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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          <p>
            <s xml:id="echoid-s7061" xml:space="preserve">
              <pb o="120" file="0126" n="126" rhead="ALHAZEN"/>
            Et quoniam linea communis circulo & ſuperficiei, in qua ſunt centrum uiſus, & axis pyramidis:</s>
            <s xml:id="echoid-s7062" xml:space="preserve"> eſt
              <lb/>
            æquidiſtans lineæ, à centro illius uiſus ad terminum axis productæ [per 28 p 1:</s>
            <s xml:id="echoid-s7063" xml:space="preserve"> quia axis ad perpen
              <lb/>
            diculum eſt utriq;</s>
            <s xml:id="echoid-s7064" xml:space="preserve">] & huic lineæ communi ſunt æquidiſtantes lineæ, circulum in prædictis pun-
              <lb/>
            ctis contingentes [per 28 p 1:</s>
            <s xml:id="echoid-s7065" xml:space="preserve"> quia per 18 p 3 diameter ipſis ad perpendiculum eſt] erunt illæ lineæ
              <lb/>
            æquidiſtantes lineæ à centro uiſus ad terminum axis ductæ [per 9 p 11.</s>
            <s xml:id="echoid-s7066" xml:space="preserve">] Quare erunt in eadem ſu-
              <lb/>
            perficie cum illa [per 35 d 1.</s>
            <s xml:id="echoid-s7067" xml:space="preserve">] Igitur utraq;</s>
            <s xml:id="echoid-s7068" xml:space="preserve"> ſuperficierum circulum contingentium, tranſit per cen-
              <lb/>
            tra uiſus:</s>
            <s xml:id="echoid-s7069" xml:space="preserve"> & communis illarum ſuperficierum ſectio, eſt linea à cẽtro uiſus ad terminum axis ducta:</s>
            <s xml:id="echoid-s7070" xml:space="preserve">
              <lb/>
            & quod inter illas ſuperficies cadit ex pyramide, apparet uiſui:</s>
            <s xml:id="echoid-s7071" xml:space="preserve"> & eſt medietas pyramidis:</s>
            <s xml:id="echoid-s7072" xml:space="preserve"> quoniam
              <lb/>
            lineas has contingentes circulum interiacet medietas circuli.</s>
            <s xml:id="echoid-s7073" xml:space="preserve"> Et ita palàm, quòd in hoc ſitu appa-
              <lb/>
            ret medietas pyramidalis ſpeculi.</s>
            <s xml:id="echoid-s7074" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div256" type="section" level="0" n="0">
          <head xml:id="echoid-head284" xml:space="preserve" style="it">37. Si recta linea à centro uiſ{us}, cum uertice ſpeculi conici conuexi recti angulum obtuſum
            <lb/>
          faciens, continuata concurr at extra ſpeculum, cum diametro circuli ad baſim par alleli conti-
            <lb/>
          nuata: duo plana educta per rect{as} à concurſu ſpeculum in dicto circulo tangentes, & later a
            <lb/>
          conica per tact{us} puncta tranſeuntia, tangent ſpeculum: & ſuperficiem conſpicuam dimidiata
            <lb/>
          maiorem, à qua ad uiſum reflexio fiat: terminabunt. 90 p 4.</head>
          <p>
            <s xml:id="echoid-s7075" xml:space="preserve">VErùm ſi linea à centro uiſus ducta ad terminum axis pyramidis, teneat cũ axe angulum ob-
              <lb/>
            tuſum ex parte ſuperiori apparente:</s>
            <s xml:id="echoid-s7076" xml:space="preserve"> & fiat circulus ſecans pyramidem æquidiſtanter baſi-
              <lb/>
            linea communis huic circulo & ſuperficiei, in qua eſt centrum uiſus & axis, eſt perpendicu-
              <lb/>
            laris ſuper axem pyramidis [per demonſtrata numero præcedente]
              <lb/>
              <figure xlink:label="fig-0126-01" xlink:href="fig-0126-01a" number="30">
                <variables xml:id="echoid-variables20" xml:space="preserve">a b e c f h g r i d m</variables>
              </figure>
            Et hæc linea communis extra producta, concurret cum linea à cen-
              <lb/>
            tro uiſus ad terminum axis ducta [per 11 ax] propter angulum acu-
              <lb/>
            tum, quem facit hæc linea cum axe ex inferiori parte [per theſin &
              <lb/>
            13 p 1:</s>
            <s xml:id="echoid-s7077" xml:space="preserve"> & propter angulum b c g rectum.</s>
            <s xml:id="echoid-s7078" xml:space="preserve">] A puncto igitur concurſus
              <lb/>
            linearum protrahantur duæ lineæ, contingêtes circulum in duobus
              <lb/>
            punctis oppoſitis:</s>
            <s xml:id="echoid-s7079" xml:space="preserve"> & producantur lineæ ab his punctis ad acumen
              <lb/>
            pyramidis:</s>
            <s xml:id="echoid-s7080" xml:space="preserve"> ſuperficies, in quibus ſunt lineæ contingentes cum his
              <lb/>
            longitudinis lineis, contingunt pyramidem:</s>
            <s xml:id="echoid-s7081" xml:space="preserve"> & in utraq;</s>
            <s xml:id="echoid-s7082" xml:space="preserve"> harum ſu-
              <lb/>
            perficierum ſunt duo puncta lineæ à centro uiſus ad terminum axis
              <lb/>
            ductæ, ſcilicet terminus axis & terminus perpendicularis, in quo ſci
