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-s7106" xml:space="preserve">
              <pb o="121" file="0127" n="127" rhead="OPTICAE LIBER IIII."/>
            ſumi punctum aliud, ad quod linea à centro uiſus accedat, & in hoc punctum tranſeat:</s>
            <s xml:id="echoid-s7107" xml:space="preserve"> nõ occulta-
              <lb/>
            tur punctum iſtud ab alio puncto, quòd non perueniat ad centrum uiſus:</s>
            <s xml:id="echoid-s7108" xml:space="preserve"> quare apparet uiſui, cum
              <lb/>
            inter ipſum & uiſum non intercidat corporis ſolidi obiectio.</s>
            <s xml:id="echoid-s7109" xml:space="preserve"> Et eadem probatio eſt de quolibet ſu-
              <lb/>
            perficiei pyramidis puncto.</s>
            <s xml:id="echoid-s7110" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div260" type="section" level="0" n="0">
          <head xml:id="echoid-head286" xml:space="preserve" style="it">39. Si recta linea à uiſu in uerticem ſpeculi conici conuexi recti, continuetur cum axe: tota
            <lb/>
          ſuperficies conica uidebitur. 92 p 4.</head>
          <p>
            <s xml:id="echoid-s7111" xml:space="preserve">ET ſi linea à centro uiſus in terminum axis cadens, intret pyramidem:</s>
            <s xml:id="echoid-s7112" xml:space="preserve"> dico quòd nullũ occul-
              <lb/>
            tatur uiſui punctũ in tota pyramidis ſuperficie.</s>
            <s xml:id="echoid-s7113" xml:space="preserve"> Sumpto enim quocunq;</s>
            <s xml:id="echoid-s7114" xml:space="preserve"> pũcto in pyramidis
              <lb/>
            ſuperficie:</s>
            <s xml:id="echoid-s7115" xml:space="preserve"> intelligatur ad ipſum linea à centro uiſus, & alia ab
              <lb/>
              <figure xlink:label="fig-0127-01" xlink:href="fig-0127-01a" number="32">
                <variables xml:id="echoid-variables22" xml:space="preserve">a d b k ſ c</variables>
              </figure>
              <gap/>
            o uſq;</s>
            <s xml:id="echoid-s7116" xml:space="preserve"> ad acumen pyramidis:</s>
            <s xml:id="echoid-s7117" xml:space="preserve"> hæ duæ lineæ includunt ſuperficiem
              <lb/>
            triangularem cũ linea à centro uiſus ad terminũ axis ducta, pyrami-
              <lb/>
            dem intrãte:</s>
            <s xml:id="echoid-s7118" xml:space="preserve"> & eſt iſtud triangulũ in ſuperficie pyramidem ſecante:</s>
            <s xml:id="echoid-s7119" xml:space="preserve">
              <lb/>
            cum omnis ſuperficies, in qua fuerit linea intrans pyramidem, ſecet
              <lb/>
            eam.</s>
            <s xml:id="echoid-s7120" xml:space="preserve"> Linea uerò à centro uiſus ad punctũ ſumptũ ducta, ſecat in illo
              <lb/>
            puncto lineã longitudinis ab eo ad acumẽ pyramidis ductã.</s>
            <s xml:id="echoid-s7121" xml:space="preserve"> Et ex li-
              <lb/>
            neis ſuperficièi, in qua ſunt hæ duæ lineæ, non ſunt, niſi duæ lineæ in
              <lb/>
            ſuperficie pyramidis, ſcilicet hæc linea longitudinis, à pũcto ad acu-
              <lb/>
            men ducta, & alia oppoſita, ſecans angulũ, quem includit hæc cũ li-
              <lb/>
            nea pyramidẽ intrante.</s>
            <s xml:id="echoid-s7122" xml:space="preserve"> Igitur linea illa oppoſita, extra pyramidẽ pro
              <lb/>
            ducta, ſecat lineam à centro ad punctũ ſumptum ductã.</s>
            <s xml:id="echoid-s7123" xml:space="preserve"> Quare linea
              <lb/>
            hæc ſecat duas lineas, quę ſolæ ex lineis huius ſuperficiei ſunt in py-
              <lb/>
            ramidis ſuperficie:</s>
            <s xml:id="echoid-s7124" xml:space="preserve"> unam extra pyramidem, aliã in puncto ſumpto.</s>
            <s xml:id="echoid-s7125" xml:space="preserve">
              <lb/>
            Quare producta in infinitum nõ concurret cũ aliqua illarum linea-
              <lb/>
            rum:</s>
            <s xml:id="echoid-s7126" xml:space="preserve"> unde nõ occultatur uiſui ſumptum punctum, ſecundũ modum
              <lb/>
