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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          <pb o="186" file="0192" n="192" rhead="ALHAZEN"/>
          <p>
            <s xml:id="echoid-s12560" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s12561" xml:space="preserve"> ſi in perpendiculari ducta à centro uiſus ad ſuperficiem contingentem pyramide
              <gap/>
              <gap/>
            ,
              <lb/>
            ſumatur punctum corporeum inter uiſum & ſpeculum:</s>
            <s xml:id="echoid-s12562" xml:space="preserve"> non refle-
              <lb/>
              <figure xlink:label="fig-0192-01" xlink:href="fig-0192-01a" number="149">
                <variables xml:id="echoid-variables139" xml:space="preserve">a b h</variables>
              </figure>
            ctetur forma eius ad uiſum per perpẽdicularem:</s>
            <s xml:id="echoid-s12563" xml:space="preserve"> quoniam punctũ
              <lb/>
            illud occultabit terminũ perpendicularis illius, & ob hoc non reflectetur
              <lb/>
            ab eo.</s>
            <s xml:id="echoid-s12564" xml:space="preserve"> Si autem nullum fuerit punctum in perpendiculari illa:</s>
            <s xml:id="echoid-s12565" xml:space="preserve"> reflectetur
              <lb/>
            quidem ad uiſum per hanc perpendicularem punctum uiſus, quod ſecat
              <lb/>
            perpendicularis ex eo:</s>
            <s xml:id="echoid-s12566" xml:space="preserve"> & illud ſolum.</s>
            <s xml:id="echoid-s12567" xml:space="preserve"> Verùm uiſu exiſtẽte in hac perpen-
              <lb/>
            diculari & in axe:</s>
            <s xml:id="echoid-s12568" xml:space="preserve"> efficietur circulus, ad cuius quodlibet punctum linea
              <lb/>
            ducta à uiſu, erit perpendicularis ſuper ſuperficiem contingentem.</s>
            <s xml:id="echoid-s12569" xml:space="preserve"> Vnde
              <lb/>
            â quolibet puncto illius circuli fieri poterit reflexio ad uiſum, ſecundum
              <lb/>
            perpendiculares.</s>
            <s xml:id="echoid-s12570" xml:space="preserve"> Et fiet reflexio partis uiſus, quam ſecant perpendicula-
              <lb/>
            res duæ, maiorem angulum in eo continentes.</s>
            <s xml:id="echoid-s12571" xml:space="preserve"> Si uerò inter uiſum & ſpe-
              <lb/>
            culum fuerit axis:</s>
            <s xml:id="echoid-s12572" xml:space="preserve"> non fiet ad ipſum reflexio per perpendicularem, niſi
              <lb/>
            puncti eius, quod ſecant perpendiculares.</s>
            <s xml:id="echoid-s12573" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div446" type="section" level="0" n="0">
          <head xml:id="echoid-head402" xml:space="preserve" style="it">99. Siuiſus & uiſibile fuerint in axe ſpeculi conici caui: poſſunt à
            <lb/>
          tota alicuius circuli peripheria inter ſe reflecti: & ιmago uidetur in
            <lb/>
          peripheria circuli, extra ſpeculi ſuperficiem deſcripti. 18 p 9.</head>
          <p>
            <s xml:id="echoid-s12574" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s12575" xml:space="preserve"> exiſtente uiſu & puncto uiſo in axe:</s>
            <s xml:id="echoid-s12576" xml:space="preserve"> poterit reflecti unum
              <lb/>
            ad aliud.</s>
            <s xml:id="echoid-s12577" xml:space="preserve"> Verbi gratia:</s>
            <s xml:id="echoid-s12578" xml:space="preserve"> ſit h centrum uiſus:</s>
            <s xml:id="echoid-s12579" xml:space="preserve"> t punctum uiſum.</s>
            <s xml:id="echoid-s12580" xml:space="preserve"> Fiat
              <lb/>
            ſuperficies ſecans pyramidem, trãſiens ſuper axis longitudinem:</s>
            <s xml:id="echoid-s12581" xml:space="preserve">
              <lb/>
            quę ſit a b g h:</s>
            <s xml:id="echoid-s12582" xml:space="preserve"> a h axis:</s>
            <s xml:id="echoid-s12583" xml:space="preserve"> a b, a g latera pyramidis:</s>
            <s xml:id="echoid-s12584" xml:space="preserve"> à puncto t du-
              <lb/>
