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-div541" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s16357" xml:space="preserve">
              <pb o="229" file="0235" n="235" rhead="OPTICAE LIBER VI."/>
            ut dictum eſt de imaginibus ſpeculorum concauorum in ſeptimo capitulo huius tractatus:</s>
            <s xml:id="echoid-s16358" xml:space="preserve"> forma
              <lb/>
            fortè erit æqualis recta:</s>
            <s xml:id="echoid-s16359" xml:space="preserve"> fortè conuerſa.</s>
            <s xml:id="echoid-s16360" xml:space="preserve"> Patet ergo, quòd forma eorum, quæ comprehenduntur in
              <lb/>
            ſpeculis columnaribus concauis, fortè erit recta, fortè conuerſa.</s>
            <s xml:id="echoid-s16361" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div543" type="section" level="0" n="0">
          <head xml:id="echoid-head471" xml:space="preserve" style="it">54. Siuiſ{us} ſit in plano lineæ rectæ, perpendiculari plano axis ſpeculi cylindracei caui: imago
            <lb/>
          uidebitur recta & euerſa: aliâ s maior: aliâs minor: aliâs æqualis ipſi lineæ: aliâs ſimplex: aliâs
            <lb/>
          multiplex. 29 p 9.</head>
          <p>
            <s xml:id="echoid-s16362" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s16363" xml:space="preserve"> iteremus formã tertiæ figurę de fallacijs ſpeculorũ cõcauorũ ijſdẽ literis exiſtentibus:</s>
            <s xml:id="echoid-s16364" xml:space="preserve"> [41.</s>
            <s xml:id="echoid-s16365" xml:space="preserve">
              <lb/>
            42.</s>
            <s xml:id="echoid-s16366" xml:space="preserve"> 43 n] & ſit circulus b z a in ſuperficie ſpeculi columnaris cõcaui:</s>
            <s xml:id="echoid-s16367" xml:space="preserve"> & ſit uiſus in d.</s>
            <s xml:id="echoid-s16368" xml:space="preserve"> Erit ergo ex-
              <lb/>
            tra ſuperficiẽ circuli:</s>
            <s xml:id="echoid-s16369" xml:space="preserve"> & erunt duæ lineæ e a, e b perpendiculares ſuper ſuperficies, cõtingentes ſu
              <lb/>
            perficiẽ colũnę:</s>
            <s xml:id="echoid-s16370" xml:space="preserve"> & erit ſuperficies trianguli d g e perpẽdicularis ſuք ſuperficiẽ circuli [ք 18 p 11] ꝗa g d
              <lb/>
            eſt perpẽdicularis ſuper ſuperficiẽ circuli [ut oſtẽſum eſt 41 n.</s>
            <s xml:id="echoid-s16371" xml:space="preserve">] Superficies ergo trianguli d g e trãſit
              <lb/>
            per totũ axẽ:</s>
            <s xml:id="echoid-s16372" xml:space="preserve"> & in neutra ſuperficie d b o, d a o eſt aliquid de axe colũnæ, niſi e, qđ eſt centrũ circuli.</s>
            <s xml:id="echoid-s16373" xml:space="preserve">
              <lb/>
            Et utraq;</s>
            <s xml:id="echoid-s16374" xml:space="preserve"> ſuperficies d b o, d a o facit in ſuperficie columnę ſectio
              <lb/>
              <figure xlink:label="fig-0235-01" xlink:href="fig-0235-01a" number="205">
                <variables xml:id="echoid-variables194" xml:space="preserve">d g p i t k n u b e a o f q l h m r</variables>
              </figure>
            nem:</s>
            <s xml:id="echoid-s16375" xml:space="preserve"> [per 9 th.</s>
            <s xml:id="echoid-s16376" xml:space="preserve"> cylindricorum Sereni] & formæ reflectuntur ex
              <lb/>
            his ſectionibus à duobus punctis a, b [ut patuit 41 n.</s>
            <s xml:id="echoid-s16377" xml:space="preserve">] Forma ergo
              <lb/>
            r reflectitur ad d ex b:</s>
            <s xml:id="echoid-s16378" xml:space="preserve"> & forma m reflectitur ex a:</s>
            <s xml:id="echoid-s16379" xml:space="preserve"> & n u erit diame
              <lb/>
            ter imaginis m r:</s>
