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-s14932" xml:space="preserve">
              <pb o="213" file="0219" n="219" rhead="OPTICAE LIBER VI."/>
            ſus [per 13 p 1.</s>
            <s xml:id="echoid-s14933" xml:space="preserve">] Igitur angulus e n d eſt acutus [per 32 p 1.</s>
            <s xml:id="echoid-s14934" xml:space="preserve">] Et ſit linea c x cõtingens ſectionẽ in pun
              <lb/>
            cto c.</s>
            <s xml:id="echoid-s14935" xml:space="preserve"> Patet ergo, ut in prædicta figura [30 n] quòd angulus d c x eſt obtuſus:</s>
            <s xml:id="echoid-s14936" xml:space="preserve"> & qđ perpẽdicularis
              <lb/>
            extracta ex c ſuper c x, ſecabit angulũ d c x:</s>
            <s xml:id="echoid-s14937" xml:space="preserve"> & cõcurret cũ e d ſub d.</s>
            <s xml:id="echoid-s14938" xml:space="preserve"> Ergo hæc perpendicularis ſecet
              <lb/>
            e d in s.</s>
            <s xml:id="echoid-s14939" xml:space="preserve"> Perpẽdicularis ergo extracta ex n ſuք lineã cõtingentẽ ſectionẽ, ſecabit ſectionẽ ultra s:</s>
            <s xml:id="echoid-s14940" xml:space="preserve"> ſed
              <lb/>
            remotius à d quã s:</s>
            <s xml:id="echoid-s14941" xml:space="preserve"> nã iſtę perpendiculares cõcurrent ultra circũferentiã ſectionis.</s>
            <s xml:id="echoid-s14942" xml:space="preserve"> Perpẽdicularis
              <lb/>
            ergo extracta ex puncto n ſuper lineã contingentẽ ſectionẽ, non ſecabit angulũ d c x:</s>
            <s xml:id="echoid-s14943" xml:space="preserve"> erit ergo
              <gap/>
            e-
              <lb/>
            motior ab n e, quàm ſit n d.</s>
            <s xml:id="echoid-s14944" xml:space="preserve"> Ergo hæc perpendicularis ſecat a d ſupra d.</s>
            <s xml:id="echoid-s14945" xml:space="preserve"> Sit ergo perpẽdicularis ex-
              <lb/>
            tracta ex n ſuper lineam cõtingentẽ ſectionẽ, linea n q.</s>
            <s xml:id="echoid-s14946" xml:space="preserve"> Et r e ſecat e n, & ſecat circumferẽtiã ſectio-
              <lb/>
            nis:</s>
            <s xml:id="echoid-s14947" xml:space="preserve"> & eſt in ſuperficie eius:</s>
            <s xml:id="echoid-s14948" xml:space="preserve"> & n q eſt in ſuperficie ſectionis.</s>
            <s xml:id="echoid-s14949" xml:space="preserve"> Si ergo r e extrahatur rectè, ſecabit n q
              <lb/>
            [quia cõtinuata ſecat angulũ n e q.</s>
            <s xml:id="echoid-s14950" xml:space="preserve">] Secet ergo in y:</s>
            <s xml:id="echoid-s14951" xml:space="preserve"> & ſuperficies a n d ſecabit ſuperficiẽ ſectionis.</s>
            <s xml:id="echoid-s14952" xml:space="preserve">
              <lb/>
            Itẽ quia punctũ e eſt extra ſuperficiẽ a n d:</s>
            <s xml:id="echoid-s14953" xml:space="preserve"> (nã ſuperficies a n d nõ eſt ſuperficies ſectionis [in qua
              <lb/>
            eſt punctũ e] quia punctũ a eſt extra ſuperficiẽ ſectionis:</s>
            <s xml:id="echoid-s14954" xml:space="preserve"> & quia a e eſt perpẽdicularis ſuper ſuperfi
              <lb/>
            ciẽ ſectionis, & e eſt in circumferentia illius) ergo n c d eſt differentia cõmunis ſuperficiei a n d &
              <lb/>
            ſuperficiei ſectionis:</s>
            <s xml:id="echoid-s14955" xml:space="preserve"> & n q concurrit cũ ſectione ultra c [ut patuit.</s>
            <s xml:id="echoid-s14956" xml:space="preserve">] Ergo n q eſt ultra ſuperficiem
              <lb/>
            a n d:</s>
            <s xml:id="echoid-s14957" xml:space="preserve"> y ergo eſt ultra lineam a p g [quæ nõ eſt in ſuperficie a n d.</s>
            <s xml:id="echoid-s14958" xml:space="preserve">] Si ergo uiſus fuerit in r, & forma
              <lb/>
            alicuius uiſibilis reflectatur à linea longitudinis:</s>
            <s xml:id="echoid-s14959" xml:space="preserve"> tunc p erit imago o:</s>
            <s xml:id="echoid-s14960" xml:space="preserve"> [per 4 n 5] & y erit imago n:</s>