              <figure xlink:label="fig-0192-02" xlink:href="fig-0192-02a" number="150">
                <variables xml:id="echoid-variables140" xml:space="preserve">a l c q g d b h</variables>
              </figure>
            catur perpendicularis ſuper lineam a b [per 12 p 1] quæ ſit t q:</s>
            <s xml:id="echoid-s12585" xml:space="preserve">
              <lb/>
            & producatur quouſq;</s>
            <s xml:id="echoid-s12586" xml:space="preserve"> q l ſit æqualis q t:</s>
            <s xml:id="echoid-s12587" xml:space="preserve"> & à puncto h duca-
              <lb/>
            tur linea ad punctum l:</s>
            <s xml:id="echoid-s12588" xml:space="preserve"> quæ ſecabit lineam longitudinis, quæ
              <lb/>
            eſt a b:</s>
            <s xml:id="echoid-s12589" xml:space="preserve"> ſecet in puncto b:</s>
            <s xml:id="echoid-s12590" xml:space="preserve"> & à puncto b ducatur æquidiſtans
              <lb/>
            lineæ t q [per 31 p 1] quæ neceſſariò perueniet ad axem:</s>
            <s xml:id="echoid-s12591" xml:space="preserve"> [ut
              <lb/>
            oſtenſum eſt 54 n] perueniat in pũcto d:</s>
            <s xml:id="echoid-s12592" xml:space="preserve"> & ducatur linea t b.</s>
            <s xml:id="echoid-s12593" xml:space="preserve">
              <lb/>
            Palàm, cum t q ſit perpendicularis ſuper a b, & t q æqualis q l:</s>
            <s xml:id="echoid-s12594" xml:space="preserve">
              <lb/>
            erit [per 4 p 1] b t q triangulum æquale triangulo b q l:</s>
            <s xml:id="echoid-s12595" xml:space="preserve"> & erit
              <lb/>
            angulus q l b æqualis angulo q t b:</s>
            <s xml:id="echoid-s12596" xml:space="preserve"> ſed [per 29 p 1] angulus q t
              <lb/>
            b æqualis eſt angulo t b d:</s>
            <s xml:id="echoid-s12597" xml:space="preserve"> & angulus d b h æqualis eſt angu-
              <lb/>
            lo q l b:</s>
            <s xml:id="echoid-s12598" xml:space="preserve"> igitur angulus t b d æqualis eſt angulo d b h.</s>
            <s xml:id="echoid-s12599" xml:space="preserve"> Et ita
              <lb/>
            [per 12 n 4] t reflectitur ad h à puncto b:</s>
            <s xml:id="echoid-s12600" xml:space="preserve"> & locus imaginis eſt
              <lb/>
            l [per 7 n.</s>
            <s xml:id="echoid-s12601" xml:space="preserve">] Igitur moto triangulo t l h:</s>
            <s xml:id="echoid-s12602" xml:space="preserve"> deſcribet punctum b
              <lb/>
            circulum in pyramide:</s>
            <s xml:id="echoid-s12603" xml:space="preserve"> & à quolibet puncto illius circuli re-
              <lb/>
            flectetur t ad h:</s>
            <s xml:id="echoid-s12604" xml:space="preserve"> l uerò extra lpeculum deſcribet circulum, qui
              <lb/>
            totus erit locus imaginis puncti t.</s>
            <s xml:id="echoid-s12605" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div448" type="section" level="0" n="0">
          <figure number="151">
            <variables xml:id="echoid-variables141" xml:space="preserve">a g e u
              <gap/>
            m q d o n z h p l</variables>
          </figure>
          <head xml:id="echoid-head403" xml:space="preserve" style="it">100. Si cõmunis ſectio ſuperficierum, reflexionis & ſpe-
            <lb/>
          culi conici caui fuerit ellipſis: uiſus & uiſibile extra axẽ in ba- ſi, aut plano ipſi parallelo, reflectentur inter ſe: aliâs ab uno: aliâs à duobus: aliâs à tribus: aliâs à quatuor ſpeculipunctis: tot́ erunt imagines, quot reflexionum puncta. 19 p 9.</head>
          <p>
            <s xml:id="echoid-s12606" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s12607" xml:space="preserve"> ſumptis duobus punctis & extra perpendicula-
              <lb/>
            rem uiſus, & extra axem in hoc ſpeculo:</s>
            <s xml:id="echoid-s12608" xml:space="preserve"> ſcilicetz, e.</s>
            <s xml:id="echoid-s12609" xml:space="preserve"> Fiat
              <lb/>
            ſuperficies æquidiſtans baſi ſuperz:</s>
            <s xml:id="echoid-s12610" xml:space="preserve"> [ut oſtẽſum eſt 52 n]
