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-div381" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s10653" xml:space="preserve">
              <pb o="163" file="0169" n="169" rhead="OPTICAE LIBER V."/>
            punctos] cõprehẽditur ueritas illius imaginis.</s>
            <s xml:id="echoid-s10654" xml:space="preserve"> Cũ aũt քpẽdicularis à pũcto uiſo ducta, fuerit ęqui
              <lb/>
            diſtãs lineæ reflexiõis:</s>
            <s xml:id="echoid-s10655" xml:space="preserve"> apparebit imago in pũcto reflexiõis.</s>
            <s xml:id="echoid-s10656" xml:space="preserve"> [utin e.</s>
            <s xml:id="echoid-s10657" xml:space="preserve">] Quoniã cũ pũctũ illud ſit ſen
              <lb/>
            ſuale [ut patet è 16 n 4] ſumpto pũcto eius intellectuali medio:</s>
            <s xml:id="echoid-s10658" xml:space="preserve"> imago cuiuſcũq;</s>
            <s xml:id="echoid-s10659" xml:space="preserve"> partis illius puncti
              <lb/>
            ſenſualis, ultra mediũ ſumptæ, erit ultra ſpeculũ:</s>
            <s xml:id="echoid-s10660" xml:space="preserve"> & imago partis citra mediũ erit inter uiſum & ſpe
              <lb/>
            culũ.</s>
            <s xml:id="echoid-s10661" xml:space="preserve"> Et cũ totalis forma ex ulteriorib.</s>
            <s xml:id="echoid-s10662" xml:space="preserve"> & citeriorib.</s>
            <s xml:id="echoid-s10663" xml:space="preserve"> partibus uideatur una & continua:</s>
            <s xml:id="echoid-s10664" xml:space="preserve"> neceſſariò
              <lb/>
            forma illius puncti ſenſualis uidebitur in ipſo ſpeculo, in loco reflexionis.</s>
            <s xml:id="echoid-s10665" xml:space="preserve"> Verũ in imaginib.</s>
            <s xml:id="echoid-s10666" xml:space="preserve"> quarũ
              <lb/>
            locus fuerit in cẽtro uiſus, non cõprehẽditur ueritas earũ:</s>
            <s xml:id="echoid-s10667" xml:space="preserve"> unde ſæpius error accidit in his ſpeculis.</s>
            <s xml:id="echoid-s10668" xml:space="preserve">
              <lb/>
            Vt aũt hoc pateat:</s>
            <s xml:id="echoid-s10669" xml:space="preserve"> erigatur ſuք ſuքficiẽ ſpeculi lignũ perpẽdiculariter, minus medietate ſemidiame
              <lb/>
            tri ſpeculi:</s>
            <s xml:id="echoid-s10670" xml:space="preserve"> & circa caput huius ligni, ſit cẽtrũ uiſus:</s>
            <s xml:id="echoid-s10671" xml:space="preserve"> & dirigatur uiſus ad pũctũ ſpeculi, cuius lõgitu,
              <lb/>
            do à ligno ſit maior, ꝗ̃ lõgitudo cẽtri uiſus à diametro, ք lignũ trãſeunte:</s>
            <s xml:id="echoid-s10672" xml:space="preserve"> uidebitur ꝗ dẽ imago illius
              <lb/>
            ligni ultra uiſum, nec erit certa cõprehẽſio eius:</s>
            <s xml:id="echoid-s10673" xml:space="preserve"> imò apparebit arcuata:</s>
            <s xml:id="echoid-s10674" xml:space="preserve"> cũ nõ ſit.</s>
            <s xml:id="echoid-s10675" xml:space="preserve"> In his ergo ſpecu-
              <lb/>
            lis nõ cõprehẽditur ueritas imaginis, niſi cuius locus fuerit ultra ſpeculũ:</s>
            <s xml:id="echoid-s10676" xml:space="preserve"> aut inter uiſum & ſpecu-
              <lb/>
            lũ.</s>
            <s xml:id="echoid-s10677" xml:space="preserve"> Cũ aũt cẽtrũ uiſus fuerit in քpẽdiculari ք lignũ trãſeũte:</s>
            <s xml:id="echoid-s10678" xml:space="preserve"> nõ plenè cõprehẽdit formã illius ligni.</s>
            <s xml:id="echoid-s10679" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div382" type="section" level="0" n="0">
          <head xml:id="echoid-head365" xml:space="preserve" style="it">62. Vιſus in centro ſpeculi ſphærici caui poſitus:
            <lb/>
          ſeipſum tantùm uidet. 4 p 8. Idem 44 n 4.</head>
          <figure number="98">
            <variables xml:id="echoid-variables88" xml:space="preserve">b c a e d</variables>
