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-s7506" xml:space="preserve">
              <pb o="128" file="0134" n="134" rhead="ALHAZEN"/>
            perficiem ſpeculi ſuper punctum ſignatum, & perpendicularis ſuper quamlibet lineam ab illo pun-
              <lb/>
            cto protractam, in ſuperficiem contingentem ſpeculum.</s>
            <s xml:id="echoid-s7507" xml:space="preserve"> Erit ergo perpen dicularis ſuper lineam re-
              <lb/>
            ctam, contingentem lineam communem ſuperficiei altæ annuli & ſuperficiei ſpeculi.</s>
            <s xml:id="echoid-s7508" xml:space="preserve"> Ponatur au-
              <lb/>
            tem uiſus in ſuperficie annuli, in capite eius, & uidebit in ſpeculo, donec comprehendat formam
              <lb/>
            corporis parui, quod eſt in acu:</s>
            <s xml:id="echoid-s7509" xml:space="preserve"> & tunc percipiet corpus illud, & punctum in ſpeculo ſignatum, &
              <lb/>
            imaginem illius corporis.</s>
            <s xml:id="echoid-s7510" xml:space="preserve"> Et linea tranſiens per corpus paruum, & per punctum in ſuperficie ſigna-
              <lb/>
            tum, eſt perpendicularis ſuper ſuperficiem, contingentem ſpeculi ſuperficiem ſuper punctũ ſigna-
              <lb/>
            tum:</s>
            <s xml:id="echoid-s7511" xml:space="preserve"> & hæc ſuperficies annuli, eſt ex ſuperficiebus reflexionis:</s>
            <s xml:id="echoid-s7512" xml:space="preserve"> & corpus paruum, & centrum uiſus
              <lb/>
            ſunt in hac ſuperficie, & punctus reflexionis eſt in hac ſuperficie:</s>
            <s xml:id="echoid-s7513" xml:space="preserve"> & hæc deinceps probabimus.</s>
            <s xml:id="echoid-s7514" xml:space="preserve">
              <lb/>
            Et imago corporis parui in hoc ſitu, erit ſuper lineam rectam, à corpore paruo protràctam ſuper ſu-
              <lb/>
            perficiem, contingentem ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7515" xml:space="preserve"> & eſt hæc linea perpendicularis ſuper lineam rectam,
              <lb/>
            contingentem lineam communem ſuperficiei ſpeculi, & ſuperficiei reflexionis, quæ eſt ſuperficies
              <lb/>
            annuli.</s>
            <s xml:id="echoid-s7516" xml:space="preserve"> Et ſuperficies reflexionis eſt ex ſuperficiebus declinantibus, ſecantibus columnam inter li-
              <lb/>
            neas longitudinis columnæ, & circulos eius æquidiſtantes baſibus:</s>
            <s xml:id="echoid-s7517" xml:space="preserve"> quia regula & ſpeculum, quod
              <lb/>
            eſt in ea, ſunt declinata.</s>
            <s xml:id="echoid-s7518" xml:space="preserve"> Linea ergo communis huic ſuperficiei & ſuperficiei ſpeculi, eſt ex ſectio-
              <lb/>
            nibus columnaribus.</s>
            <s xml:id="echoid-s7519" xml:space="preserve"> Et ita explanabimus locum imaginis, ut mutetur ſitus regulæ, in qua eſt ſpe-
              <lb/>
            culum & declinetur ſuper ſuperficiem eius aliqua declinatione maiore uel minore.</s>
            <s xml:id="echoid-s7520" xml:space="preserve"> Palàm ergo ex
              <lb/>
            his, quòd imago percipitur, ubi perpendicularis à uiſo puncto ad ſpeculi ſuperficiem ducta, concur
              <lb/>
            rit cum linea reflexionis.</s>
            <s xml:id="echoid-s7521" xml:space="preserve"> Et hic eſt ſitus prædictus.</s>
            <s xml:id="echoid-s7522" xml:space="preserve"> Eadem poterit adhiberi operatio in ſpeculo py-
              <lb/>
            ramidali exteriore:</s>
            <s xml:id="echoid-s7523" xml:space="preserve"> & idem patebit ſiue ſintimagines rerum uiſarum in ſectionibus pyramidalibus,