              <lb/>
            licet concurrunt linea illa & perpendicularis.</s>
            <s xml:id="echoid-s7083" xml:space="preserve"> Quare linea illa, quæ
              <lb/>
            ducitur à cẽtro uiſus per terminum axis, eſt in utraq;</s>
            <s xml:id="echoid-s7084" xml:space="preserve"> ſuperficie [per
              <lb/>
            1 p 11.</s>
            <s xml:id="echoid-s7085" xml:space="preserve">] Igitur utraq;</s>
            <s xml:id="echoid-s7086" xml:space="preserve"> ſuperficies tranſit per cẽtrum uiſus.</s>
            <s xml:id="echoid-s7087" xml:space="preserve"> Et includunt
              <lb/>
            hæ ſuperficies ex inferiori parte minorẽ partem pyramidis medie-
              <lb/>
            tate:</s>
            <s xml:id="echoid-s7088" xml:space="preserve"> quia lineæ contingentes circulum, includunt partem eius mi-
              <lb/>
            norem medietate.</s>
            <s xml:id="echoid-s7089" xml:space="preserve"> Vnde ex parte ſuperiori interiacet ſuperficies py-
              <lb/>
            ramidem contingentes pars medietate maior:</s>
            <s xml:id="echoid-s7090" xml:space="preserve"> & illa eſt, quæ appa-
              <lb/>
            ret uiſui.</s>
            <s xml:id="echoid-s7091" xml:space="preserve"> Quare in hoc ſitu comprehendit uiſus partem pyramidis
              <lb/>
            medietate maiorem.</s>
            <s xml:id="echoid-s7092" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div258" type="section" level="0" n="0">
          <head xml:id="echoid-head285" xml:space="preserve" style="it">38. Sirecta linea à uiſu per uerticem ſpeculi conici conuexi recti, continuetur cum conico
            <lb/>
          latere: tota ſuperficies, præter dictum lat{us}, uidebitur. 91 p 4.</head>
          <p>
            <s xml:id="echoid-s7093" xml:space="preserve">SI autem linea à centro uiſus ad terminum axis producta, cadit ſuper latus pyramidis, ut ex ea
              <lb/>
            & latere unum efficiatur continuum latus:</s>
            <s xml:id="echoid-s7094" xml:space="preserve"> Dico quòd non la-
              <lb/>
              <figure xlink:label="fig-0126-02" xlink:href="fig-0126-02a" number="31">
                <variables xml:id="echoid-variables21" xml:space="preserve">a b h c</variables>
              </figure>
            tebit uiſum ex hac pyramide, præter lineam quandam intelle-
              <lb/>
            ctualem.</s>
            <s xml:id="echoid-s7095" xml:space="preserve"> Quoniam omnis ſuperficies, in qua eſt linea à centro uiſus
              <lb/>
            ad terminum axis ducta, & ſecundum lateris longitudinem prolon-
              <lb/>
            gata, ſecat pyramidem, una tantùm excepta, quæ contingit pyrami-
              <lb/>
            dem in latere, quod eſt pars lineæ:</s>
            <s xml:id="echoid-s7096" xml:space="preserve"> & hoc ſolùm latus intellectuale,
              <lb/>
            in tota pyramidis ſuperficie ſub hoc ſitu uiſum præterit.</s>
            <s xml:id="echoid-s7097" xml:space="preserve"> Et huius rei
              <lb/>
            ueritas patet ex hoc.</s>
            <s xml:id="echoid-s7098" xml:space="preserve"> Quòd quocunq;</s>
            <s xml:id="echoid-s7099" xml:space="preserve"> pyramidis puncto ſumpto ex-
              <lb/>
            tra latus intellectuale, ſi ad ipſum ducatur linea à centro uiſus, & ab
              <lb/>
            eo linea longitudinis pyramidis ad terminum axis, efficient hæ duæ
              <lb/>
            lineę triangulum cum linea lateri applicata:</s>
            <s xml:id="echoid-s7100" xml:space="preserve"> & erit triangulum in ſu-
              <lb/>
            perficie â centro uiſus intellecta, pyramidem ſecante.</s>
            <s xml:id="echoid-s7101" xml:space="preserve"> [Nam ſi conus
              <lb/>
            ſecetur plano per axem:</s>
            <s xml:id="echoid-s7102" xml:space="preserve"> cõmunis ſectio eſt triangulum per 3 th 1 co-
              <lb/>
            nico.</s>
            <s xml:id="echoid-s7103" xml:space="preserve"> Apollonij] Et ex his lineis huius ſuperficiei nõ niſi duæ cadunt
              <lb/>
            in ſuperficiem pyramidis, ſcilicet linea longitudinis, à punct
              <gap/>
            ſum-
              <lb/>
            pto ad acumen pyramidis, & linea oppoſita huic ex altera parte.</s>
            <s xml:id="echoid-s7104" xml:space="preserve"> Et
              <lb/>
            linea à centro uiſus ad punctum ſumptum ducta, ſecat lineam longi-
              <lb/>
            tudinis in puncto ſumpto, & lineam lateris continuati cum uiſu in
              <lb/>
            centro uiſus.</s>
            <s xml:id="echoid-s7105" xml:space="preserve"> Quare huic lineæ à centro uiſus non accidet concurſus
              <lb/>
            cum aliqua line arum, niſi in ipſo centro uiſus.</s>
            <s xml:id="echoid-s7106" xml:space="preserve"> Cum igitur non poſsit
              <lb/>
            </s>
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