          </figure>
          <p>
            <s xml:id="echoid-s10680" xml:space="preserve">SIuerò uiſus fuerit ín diametro ſphęrę, & in cẽ
              <lb/>
            tro eius (cũ quęlibet linea ab eo ad ſpeculum
              <lb/>
            ducta ſit perpẽdicularis ſuper ſpeculũ) [quia
              <lb/>
            perpẽdicularis eſt plano ſpeculum tangẽti ք 4 th 1.</s>
            <s xml:id="echoid-s10681" xml:space="preserve">
              <lb/>
            ſphęr.</s>
            <s xml:id="echoid-s10682" xml:space="preserve"> uel 25 n 4:</s>
            <s xml:id="echoid-s10683" xml:space="preserve"> eaq́;</s>
            <s xml:id="echoid-s10684" xml:space="preserve"> de cauſſa in ſe ipſam reflecti-
              <lb/>
            tur per 11 n 4] nõ cõprehẽdetur forma alicuius pũ
              <lb/>
            cti, niſi puncti portionis oculi, interiacentis latera
              <lb/>
            pyramidis uiſualis, quę à cẽtro ſpeculi intelligitur
              <lb/>
            ꝓtẽdi.</s>
            <s xml:id="echoid-s10685" xml:space="preserve"> Quoniã forma cuiuslibet alterius pũcti ca
              <lb/>
            det in ſpeculũ ſuք lineã declinatã, & neceſſariò re-
              <lb/>
            flectetur ſuք declinatã.</s>
            <s xml:id="echoid-s10686" xml:space="preserve"> Quare linea reflexionis nõ
              <lb/>
            trãſibit per centrũ:</s>
            <s xml:id="echoid-s10687" xml:space="preserve"> & ita nõ cõtinget centrũ uiſus.</s>
            <s xml:id="echoid-s10688" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div383" type="section" level="0" n="0">
          <head xml:id="echoid-head366" xml:space="preserve" style="it">63. Semidiameter ſpeculi ſphærici caui, in qua
            <lb/>
          eſt uiſ{us} extra cẽtrũ: nullum ſui punctũ obliquè
            <lb/>
          ſpeculo incidẽs ad uiſum reflectit: reliqua uerò ſemidiameter prædictæ cõtinua, reflectit. 5 p 8.</head>
          <p>
            <s xml:id="echoid-s10689" xml:space="preserve">SIuerò fuerit uiſus in diametro:</s>
            <s xml:id="echoid-s10690" xml:space="preserve"> non comprehendet formam alterius puncti ſemidiametri, in
              <lb/>
            qua eſt.</s>
            <s xml:id="echoid-s10691" xml:space="preserve"> Quoniã angulus, quem efficient duæ lineæ à puncto ſumpto in ſemidiametro, & à cen-
              <lb/>
            tro uiſus ιn idẽ ſpeculi punctũ, non diuidetur per perpendicularem ab illo puncto ſpeculi du-
              <lb/>
            ctam:</s>
            <s xml:id="echoid-s10692" xml:space="preserve"> cum illa perpendicularis tendat ad centrum ſpeculi:</s>
            <s xml:id="echoid-s10693" xml:space="preserve"> [per 4 th.</s>
            <s xml:id="echoid-s10694" xml:space="preserve"> 1 ſphær.</s>
            <s xml:id="echoid-s10695" xml:space="preserve">] Sed formam alicuius
              <lb/>
            puncti alterius ſemidiametri percipere poterit.</s>
            <s xml:id="echoid-s10696" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div384" type="section" level="0" n="0">
          <head xml:id="echoid-head367" xml:space="preserve" style="it">64. In ſpeculo ſphærico cauo perpendiculari incidentiæ, & linea reflexionis concurrentib{us}:
            <lb/>
          eſt: ut perpendicularis incidentiæ ad rectam inter centrum ſpeculi & locum imaginis: ſic re-
            <lb/>
          cta inter uiſibile & finem contingentiæ, adrectam inter finem contingentiæ & locum ima-
            <lb/>
          ginis. 13 p 8.</head>
          <p>
            <s xml:id="echoid-s10697" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s10698" xml:space="preserve"> uiſo pũcto in huiuſmodi ſpeculo,
              <lb/>
              <figure xlink:label="fig-0169-02" xlink:href="fig-0169-02a" number="99">
                <variables xml:id="echoid-variables89" xml:space="preserve">l b z c g q a b e</variables>
              </figure>
            cũ non fuerit perpendicularis ęquidiſtans