            <s xml:id="echoid-s16380" xml:space="preserve"> [ſunt enim puncta n & u imagines punctorum
              <lb/>
            r & m per 7 n 5] & eſt minor quàm m r:</s>
            <s xml:id="echoid-s16381" xml:space="preserve"> [ut demonſtratum eſt 42
              <lb/>
            n.</s>
            <s xml:id="echoid-s16382" xml:space="preserve">] Et ſimiliter duo puncta h, l reflectentur ad d ex duobus pun-
              <lb/>
            ctis à, b:</s>
            <s xml:id="echoid-s16383" xml:space="preserve"> & erit t k diameter imaginis l h:</s>
            <s xml:id="echoid-s16384" xml:space="preserve"> & erit e i æqualis [ut pa-
              <lb/>
            tuit 41 n] & erit p i diameter imaginis f q:</s>
            <s xml:id="echoid-s16385" xml:space="preserve"> & eſt maior illa.</s>
            <s xml:id="echoid-s16386" xml:space="preserve"> Et o-
              <lb/>
            mnes iſtæ imagines erunt conuerſæ [ut oſtenſum eſt 43 n.</s>
            <s xml:id="echoid-s16387" xml:space="preserve">] Et ſi
              <lb/>
            uiſus fuerit in o, & lineæ p i, t k, n u fuerint uiſibiles:</s>
            <s xml:id="echoid-s16388" xml:space="preserve"> erunt è con-
              <lb/>
            trario:</s>
            <s xml:id="echoid-s16389" xml:space="preserve"> tunc enim diameter imaginis p i erit minor ipſa:</s>
            <s xml:id="echoid-s16390" xml:space="preserve"> & diame-
              <lb/>
            ter imaginis n u erit maior ipſa:</s>
            <s xml:id="echoid-s16391" xml:space="preserve"> & diameter t k erit ei æqualis.</s>
            <s xml:id="echoid-s16392" xml:space="preserve"> Et
              <lb/>
            oẽs imagines erũt rectæ.</s>
            <s xml:id="echoid-s16393" xml:space="preserve"> Et omnia iſta oſtẽſa ſunt in prædicto ca
              <lb/>
            pitulo.</s>
            <s xml:id="echoid-s16394" xml:space="preserve"> Item cum utraq;</s>
            <s xml:id="echoid-s16395" xml:space="preserve"> extremitas alicuius harũ habuerit unam
              <lb/>
            imaginẽ, & aliquod punctũ in medio habuerit plures imagines:</s>
            <s xml:id="echoid-s16396" xml:space="preserve">
              <lb/>
            tũc illa linea habebit totimagines, quot punctũ mediũ habet.</s>
            <s xml:id="echoid-s16397" xml:space="preserve"> Et
              <lb/>
            ſi utraq;</s>
            <s xml:id="echoid-s16398" xml:space="preserve"> extremitas, uel altera habuerit plures imagines, & pun-
              <lb/>
            ctum mediũ habuerit unã:</s>
            <s xml:id="echoid-s16399" xml:space="preserve"> tunc linea tot habebit imagines, quot
              <lb/>
            habet punctũ extremũ.</s>
            <s xml:id="echoid-s16400" xml:space="preserve"> Et ſi utraq;</s>
            <s xml:id="echoid-s16401" xml:space="preserve"> extremitas uel altera habue-
              <lb/>
            rit multas imagines, & pũctũ mediũ habuerit multas imagines:</s>
            <s xml:id="echoid-s16402" xml:space="preserve">
              <lb/>
            tunc linea tot habebit imagines ſecundum maiorem numerum.</s>
            <s xml:id="echoid-s16403" xml:space="preserve">
              <lb/>
            Et hoc patebit, ut de imaginibus patuit ſpeculorum ſphærico-
              <lb/>
            rum concauorum.</s>
            <s xml:id="echoid-s16404" xml:space="preserve"> In ſpeculis ergo columnaribus concauis
              <lb/>
            accidit fallacia in omnibus, quæ in eis comprehenduntur, ſicut
              <lb/>
            accidit in ſpeculis ſphæricis concauis:</s>
            <s xml:id="echoid-s16405" xml:space="preserve"> ſcilicet de formis ſpecie-
              <lb/>
            rum uiſibilium, & de quantitatibus:</s>
            <s xml:id="echoid-s16406" xml:space="preserve"> & de numero ſuarum ima-