              <lb/>
            ſiue in ijs, quæ fiunt ſecundum lineas longitudinis.</s>
            <s xml:id="echoid-s7524" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div283" type="section" level="0" n="0">
          <head xml:id="echoid-head308" xml:space="preserve" style="it">5. Rectarum linearum ab eodem uiſibilis puncto in ſpecula planum uel conuexum caden-
            <lb/>
          tium: minima eſt perpendicularis. 21 p 1.</head>
          <p>
            <s xml:id="echoid-s7525" xml:space="preserve">SI à puncto uiſo ad ſpeculi ſuperficiem ducantur lineę:</s>
            <s xml:id="echoid-s7526" xml:space="preserve"> quæ perpendicularis eſt, minor eſt quali
              <lb/>
            bet alia.</s>
            <s xml:id="echoid-s7527" xml:space="preserve"> Quoniã quælibet alia prius ſecat communẽ lineã ſuperficiei cõtingentis ſpeculum, in
              <lb/>
            quam orthogonaliter cadit perpendicularis, & ſuperficiei reflexionis, antequã ueniat ad ſpe-
              <lb/>
            culum:</s>
            <s xml:id="echoid-s7528" xml:space="preserve"> & quælibet linea à puncto uiſo in hac ſuperfi-
              <lb/>
              <figure xlink:label="fig-0134-01" xlink:href="fig-0134-01a" number="38">
                <variables xml:id="echoid-variables28" xml:space="preserve">d b c e f g b d
                  <gap/>
                </variables>
              </figure>
            cie, ad hanc lineã cõmunẽ ducta, eſt maior perpendi
              <lb/>
            culari [per 19 p 1] quia maiorẽ reſpicit angulũ [rectũ
              <lb/>
            nẽpe a e f in triangulo a e f.</s>
            <s xml:id="echoid-s7529" xml:space="preserve">] Quare patet propoſitũ.</s>
            <s xml:id="echoid-s7530" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div285" type="section" level="0" n="0">
          <head xml:id="echoid-head309" xml:space="preserve" style="it">6. In ſpeculo ſpbærico cauo, imago uidetur in
            <lb/>
          concurſu perpendicularis incidentiæ & lineæ refle
            <lb/>
          xionis. 37 p 5.</head>
          <p>
            <s xml:id="echoid-s7531" xml:space="preserve">IN ſpeculis ſphæricis concauis comprehendun-
              <lb/>
            tur imagines quædam ultra ſpeculum:</s>
            <s xml:id="echoid-s7532" xml:space="preserve"> quædam
              <lb/>
            in ſuperficie:</s>
            <s xml:id="echoid-s7533" xml:space="preserve"> quædam citra ſuperficiem.</s>
            <s xml:id="echoid-s7534" xml:space="preserve"> Et harũ
              <lb/>
            quædam comprehenduntur in ueritate, quædam
              <lb/>
            præter ueritatem.</s>
            <s xml:id="echoid-s7535" xml:space="preserve"> Omnes, quarum comprehenditur
              <lb/>
            ueritas, apparent in loco ſectionis perpendicularis
              <lb/>
            & lineæ reflexionis:</s>
            <s xml:id="echoid-s7536" xml:space="preserve"> quod ſic patebit.</s>
            <s xml:id="echoid-s7537" xml:space="preserve"> Fiat pyramis,
              <lb/>
            & eius axis ſit orthogonalis ſuper baſim:</s>
            <s xml:id="echoid-s7538" xml:space="preserve"> & diame-
              <lb/>
            ter baſis ſit minor medietate diametri ſphæræ:</s>
            <s xml:id="echoid-s7539" xml:space="preserve"> & li-
              <lb/>
            nea longitudinis pyramidis, ſit maior eadẽ ſemidia-
              <lb/>
            metro:</s>
            <s xml:id="echoid-s7540" xml:space="preserve"> & ſecetur ex parte baſis, ad quantitatẽ eius, ſcilicet ſemidiametri:</s>
