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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            <s xml:id="echoid-s14579" xml:space="preserve">
              <pb o="209" file="0215" n="215" rhead="OPTICAE LIBER VI."/>
            [per 18 p 1] angulus m z d maior angulo m d z.</s>
            <s xml:id="echoid-s14580" xml:space="preserve"> Igitur d z l maior duobus angulis z d e, z e d.</s>
            <s xml:id="echoid-s14581" xml:space="preserve">
              <lb/>
            [conſtat enim è duobus angulis m z l & m z d,
              <lb/>
              <figure xlink:label="fig-0215-01" xlink:href="fig-0215-01a" number="184">
                <variables xml:id="echoid-variables174" xml:space="preserve">e c s ſ o f i g m b k z d t q p h y n r u a x</variables>
              </figure>
            quorum ille angulo z e d, hic angulo z d e maior
              <lb/>
            eſt concluſus.</s>
            <s xml:id="echoid-s14582" xml:space="preserve">] Sed angulus d z l ęqualis eſt an-
              <lb/>
            gulo n z c [per 15 p 1] & angulus e z c ęqualis
              <lb/>
            duobus angulis z d e, z e d [per 32 p 1.</s>
            <s xml:id="echoid-s14583" xml:space="preserve">] Quare an
              <lb/>
            gulus n z c maior eſt angulo e z c:</s>
            <s xml:id="echoid-s14584" xml:space="preserve"> ſecetur ad ę-
              <lb/>
            qualitatem per lineam f z:</s>
            <s xml:id="echoid-s14585" xml:space="preserve"> quę quidem concur-
              <lb/>
            ret cum linea n q:</s>
            <s xml:id="echoid-s14586" xml:space="preserve"> [per lemma Procli ad 29 p 1:</s>
            <s xml:id="echoid-s14587" xml:space="preserve">
              <lb/>
            quia n q, c d ſunt parallelę per fabricationem.</s>
            <s xml:id="echoid-s14588" xml:space="preserve">]
              <lb/>
            Concurrat ſuper punctum f.</s>
            <s xml:id="echoid-s14589" xml:space="preserve"> Cum ergo angulus
              <lb/>
            f z c ſit ęqualis angulo c z e:</s>
            <s xml:id="echoid-s14590" xml:space="preserve"> reflectetur f ad e à
              <lb/>
            puncto z.</s>
            <s xml:id="echoid-s14591" xml:space="preserve"> [per 12 n 4] q uerò reflectetur ad e à
              <lb/>
            puncto lineę longitudinis, quę tranſit per z à pũ
              <lb/>
            cto, quod eſt ultra z.</s>
            <s xml:id="echoid-s14592" xml:space="preserve"> Si enim à puncto citra z, id
              <lb/>
            eſt propinquiore e:</s>
            <s xml:id="echoid-s14593" xml:space="preserve"> linea ducta à puncto q ad
              <lb/>
            punctum illud reflexionis, ſecabit lineam f z:</s>
            <s xml:id="echoid-s14594" xml:space="preserve"> &
              <lb/>
            ita punctum ſectionis reflectetur ad e à duobus
              <lb/>
            punctis:</s>
            <s xml:id="echoid-s14595" xml:space="preserve"> quod eſt impoſsibile [& contra 46 n 5.</s>
            <s xml:id="echoid-s14596" xml:space="preserve">]
              <lb/>
            Sumatur ergo ultra punctum z pũctum k, à quo
              <lb/>
            reflectatur q ad e:</s>
            <s xml:id="echoid-s14597" xml:space="preserve"> & ducatur linea e k, donec cõ
              <lb/>
            currat cum linea n q, in puncto p [concurret au-
              <lb/>
            tem per lemma Procli ad 29 p 1.</s>
            <s xml:id="echoid-s14598" xml:space="preserve">] Erit p imago
              <lb/>
            q [per 4 n 5.</s>
