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

Table of figures

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[11] b e g a h d k f z
[12] d a a b c
[13] a e g b f z q x c u d
[14] e r g b z f k m a n l c u d
[15] n m a b k c e d f g p h q ſ r o
[16] a r t
[17] d z c s f r t q k l h b n m a
[18] d z c s f r t q k l h b n m a
[19] n m l b h i k e p t r o s u q a f d g c
[Figure 20]
[21] p k c z q x y b
[Figure 22]
[Figure 23]
[24] e d f a c b
[25] a s b c
[26] a k f s d m b g c h
[27] a e g c b d h f
[28] a b f g c d n
[29] b a f l g e k h n d c
[30] a b e c f h g r i d m
[31] a b h c
[32] a d b k ſ c
[33] b ſ a u f d c h n g r k s x q p
[34] f d d e r b g c h i p ſ q s n k
[35] f a r d e b g c h p ſ s n k
[36] ſ g d f h b a
[37] a d f t e b
[38] d b c e f g b d
[39] a f b c d e
[40] a f b c d e g
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        <div xml:id="echoid-div269" type="section" level="0" n="0">
          <pb o="124" file="0130" n="130" rhead="ALHAZEN"/>
        </div>
        <div xml:id="echoid-div271" type="section" level="0" n="0">
          <head xml:id="echoid-head293" xml:space="preserve" style="it">46. In ſpeculo cylindraceo cauo ſuperficies reflexionis quatuor habet puncta: uiſ{us}, uiſibilis,
            <lb/>
          reflexionis, & axis, in quod perpendicularis à reflexionis puncto ducta, cadit. 3 p 9.83 p 4.</head>
          <p>
            <s xml:id="echoid-s7284" xml:space="preserve">IN ſpeculis columnaribus concauis poteſt comprehendi totum ſpeculum:</s>
            <s xml:id="echoid-s7285" xml:space="preserve"> ſi fuerit uiſus intra
              <lb/>
            ipſum:</s>
            <s xml:id="echoid-s7286" xml:space="preserve"> ſed eo extrà ſito, uidebitur maior medietate ſpeculi portio, quæ ſcilicet interiacet duas
              <lb/>
            ſuperficies à centro uiſus procedentes, columnam contingentes.</s>
            <s xml:id="echoid-s7287" xml:space="preserve"> Intelligemus autem ſuperfi-
              <lb/>
            ciem à centro uiſus procedẽtem, baſibus columnæ æquidiſtantem:</s>
            <s xml:id="echoid-s7288" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0130-01" xlink:href="fig-0130-01a" number="37">
                <variables xml:id="echoid-variables27" xml:space="preserve">a d f
                  <gap/>
                t e b</variables>
              </figure>
            hæc ſuperficies aut cadet in columnã, aut nõ:</s>
            <s xml:id="echoid-s7289" xml:space="preserve"> ſi ceciderit, linea com-
              <lb/>
            munis huic ſuperficiei & columnæ erit circulus [per 5th.</s>
            <s xml:id="echoid-s7290" xml:space="preserve"> Sereni de
              <lb/>
            ſectione cylindri:</s>
            <s xml:id="echoid-s7291" xml:space="preserve">] & linea uiſualis, tranſiens per centrum huius cir-
              <lb/>
            culi, cadet orthogonaliter ſuper ſuperficiem, contingentem colu-
              <lb/>
            mnam in puncto, in quod cadit linea [ut dem õſtratũ eſt 32 n] & fiet
              <lb/>
            reflexio per eandem lineam ad eius originem [per 11 n.</s>
            <s xml:id="echoid-s7292" xml:space="preserve"> Itaq;</s>
            <s xml:id="echoid-s7293" xml:space="preserve"> cum li-
              <lb/>
            nea recta (quæ per 1 p 11 in uno eſt plano) tranſeat per puncta uiſus,
              <lb/>
            uiſibilis, reflexionis, & axis, in quod perpendicularis à reflexionis
              <lb/>
            puncto ducta, cadit:</s>
            <s xml:id="echoid-s7294" xml:space="preserve"> erũt ipĩa in uno reflexionis plano.</s>
            <s xml:id="echoid-s7295" xml:space="preserve">] Quodcunq;</s>