            <s xml:id="echoid-s7541" xml:space="preserve"> & fiat ſuper ſectionẽ circu
              <lb/>
            lus:</s>
            <s xml:id="echoid-s7542" xml:space="preserve"> & ſecetur pyramis ſuper hũc circulũ.</s>
            <s xml:id="echoid-s7543" xml:space="preserve"> Poſtea in medio ſpeculi fiat circulus ad quantitatẽ baſis py
              <lb/>
            ramidis remanentis:</s>
            <s xml:id="echoid-s7544" xml:space="preserve"> & aptetur huic circulo pyramis, & firmetur cum cera.</s>
            <s xml:id="echoid-s7545" xml:space="preserve"> Deinde ſtatuatur uiſus
              <lb/>
            in ſitu, in quo imaginem pyramidis poſsit comprehendere:</s>
            <s xml:id="echoid-s7546" xml:space="preserve"> & adhibeatur lux, ut certior fiat com-
              <lb/>
            prehenſio:</s>
            <s xml:id="echoid-s7547" xml:space="preserve"> non uidebis quidem pyramidem huic coniumctam, ſed comprehendes hanc ultra ſpecu-
              <lb/>
            lum extenſam:</s>
            <s xml:id="echoid-s7548" xml:space="preserve"> unde apparebit pyramis quædam continua, cuius baſis ultra ſpeculum eſt, & pars
              <lb/>
            cius pyramis cerea.</s>
            <s xml:id="echoid-s7549" xml:space="preserve"> Et ſi in hac pyramide ſignetur linea longitudinis cum incauſto:</s>
            <s xml:id="echoid-s7550" xml:space="preserve"> uidebitur hæc
              <lb/>
            linea protendi ſuper ſuperficiẽ pyramidis apparentis.</s>
            <s xml:id="echoid-s7551" xml:space="preserve"> Et quoniã uertex pyramidis eſt centrũ ſphæ-
              <lb/>
            ræ:</s>
            <s xml:id="echoid-s7552" xml:space="preserve"> linea à uertice ſecundum longitudinem pyramidis ducta, erit perpendicularis ſuper lineam, con
              <lb/>
            tingentem quemlibet circulum ſphæræ, per caput lineæ tranſeuntem[quodlibet enim conilatus æ-
              <lb/>
            quatur ſemidiametro ſphæræ per fabricam:</s>
            <s xml:id="echoid-s7553" xml:space="preserve"> uertex igitur coni eſt centrum maximi in ſphæra circu-
              <lb/>
            li:</s>
            <s xml:id="echoid-s7554" xml:space="preserve"> cuius ſemidiameter eſt latus:</s>
            <s xml:id="echoid-s7555" xml:space="preserve"> itaque per 18 p 3 ad lineam tan gentem eſt perpendiculare.</s>
            <s xml:id="echoid-s7556" xml:space="preserve">] Quare
              <lb/>
            quælibet linea longitudinis pyramidis apparentis, eſt perpendicularis ſuper lineam, contingen-
              <lb/>
            tem lineam cõmunem ſuperficiei reflexionis & ſuperficiei ſphæræ:</s>
            <s xml:id="echoid-s7557" xml:space="preserve"> quę quidem linea cõmunis eſt
              <lb/>
            circulus [per 1 th 1 ſphæ.</s>
            <s xml:id="echoid-s7558" xml:space="preserve">] & quodlibet punctum pyramidis in hac uidetur perpendiculari:</s>
            <s xml:id="echoid-s7559" xml:space="preserve"> & quæ-
              <lb/>
            libet perpendicularis eſt in ſuperficie reflexionis [per 23 n 4:</s>
            <s xml:id="echoid-s7560" xml:space="preserve">] quoniam punctum uiſum & ima-
              <lb/>
            go eius ſunt in perpendiculari, & in hac ſuperficie:</s>
            <s xml:id="echoid-s7561" xml:space="preserve"> & omnis imago comprehenditur in linea re-
              <lb/>
            flexionis [per 21 n 4.</s>
            <s xml:id="echoid-s7562" xml:space="preserve">] Quare imago cuiuſcũq;</s>
            <s xml:id="echoid-s7563" xml:space="preserve"> puncti pyramidis, erit in puncto ſectionis perpendi-
              <lb/>
            </s>
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