            <s xml:id="echoid-s14599" xml:space="preserve">] Sed h reflectitur ad e à puncto
              <lb/>
            ſectionis columnę [ſunt enim h & e in diuerſis
              <lb/>
            planis.</s>
            <s xml:id="echoid-s14600" xml:space="preserve">] Si ergo à puncto h ducatur perpen-
              <lb/>
            dicularis ſuper lineam, cõtingentem ſectionem
              <lb/>
            in aliquo puncto:</s>
            <s xml:id="echoid-s14601" xml:space="preserve"> perpendicularis illa concur-
              <lb/>
            ret cum perpendiculari c z d ſub axe [per 24 n.</s>
            <s xml:id="echoid-s14602" xml:space="preserve">]
              <lb/>
            Concurrat in puncto u.</s>
            <s xml:id="echoid-s14603" xml:space="preserve"> Similiter à puncto l eſt
              <lb/>
            ducere unam perpendicularem ſuper ſectio-
              <lb/>
            nem, à cuius puncto reflectatur t ad e.</s>
            <s xml:id="echoid-s14604" xml:space="preserve"> Et quo-
              <lb/>
            niam [ex theſi] puncta h, t ſunt eiuſdem ſitus,
              <lb/>
            reſpectu lineæ e d, & puncta ſectionis ſimiliter,
              <lb/>
            per quæ tranſeunt perpendiculares ab ipſis du-
              <lb/>
            ctæ.</s>
            <s xml:id="echoid-s14605" xml:space="preserve"> Igitur illæ duæ perpendiculares concurrent in idem punctum lineę e d.</s>
            <s xml:id="echoid-s14606" xml:space="preserve"> Concurrant ergo in
              <lb/>
            puncto u.</s>
            <s xml:id="echoid-s14607" xml:space="preserve"> Et quia linea e b concurrit cum h u:</s>
            <s xml:id="echoid-s14608" xml:space="preserve"> ſit concurſus in puncto r.</s>
            <s xml:id="echoid-s14609" xml:space="preserve"> Similiter e g concurrat
              <lb/>
            cum t u in puncto y:</s>
            <s xml:id="echoid-s14610" xml:space="preserve"> & ducatur linea r y.</s>
            <s xml:id="echoid-s14611" xml:space="preserve"> Palàm [per 4 n 5] quòd r eſt imago h:</s>
            <s xml:id="echoid-s14612" xml:space="preserve"> & y eſt imago t:</s>
            <s xml:id="echoid-s14613" xml:space="preserve"> &
              <lb/>
            habemus triangulum e r y:</s>
            <s xml:id="echoid-s14614" xml:space="preserve"> extra ſuperficiem huius trianguli eſt punctum z:</s>
            <s xml:id="echoid-s14615" xml:space="preserve"> & in ſuperficie huius
              <lb/>
            trianguli altior eſt linea e p:</s>
            <s xml:id="echoid-s14616" xml:space="preserve"> & ita p eſt extra.</s>
            <s xml:id="echoid-s14617" xml:space="preserve"> Quare linea r p y erit curua:</s>
            <s xml:id="echoid-s14618" xml:space="preserve"> & illa eſt imago lineæ t h.</s>
            <s xml:id="echoid-s14619" xml:space="preserve">
              <lb/>
            Et eſt quidem hęc imago curuitatis non modicæ.</s>
            <s xml:id="echoid-s14620" xml:space="preserve"> Quod eſt propoſitum.</s>
            <s xml:id="echoid-s14621" xml:space="preserve"> Palàm ergo, quòd in his
              <lb/>
            ſpeculis, ſi linea recta uiſa ęquidiſtans fuerit lineę longitudinis columnæ:</s>
            <s xml:id="echoid-s14622" xml:space="preserve"> erit imago eius recta, aut
              <lb/>
            accedens ad rectitudinem.</s>
            <s xml:id="echoid-s14623" xml:space="preserve"> Siuerò linea recta uiſa ęquidiſtans fuerit columnæ:</s>
            <s xml:id="echoid-s14624" xml:space="preserve"> erit imago eius cur-
              <lb/>