              <lb/>
            lineę reflexionis:</s>
            <s xml:id="echoid-s10699" xml:space="preserve"> linea à centro ſpeculi ad
              <lb/>
            punctũ uifum ducta, ſe habebit ad lineã ab eodem
              <lb/>
            centro ad locũ imaginis ductam, ſicut linea à pun
              <lb/>
            ctò uiſo ad punctum, (quod diximus) contingen-
              <lb/>
            tię [17 n] ſe habet ad lineam à puncto contingen
              <lb/>
            tiæ, ad locum imaginis ductam.</s>
            <s xml:id="echoid-s10700" xml:space="preserve"> Verbigratia:</s>
            <s xml:id="echoid-s10701" xml:space="preserve"> ſit e
              <lb/>
            centrum ſpeculi:</s>
            <s xml:id="echoid-s10702" xml:space="preserve"> b punctum uiſum:</s>
            <s xml:id="echoid-s10703" xml:space="preserve"> a centrum ui-
              <lb/>
            ſus:</s>
            <s xml:id="echoid-s10704" xml:space="preserve"> g punctum reflexionis:</s>
            <s xml:id="echoid-s10705" xml:space="preserve"> linea contingentiæ z
              <lb/>
            g.</s>
            <s xml:id="echoid-s10706" xml:space="preserve"> z g autẽ aut concurret cum e b:</s>
            <s xml:id="echoid-s10707" xml:space="preserve"> aut erit æquidi-
              <lb/>
            ſtãs ei.</s>
            <s xml:id="echoid-s10708" xml:space="preserve"> Cõcurrat in puncto t.</s>
            <s xml:id="echoid-s10709" xml:space="preserve"> Linea uerô e b cõcur
              <lb/>
            rit cũ a g [ex theſi,] ſed non in puncto g:</s>
            <s xml:id="echoid-s10710" xml:space="preserve"> cũ b e, a g
              <lb/>
            ſint duę lineę.</s>
            <s xml:id="echoid-s10711" xml:space="preserve"> Igitur aut cõcurrit ultra g:</s>
            <s xml:id="echoid-s10712" xml:space="preserve"> aut inter
              <lb/>
            g & a:</s>
            <s xml:id="echoid-s10713" xml:space="preserve"> aut in a:</s>
            <s xml:id="echoid-s10714" xml:space="preserve"> aut ultra a.</s>
            <s xml:id="echoid-s10715" xml:space="preserve"> Sit ultra g, & in pũcto h.</s>
            <s xml:id="echoid-s10716" xml:space="preserve">
              <lb/>
            Dico ergo, quòd eſt proportio e b ad e h, ſicut b t
              <lb/>
            ad t h.</s>
            <s xml:id="echoid-s10717" xml:space="preserve"> Produeatur perpẽdicularis e g:</s>
            <s xml:id="echoid-s10718" xml:space="preserve"> & à puncto
              <lb/>
            h ducatur ęquidiſtans lineæ b g:</s>
            <s xml:id="echoid-s10719" xml:space="preserve"> [per 31 p 1] quę cõ
              <lb/>
            curret cũ e g:</s>
            <s xml:id="echoid-s10720" xml:space="preserve"> [per lẽma Procli ad 29 p 1] ſit cõcur-
              <lb/>
            ſus l:</s>
            <s xml:id="echoid-s10721" xml:space="preserve"> & à puncto b ducatur ęquidiſtãs g h:</s>
            <s xml:id="echoid-s10722" xml:space="preserve"> [quę ne
              <lb/>
            ceſſariò cõcurret cũ z t:</s>
            <s xml:id="echoid-s10723" xml:space="preserve"> [per dictũ lẽma] ſit cõcur-
              <lb/>
            ſus q.</s>
            <s xml:id="echoid-s10724" xml:space="preserve"> Palã [per 12 n 4] quòd angulus b g e eſt ęqua
              <lb/>
            lis a g e:</s>
            <s xml:id="echoid-s10725" xml:space="preserve"> ſed angulus b g e eſt æqualis angulo g l h:</s>
            <s xml:id="echoid-s10726" xml:space="preserve">
              <lb/>
            [exterior interiori & oppoſito ք 29 p 1] & [ք 15 p
              <lb/>
            1] angulus a g e ęqualis angulo l g h:</s>
            <s xml:id="echoid-s10727" xml:space="preserve"> ergo angulus g l h ęqualis eſt angulo l g h.</s>
            <s xml:id="echoid-s10728" xml:space="preserve"> Igitur [ք 6 p 1] lh ęqua
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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