            <s xml:id="echoid-s7296" xml:space="preserve">
              <lb/>
            aliud ſumatur punctum, linea perpendiculariter ab hoc puncto du-
              <lb/>
            cta, cadet in axem [ut patuit 40 n:</s>
            <s xml:id="echoid-s7297" xml:space="preserve">] & linea uiſualis in punctũ illud
              <lb/>
            cadens, faciet angulum acutum cum linea perpendiculari [ut oſten-
              <lb/>
            ſum eſt ſuperiore numero] cũ ſit inter perpendicularẽ & contingen
              <lb/>
            tem.</s>
            <s xml:id="echoid-s7298" xml:space="preserve"> Et quòd hęc linea cadat intra ſpeculũ, planum eſt ex hoc:</s>
            <s xml:id="echoid-s7299" xml:space="preserve"> quòd
              <lb/>
            cadit inter ſuperficies portionem contingentes.</s>
            <s xml:id="echoid-s7300" xml:space="preserve"> Poterimus igitur in
              <lb/>
            eadem reflexionis ſuperficie ex angulo, quem facit perpendicularis
              <lb/>
            cum contingente, excipere angulum acutum, æqualem angulo acu
              <lb/>
            to prædicto:</s>
            <s xml:id="echoid-s7301" xml:space="preserve"> & cadet linea reflexionis, hunc angulum continens, in-
              <lb/>
            tra columnam:</s>
            <s xml:id="echoid-s7302" xml:space="preserve"> quoniam cadet inter perpendicularem & lineam lõ-
              <lb/>
            gitudinis, per terminum perpendicularis tranſeuntem.</s>
            <s xml:id="echoid-s7303" xml:space="preserve"> Erunt igitur in ſuperficie reflexionis cen-
              <lb/>
            trum uiſus, punctum reflexionis, punctum uiſum, punctum axis, in quod cadit perpendicularis.</s>
            <s xml:id="echoid-s7304" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div273" type="section" level="0" n="0">
          <head xml:id="echoid-head294" xml:space="preserve" style="it">47. Si communis ſectio ſuperficierum, reflexionis & ſpeculi cylindracei caui, fuerit lat{us} cy-
            <lb/>
          lindr aceum, aut circul{us}: reflexio à quocun ſectionis puncto facta, in eadem ſuperficie fiet.</head>
          <p>
            <s xml:id="echoid-s7305" xml:space="preserve">ET ſi hoc modo ſtatuatur uiſus, ut communis linea ſuperficiei reflexionis & ſuperficiei colu-
              <lb/>
            mnæ ſit linea longitudinis;</s>
            <s xml:id="echoid-s7306" xml:space="preserve"> à quo cunq;</s>
            <s xml:id="echoid-s7307" xml:space="preserve"> puncto cõmunis lineæ fiat reflexio:</s>
            <s xml:id="echoid-s7308" xml:space="preserve"> in una determi-
              <lb/>
            nata erit ſuperficie, omnibus his reflexionibus communi, ea ſcilicet, in qua centrum uiſus, &
              <lb/>
            axis columnæ totus, ſicut dictum eſt ſuperius in columnari ſpeculo non concauo [32 n.</s>
            <s xml:id="echoid-s7309" xml:space="preserve">] Similiter
              <lb/>
            ſi linea communis fuerit circulus, omnes reflexiones à punctis illius circuli factæ, procedent in ea-
              <lb/>
            dem ſuperficie, ſicut in alijs circulis patuit.</s>
            <s xml:id="echoid-s7310" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div274" type="section" level="0" n="0">
          <head xml:id="echoid-head295" xml:space="preserve" style="it">48. Si communis ſectio ſuperficierum, reflexionis & ſpeculi cylindracei caui fuerit elli-
            <lb/>
          pſis: à plurib{us} ei{us} punctis idem uiſibile ad eundem uiſum, in eadem ſuperficie reflecti po-
            <lb/>
          teſt. 9 p 9.</head>
          <p>