              <lb/>
            faciet circulum in ſpeculo [per 4 th.</s>
            <s xml:id="echoid-s12611" xml:space="preserve"> 1 coni.</s>
            <s xml:id="echoid-s12612" xml:space="preserve"> Apoll.</s>
            <s xml:id="echoid-s12613" xml:space="preserve">] e aut erit in
              <lb/>
            hoc circulo, aut in alia ſuperficie ipſi æquidiſtante.</s>
            <s xml:id="echoid-s12614" xml:space="preserve"> Sit in ſuperfi-
              <lb/>
            cieillius circuli:</s>
            <s xml:id="echoid-s12615" xml:space="preserve"> & ducatur linea e z.</s>
            <s xml:id="echoid-s12616" xml:space="preserve"> Palàm [per demonſtrata in
              <lb/>
            ſpeculis ſphæricis cauis 86 n] quòd z reflectetur ad e à circulo
              <lb/>
            illo ex una parte, aut ab uno pũcto:</s>
            <s xml:id="echoid-s12617" xml:space="preserve"> aut à duobus:</s>
            <s xml:id="echoid-s12618" xml:space="preserve"> aut à tribus:</s>
            <s xml:id="echoid-s12619" xml:space="preserve"> ex
              <lb/>
            alia uerò ab uno.</s>
            <s xml:id="echoid-s12620" xml:space="preserve"> Sumatur igitur punctum circuli, à quo reflecti-
              <lb/>
            tur ad ipſum:</s>
            <s xml:id="echoid-s12621" xml:space="preserve"> & ſit h:</s>
            <s xml:id="echoid-s12622" xml:space="preserve"> centrum circuli t:</s>
            <s xml:id="echoid-s12623" xml:space="preserve"> & ducantur lineæ z h, e h:</s>
            <s xml:id="echoid-s12624" xml:space="preserve">
              <lb/>
            & diameter t h diuidet quidem angulum illum per æqualia:</s>
            <s xml:id="echoid-s12625" xml:space="preserve"> [per
              <lb/>
            13 n 4] & ſecabit lineam e z:</s>
            <s xml:id="echoid-s12626" xml:space="preserve"> [quia ſecat angulum ipſi e z ſubten-
              <lb/>
            ſum] ſecet in puncto q:</s>
            <s xml:id="echoid-s12627" xml:space="preserve"> & ſit a uertex pyramidis:</s>
            <s xml:id="echoid-s12628" xml:space="preserve"> a h linea longi-
              <lb/>
            tudinis.</s>
            <s xml:id="echoid-s12629" xml:space="preserve"> À
              <unsure/>
            puncto q ducatur linea perpẽdicularis ſuper lineam
              <lb/>
            a h:</s>
            <s xml:id="echoid-s12630" xml:space="preserve"> [per 12 p 1] quæ ſit q m:</s>
            <s xml:id="echoid-s12631" xml:space="preserve"> quæ quidem perueniet ad axem:</s>
            <s xml:id="echoid-s12632" xml:space="preserve"> [ut
              <lb/>
            oſtẽſum eſt 54 n] qui eſt a d:</s>
            <s xml:id="echoid-s12633" xml:space="preserve"> & cadat in ipſum in puncto d:</s>
            <s xml:id="echoid-s12634" xml:space="preserve"> & du-
              <lb/>
            cantur lineæ z m, e m:</s>
            <s xml:id="echoid-s12635" xml:space="preserve"> à puncto z ducatur in ſuperficie circuli li-
              <lb/>
            nea æquidiſtans lineæ q h:</s>
            <s xml:id="echoid-s12636" xml:space="preserve"> [per 31 p 1] quæ ſit z l:</s>
            <s xml:id="echoid-s12637" xml:space="preserve"> concurret qui-
              <lb/>
            dem [per lemma Procli ad 29 p 1] e h cũilla:</s>
            <s xml:id="echoid-s12638" xml:space="preserve"> ſit cõcurſus in pun
              <lb/>
            ctol:</s>
            <s xml:id="echoid-s12639" xml:space="preserve"> & à puncto h ducatur perpendicularis ſuper l z:</s>
            <s xml:id="echoid-s12640" xml:space="preserve"> quæ ſit h p.</s>
            <s xml:id="echoid-s12641" xml:space="preserve">
              <lb/>
            Deinde in ſuperficie e m z ducatur linea æquidiſtans lineæ q m:</s>
            <s xml:id="echoid-s12642" xml:space="preserve">
              <lb/>
            quæ ſit z o:</s>
            <s xml:id="echoid-s12643" xml:space="preserve"> & cõcurrat e m cum ea in puncto o:</s>
            <s xml:id="echoid-s12644" xml:space="preserve"> [cõcurret aũt per lemma Procli ad 29 p 1] & ducatu
              <gap/>
              <lb/>
            </s>
          </p>
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