentia, & eſt declinata ſuper ipſam:</s>
            <s xml:id="echoid-s7002" xml:space="preserve"> ergo & ſuper axem erit illa ſuperficies reflexionis decli-
              <lb/>
            nata:</s>
            <s xml:id="echoid-s7003" xml:space="preserve"> & in ſuperficie plana ſuper lineam aliquam declinata nõ poteſt intelligi, niſi una linea ortho-
              <lb/>
            gonaliter cadens in illam.</s>
            <s xml:id="echoid-s7004" xml:space="preserve"> Sed ſi à duobus ſuperficiei reflexionis punctis fieret reflexio in eadem
              <lb/>
            ſuperficie:</s>
            <s xml:id="echoid-s7005" xml:space="preserve"> eſſent duæ lineæ illius ſuperficiei orthogonales ſuper axem:</s>
            <s xml:id="echoid-s7006" xml:space="preserve"> quod eſſe non poteſt, cum
              <lb/>
            ſuperficies illa ſit declinata ſuper eum.</s>
            <s xml:id="echoid-s7007" xml:space="preserve"> Nam perpendicularis à puncto reflexionis cadit in circu-
              <lb/>
            lum, æquidiſtantem baſibus columnæ, & in punctum axis, & eſt ſectio cõmunis ſuperficiei circuli
              <lb/>
            & ſuperficiei reflexionis.</s>
            <s xml:id="echoid-s7008" xml:space="preserve"> Si ergo ab alio lineæ communis puncto, in eadem ſuperficie fieret refle-
              <lb/>
            xio:</s>
            <s xml:id="echoid-s7009" xml:space="preserve"> alia perpendicularis ab alio puncto ducta:</s>
            <s xml:id="echoid-s7010" xml:space="preserve"> eſſet diameter alte
              <gap/>
            ius circuli columnæ, huic æqui-
              <lb/>
            diſtãtis, & caderet in punctũ axis, in quod nõ cadit ſuperficies reflexionis.</s>
            <s xml:id="echoid-s7011" xml:space="preserve"> Et ita in omnibus ſuper-
              <lb/>
            ficiebus reflexionis eſt intelligendũ:</s>
            <s xml:id="echoid-s7012" xml:space="preserve"> quòd ab uno puncto tantùm lineæ communis fiat reflexio in
              <lb/>
            </s>
          </p>
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