            <s xml:id="echoid-s14961" xml:space="preserve">
              <lb/>
            & a uidebitur in ſuo loco:</s>
            <s xml:id="echoid-s14962" xml:space="preserve"> quia eſt in uertice pyramidis.</s>
            <s xml:id="echoid-s14963" xml:space="preserve"> Et erit imago lineæ a o n linea tranſiens per
              <lb/>
            pũcta a, p, y:</s>
            <s xml:id="echoid-s14964" xml:space="preserve"> ſed hæc linea eſt cõuexa:</s>
            <s xml:id="echoid-s14965" xml:space="preserve"> quia eſt ultra lineã a p g.</s>
            <s xml:id="echoid-s14966" xml:space="preserve"> Sit ergo linea a p y.</s>
            <s xml:id="echoid-s14967" xml:space="preserve"> Et patuitiã, quòd
              <lb/>
            formæ omniũ punctorũ, quæ ſunt in a n, reflectantur ad r ex a e.</s>
            <s xml:id="echoid-s14968" xml:space="preserve"> Lineæ ergo radiales, per quas refle
              <lb/>
            ctuntur illæ formæ, ſunt in ſuperficie trianguli r a e.</s>
            <s xml:id="echoid-s14969" xml:space="preserve"> Omnes ergo imagines lineæ a n ſunt in hac ſu-
              <lb/>
            perficie.</s>
            <s xml:id="echoid-s14970" xml:space="preserve"> Ergo linea a p y conuexa eſt in hac ſuperficie:</s>
            <s xml:id="echoid-s14971" xml:space="preserve"> & p eſt propinquius r quàm y.</s>
            <s xml:id="echoid-s14972" xml:space="preserve"> Et erit
              <lb/>
            conuexitas imaginis huius ex parte uiſus:</s>
            <s xml:id="echoid-s14973" xml:space="preserve"> & erit conuexitas parua:</s>
            <s xml:id="echoid-s14974" xml:space="preserve"> & diameter huius imaginis e-
              <lb/>
            rit minor ipſa linea, modica quantitate.</s>
            <s xml:id="echoid-s14975" xml:space="preserve"> Imagines ergo linearum rectarum, quæ extrahuntur ex
              <lb/>
            uertice pyramidis obliquè ſuper axem:</s>
            <s xml:id="echoid-s14976" xml:space="preserve"> comprehenduntur à uiſu in tali ſpeculo conuexæ.</s>
            <s xml:id="echoid-s14977" xml:space="preserve"> Et for-
              <lb/>
            mę harum linearum reflectuntur à lineis rectis extenſis in longitudine pyramidis.</s>
            <s xml:id="echoid-s14978" xml:space="preserve"> Et hoc eſt, quod
              <lb/>
            uoluimus declarare.</s>
            <s xml:id="echoid-s14979" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div506" type="section" level="0" n="0">
          <head xml:id="echoid-head448" xml:space="preserve" style="it">33. Si recta linea ſit parallela latitudini ſpeculi conici conuexi: & uiſ{us} ſit extra planum di-
            <lb/>
          ctæ lineæ baſi parallelum: reflectetur ab ellipſi: & imago uidebitur maximè curua. 56 p 7.</head>
          <p>
            <s xml:id="echoid-s14980" xml:space="preserve">FOrmæ uerò linearũ æquidiſtantiũ latitudini ſpeculi pyramidalis cõuexi, reflectuntur à lineis
              <lb/>
            conuexis in ſuperficie ſpeculi:</s>
            <s xml:id="echoid-s14981" xml:space="preserve"> & conuexitas harum linearum patet, ut in ſpeculo columnari
              <lb/>
            conuexo [29 n.</s>
            <s xml:id="echoid-s14982" xml:space="preserve">] Et per illam eandem uiam etiam ſimiliter patebit, quòd imagines harum li-
              <lb/>
            nearum erunt nimium cõuexæ & manifeſtæ ſenſui.</s>
            <s xml:id="echoid-s14983" xml:space="preserve"> Et erit centrum uiſus extra ſuperficies, in qui-
              <lb/>
            bus eſt cõuexitas formarum harum linearum.</s>
            <s xml:id="echoid-s14984" xml:space="preserve"> Et erunt diametri imaginum harum linearum mul-
              <lb/>
            tò minores ipſis lineis.</s>
            <s xml:id="echoid-s14985" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div507" type="section" level="0" n="0">
          <head xml:id="echoid-head449" xml:space="preserve" style="it">34. Si recta linea nec uertici ſpeculi conici conuexi obliquè incidat, nec latitudini ei{us} ſit paral