              <lb/>
            ginum:</s>
            <s xml:id="echoid-s16407" xml:space="preserve"> & de rectitudine, & de cõuerſione, cum fallacijs, quę appropriantur reflexioni.</s>
            <s xml:id="echoid-s16408" xml:space="preserve"> Et fallaciæ e-
              <lb/>
            runt inhis, ut in ſpeculis prædictis.</s>
            <s xml:id="echoid-s16409" xml:space="preserve"> Ethoc eſt, quod uoluimus declarare in hoc capitulo.</s>
            <s xml:id="echoid-s16410" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div545" type="section" level="0" n="0">
          <head xml:id="echoid-head472" xml:space="preserve">DE ERRORIBVS, QVI ACCIDVNT IN SPECVLIS
            <lb/>
          pyramidalibus concauis. Cap. IX.</head>
          <p>
            <s xml:id="echoid-s16411" xml:space="preserve">IN his autem accidunt illæ fallaciæ, quæ accidunt in ſpeculis columnaribus concauis.</s>
            <s xml:id="echoid-s16412" xml:space="preserve"> Debilitas
              <lb/>
            uerò coloris & lucis:</s>
            <s xml:id="echoid-s16413" xml:space="preserve"> & diuerſitas poſitionis, & remotionis accidunt in his, ſicut in omnibus ſpe
              <lb/>
            culis:</s>
            <s xml:id="echoid-s16414" xml:space="preserve"> nam cauſſa huius eſt reflexio.</s>
            <s xml:id="echoid-s16415" xml:space="preserve"> Accidit etiam in his ſpeculis multitudo imaginum, ſicut in
              <lb/>
            ſpeculis columnaribus & ſphæricis concauis dictũ in capitulo [ſecũdo libri quinti] de imaginibus.</s>
            <s xml:id="echoid-s16416" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div546" type="section" level="0" n="0">
          <head xml:id="echoid-head473" xml:space="preserve" style="it">55. Si lineæ: recta uel curua obliquè incidant uertici ſpeculi conici caui: reflectentur à latere
            <lb/>
          conico ad uiſum inter ipſas & ſpeculi ſuperficiem poſitum: & imago rectæ uidebitur parum cur-
            <lb/>
          ua: curuæ, recta. 31 p 9.</head>
          <p>
            <s xml:id="echoid-s16417" xml:space="preserve">ACcidit etiam in eis, quod in columnaribus concauis, ſcilicet ut rectum uideatur conuexum
              <lb/>
            & concauum.</s>
            <s xml:id="echoid-s16418" xml:space="preserve"> Huius autem demonſtratio eſt:</s>
            <s xml:id="echoid-s16419" xml:space="preserve"> quod rectæ lineæ, quæ extenduntur in longi-
              <lb/>
            tudine ſpeculi, quæ tranſeunt per uerticem pyramidis, & quæ ſunt prope illas, uidentur con
              <lb/>
            uexæ, & fortè rectæ.</s>
            <s xml:id="echoid-s16420" xml:space="preserve"> Et demonſtratio ſuper hoc eſt, ut demonſtratio in ſpeculis columnaribus con-
              <lb/>
            cauis.</s>
            <s xml:id="echoid-s16421" xml:space="preserve"> Nam ſi itera uerimus ſecundam figuram de fallacijs ſpeculorum pyramidalium conuexorum
              <lb/>
            [quæ eſt 32 n] inueniemus diametrum imaginis lineæ rectæ poſitæ in illo ſpeculo, quæ eſt illic linea
              <lb/>
            a n, intra concauitatẽ ſpeculi pyramidalis:</s>
            <s xml:id="echoid-s16422" xml:space="preserve"> & inueniemus punctũ, quod eſt ſub ſuperficie contingen
              <lb/>
            te pyramidẽ, tranſeuntẽ per lineã longitudinis, à qua reflectitur forma lineę rectę ad uiſum:</s>
            <s xml:id="echoid-s16423" xml:space="preserve"> quod il-
              <lb/>
            lic punctum f.</s>
            <s xml:id="echoid-s16424" xml:space="preserve"> Si igitur fuerit punctum illud centrum uiſus:</s>
            <s xml:id="echoid-s16425" xml:space="preserve"> erunt omnia puncta, quę ſunt in diame-
              <lb/>
            </s>
          </p>
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