            ua, curuitate non modica.</s>
            <s xml:id="echoid-s14625" xml:space="preserve"> Lineę autem inter has duas ſitę, quę magis accedunt ad ſitum lineę ęqui-
              <lb/>
            diſtantis, reſpectu columnę, habebunt imagines ſuas rectitudini magis uicinas:</s>
            <s xml:id="echoid-s14626" xml:space="preserve"> & imagines earũ,
              <lb/>
            quæ propinquiores ſunt ſitui ęquidiſtantium latitudini, erunt magis curuę:</s>
            <s xml:id="echoid-s14627" xml:space="preserve"> & minuetur, uel augmẽ
              <lb/>
            tabitur curuitas imaginum ſecundum acceſſum uel elongationem linearum ad alterum horum ſi-
              <lb/>
            tuum.</s>
            <s xml:id="echoid-s14628" xml:space="preserve"> Et hoc eſt propoſitum.</s>
            <s xml:id="echoid-s14629" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div500" type="section" level="0" n="0">
          <head xml:id="echoid-head444" xml:space="preserve">DE ERRORIBVS, QVI ACCIDVNT IN SPECVLIS
            <lb/>
          pyramidalibus conuexis. Cap. VI.</head>
          <head xml:id="echoid-head445" xml:space="preserve" style="it">30. Si duæ rectæ à duob{us} punctis ellipſis conicæ, inæquabiliter à uertice diſtantib{us}, ſint per-
            <lb/>
          pendiculares duab{us} rectis, ellipſin in dictis punctis tangentib{us}: ultra axem concurrent. Opor
            <lb/>
          tet autem ut perpendicularis à puncto propinquiore, & recta à longinquiore ad axem ductæ,
            <lb/>
          acutum angulum comprehendant. 113 p 1. 45 p 7.</head>
          <p>
            <s xml:id="echoid-s14630" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s14631" xml:space="preserve"> in ſpeculis pyramidalibus exterioribus ij dem errores accidunt, qui in ſphæricis ex-
              <lb/>
            terioribus eueniunt.</s>
            <s xml:id="echoid-s14632" xml:space="preserve"> Lineę enim uiſę ęquidiſtantes, reſpectu pyramidis, aut rectę uidentur,
              <lb/>
            aut fortè ęquidiſtantes latitudini curuę:</s>
            <s xml:id="echoid-s14633" xml:space="preserve"> & intermedię augmentant uel diminuunt curuita-
              <lb/>
            tem ſecundum propinquitatem earum uel remotionem.</s>
            <s xml:id="echoid-s14634" xml:space="preserve"> Et hoc probabitur.</s>
            <s xml:id="echoid-s14635" xml:space="preserve"> Quiddam tamen prę-
              <lb/>
            mittendum proponamùs:</s>
            <s xml:id="echoid-s14636" xml:space="preserve"> & eſt.</s>
            <s xml:id="echoid-s14637" xml:space="preserve"> Si ſumatur in ſuperficie pyramidis, punctum reflexionis:</s>
            <s xml:id="echoid-s14638" xml:space="preserve"> & fiat ſe-
              <lb/>
            ctio tranſiens per punctum illud:</s>
            <s xml:id="echoid-s14639" xml:space="preserve"> & in ſectione ſumatur punctum remotius à uertice pyramidis,
              <lb/>
            puncto reflexionis:</s>
            <s xml:id="echoid-s14640" xml:space="preserve"> & à puncto ſumpto ducatur perpendicularis ſuper contingentem ſectionem:</s>
            <s xml:id="echoid-s14641" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0215-02" xlink:href="fig-0215-02a" number="185">
                <description xml:id="echoid-description3" xml:space="preserve">CIN EMATH EQUE FRANCAISE</description>
                <description xml:id="echoid-description4" xml:space="preserve">BIBLIOTHEQUE MUSEE</description>
              </figure>
            </s>
          </p>
        </div>
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