            <lb/>
          lela: imaginem uariæ obliquitatis prouario ſit u uiſui offeret. 57 p 7.</head>
          <p>
            <s xml:id="echoid-s14986" xml:space="preserve">DE lineis uerò obliquis exiſtentibus inter hos duos modos, quę appropinquant in ſuo motu
              <lb/>
            lineis extenſis in longitudine pyramidis, habent formas parũ conuexas:</s>
            <s xml:id="echoid-s14987" xml:space="preserve"> quę uerò appropin
              <lb/>
            quant lineis æquidiſtantibus latitudini pyramidis, habent formas manifeſtè conuexas.</s>
            <s xml:id="echoid-s14988" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div508" type="section" level="0" n="0">
          <head xml:id="echoid-head450" xml:space="preserve" style="it">35. In ſpeculo conico conuexo imago conica uidetur. 58 p 7. 40 p 6.</head>
          <p>
            <s xml:id="echoid-s14989" xml:space="preserve">SEd tamen lineæ tortuoſæ, quæ appropinquant uertici pyramidis, habent formas minores, &
              <lb/>
            ſtrictiores & conuexiores.</s>
            <s xml:id="echoid-s14990" xml:space="preserve"> Quæ uerò appropinquant baſi pyramidis, habent formas amplio-
              <lb/>
            res, propter illud, quod declaratum fuit in ſpeculus ſphæricis conuexis:</s>
            <s xml:id="echoid-s14991" xml:space="preserve"> ſcilicet quòd quantò
              <lb/>
            minus fuerit ſpeculum, tantò minores erunt circuli, qui cadunt in ſuperficiem eius:</s>
            <s xml:id="echoid-s14992" xml:space="preserve"> & ſic ima-
              <lb/>
            gines erunt propinquiores centro:</s>
            <s xml:id="echoid-s14993" xml:space="preserve"> idcirco erunt minores.</s>
            <s xml:id="echoid-s14994" xml:space="preserve"> Et ſimiliter ſectiones, quæ cadunt
              <lb/>
            in ſpeculũ pyramidale, quæ ſunt ex parte uerticis pyramidis, ſunt ſtrictiores & minores:</s>
            <s xml:id="echoid-s14995" xml:space="preserve"> & ſic ima-
              <lb/>
            go erit propinquior puncto, in quo cõcurrunt perpendiculares, exeuntes à linea uiſibili perpendi-
              <lb/>
            culariter ſuper lineas contingentes ſectiones, quæ ſunt differentiæ communes:</s>
            <s xml:id="echoid-s14996" xml:space="preserve"> & ideo iſtę ima-
              <lb/>
            gines erunt minores.</s>
            <s xml:id="echoid-s14997" xml:space="preserve"> Sectiones uerò, quæ ſunt ex parte baſis pyramidis, è contrario.</s>
            <s xml:id="echoid-s14998" xml:space="preserve"> Vnde ac-
              <lb/>
            cidit, ut forma comprehenſa in ſpeculo pyramidali conuexo ſit pyramidata:</s>
            <s xml:id="echoid-s14999" xml:space="preserve"> quod ſcilicet fuerit ex
              <lb/>
            parte uerticis ſpeculi, erit ſtrictius, & quod ex parte baſis, erit amplius:</s>
            <s xml:id="echoid-s15000" xml:space="preserve"> & conuexitas latitudinis
              <lb/>
            formæ erit manifeſta.</s>
            <s xml:id="echoid-s15001" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div509" type="section" level="0" n="0">
          <head xml:id="echoid-head451" xml:space="preserve" style="it">36. Imago uiſibilis propinqui ſpeculo conico conuexo, maior: longinqui, minor uidetur. 59 p 7.</head>
          <p>
            <s xml:id="echoid-s15002" xml:space="preserve">ET accidit etiam in his ſpeculis, quòd quantò magis res uiſa appropinquauerit ſpeculo, tantò
              <lb/>
            uidebitur maior:</s>
            <s xml:id="echoid-s15003" xml:space="preserve"> & quantò magis erit remota, tantò uidebitur minor.</s>
            <s xml:id="echoid-s15004" xml:space="preserve"> Fallaciæ ergo, quæ ac-
              <lb/>
            cidunt in his ſpeculis, ſunt ſimiles in omnibus diſpoſitionibus, illis, quæ accidunt in ſpecu-
              <lb/>
            lis columnaribus conuexis, præterquam in pyramidatione formæ.</s>
            <s xml:id="echoid-s15005" xml:space="preserve"/>
          </p>
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