            <s xml:id="echoid-s7311" xml:space="preserve">ET ſi ſectio columnaris, fuerit linea communis:</s>
            <s xml:id="echoid-s7312" xml:space="preserve"> à duobus quidem eius punctis tantùm fiet re-
              <lb/>
            flexio in eadẽ ſuperficie, licet in ſuperioribus columnis [33 n] tantùm ab uno puncto in uni-
              <lb/>
            ca ſuperficie fieret reflexio, unico uiſu adhibito:</s>
            <s xml:id="echoid-s7313" xml:space="preserve"> quoniam illic latebant uiſum puncta ſectio-
              <lb/>
            nis ſe reſpicientia, per quæ ſcilicet tranſit circulus columnæ baſibus æquidiſtans:</s>
            <s xml:id="echoid-s7314" xml:space="preserve"> uiſo enim uno il-
              <lb/>
            lorum punctorum, latebat aliud, propter minoris columnæ portionis apparentiam:</s>
            <s xml:id="echoid-s7315" xml:space="preserve"> ſed in his appa
              <lb/>
            ret maior columnæ portio:</s>
            <s xml:id="echoid-s7316" xml:space="preserve"> unde ab uno uiſu percipiuntur puncta terminantia diametrum circuli,
              <lb/>
            æquidiſtantis baſibus columnæ.</s>
            <s xml:id="echoid-s7317" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div275" type="section" level="0" n="0">
          <head xml:id="echoid-head296" xml:space="preserve" style="it">49. Si uiſ{us} fuerit intra ſpeculum conicum cauum: tota ei{us} ſuperficies uidebitur: ſi extra &
            <lb/>
          recta à uiſu continuetur cum axe, uel conico latere: tot a occultabitur. 5. 2. 9. 3 p 9.</head>
          <p>
            <s xml:id="echoid-s7318" xml:space="preserve">IN ſpeculis pyramidalibus concauis, ſi fuerit uiſus intra ſpeculum:</s>
            <s xml:id="echoid-s7319" xml:space="preserve"> uidebit ipſum totum:</s>
            <s xml:id="echoid-s7320" xml:space="preserve"> ſi uerò
              <lb/>
            extra, & linea à cẽtro uiſus ad acumen pyramidis ducta, intret pyramidem, aut applicetur lineæ
              <lb/>
            longitudinis pyramidis, nihil uidebitur ex ſpeculò.</s>
            <s xml:id="echoid-s7321" xml:space="preserve"> Quohiam quæcunq;</s>
            <s xml:id="echoid-s7322" xml:space="preserve"> alia linea ab oculo ad
              <lb/>
            pyramidem ducta, cadet in pyramidis ſuperficiem exteriorem:</s>
            <s xml:id="echoid-s7323" xml:space="preserve"> unde occultabitur interior ſuperfi-
              <lb/>
            cies.</s>
            <s xml:id="echoid-s7324" xml:space="preserve"> Si autem auferatur portio à pyramide, poterit uideri pars pyramidis, cadens inter contingen-
              <lb/>
            tes ſuperficies à centro ductas, ſcilicet maior.</s>
            <s xml:id="echoid-s7325" xml:space="preserve"> Et ſi linea à centro uiſus, ſit perpendicularis ſuper ſu-
              <lb/>
            perficiem contingentem pyramidem, & continuetur axi:</s>
            <s xml:id="echoid-s7326" xml:space="preserve"> erunt lineæ communes (ſicut dictum eſt
              <lb/>
            in alijs pyramidalibus) aut lineæ longitudinis pyramidum, aut ſectiones.</s>
            <s xml:id="echoid-s7327" xml:space="preserve"> Et in his à duobus pun-
              <lb/>
            ctis ſectionis poterit fieri reflexio, in eadem ſuperficie, reſpectu eiuſdem uiſus.</s>
            <s xml:id="echoid-s7328" xml:space="preserve"> Et in ſuperficie re-
              <lb/>
            flexionis erunt, centrum uiſus, punctum uiſum, punctum reflexionis, punctum axis, in quod cadit
              <lb/>
            perpendicularis.</s>
            <s xml:id="echoid-s7329" xml:space="preserve"/>
          </p>
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