            ſuprà dictum.</s>
            <s xml:id="echoid-s7127" xml:space="preserve"> In hoc ſitu ergo nulla ſuperficιerũ pyramidem tangen
              <lb/>
            tium tranſibit per centrũ uiſus, ſed quęlibet ſecabit lineam à uiſu ſu-
              <lb/>
            per terminum axis pyramidem intrãtis, inter uiſum & pyramidem:</s>
            <s xml:id="echoid-s7128" xml:space="preserve">
              <lb/>
            & eſt in termino axis.</s>
            <s xml:id="echoid-s7129" xml:space="preserve"> Cum uero linea uiſus lineæ longitudinis pyra
              <lb/>
            midis applicatur:</s>
            <s xml:id="echoid-s7130" xml:space="preserve"> nulla ſuperficierum pyramidem tangentium pertinetad centrum uiſus præter il-
              <lb/>
            lam, quæ in prædicta linea contingit pyramidem:</s>
            <s xml:id="echoid-s7131" xml:space="preserve"> & omnes ſuperficies contingẽtes, ſecabunt lineã
              <lb/>
            illam inter uiſum & uerticem pyramιdis.</s>
            <s xml:id="echoid-s7132" xml:space="preserve"> Similiter in ſitu, in quo duæ ſuperficies contingentes py-
              <lb/>
            ramidẽ per centrũ uiſus tranſeunt:</s>
            <s xml:id="echoid-s7133" xml:space="preserve"> quælibet ſuperficies tangens pyramidẽ in portione pyramidis
              <lb/>
            apparẽte, quę duas contingẽtes interiacet, à centro uiſus diuertit:</s>
            <s xml:id="echoid-s7134" xml:space="preserve"> & ſuper quodcunq;</s>
            <s xml:id="echoid-s7135" xml:space="preserve"> punctũ illius
              <lb/>
            portionis cadat linea uiſualis:</s>
            <s xml:id="echoid-s7136" xml:space="preserve"> ſecabit pyramidẽ, cũ intercidat inter duas cõtingẽtes uiſuales:</s>
            <s xml:id="echoid-s7137" xml:space="preserve"> & ſu-
              <lb/>
            perficies, in qua fuerit linea hæc uiſualis, & linea longitudinis pyramidis, ſecabit pyramidẽ:</s>
            <s xml:id="echoid-s7138" xml:space="preserve"> & erit
              <lb/>
            hæc uiſualis ſuperficies cuicunq;</s>
            <s xml:id="echoid-s7139" xml:space="preserve"> ſuperficiei pyramidis in hac portione, continua:</s>
            <s xml:id="echoid-s7140" xml:space="preserve"> quare & uiſus.</s>
            <s xml:id="echoid-s7141" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div262" type="section" level="0" n="0">
          <head xml:id="echoid-head287" xml:space="preserve" style="it">40. Si communis ſectio ſuperficierum, reflexionis & ſpeculi conici conuexi fuerit lat{us} coni-
            <lb/>
          cum: à quolιbet conſpicuæ ſuperficiei puncto ad uiſum reflexio fieri poteſt. 31 p 7.</head>
          <p>
            <s xml:id="echoid-s7142" xml:space="preserve">DIco ergo, quòd in quolibet ſitu, à quolibet puncto poteſt fieri reflexio.</s>
            <s xml:id="echoid-s7143" xml:space="preserve"> Sumatur enim pun-
              <lb/>
            ctum, & intelligatur circulus per punctum tranſiens, baſi py-
              <lb/>
              <figure xlink:label="fig-0127-02" xlink:href="fig-0127-02a" number="33">
                <variables xml:id="echoid-variables23" xml:space="preserve">b ſ a u f d c h n g r k s x q p</variables>
              </figure>
            ramidi æquidiſtãs:</s>
            <s xml:id="echoid-s7144" xml:space="preserve"> diameter igitur huius circuli ab hoc pun-
              <lb/>
            cto incipiens, erit perpendicularis ſuper axem [per 3 d 11] cũ axis ſit
              <lb/>
            perpendicularis ſuper circuli ſuperficiẽ [per 18 d 11, & conuerſam 14
              <lb/>
            p 11.</s>
            <s xml:id="echoid-s7145" xml:space="preserve">] Quare linea longitudinis à puncto ad acumẽ pyramidis ducta,
              <lb/>
            tenet angulum acutum cum diametro, & acutum cum axis termino
              <lb/>
            in eadem ſuperficie [per 32 p 1, quia angulus ab axe & ſemidiametro
              <lb/>
            g d comprehenſus, eſt rectus.</s>
            <s xml:id="echoid-s7146" xml:space="preserve">] Sit linea uiſualis ſuper punctũ cadens
              <lb/>
            in ſuperficie, in qua eſt linea lõgitudinis & axis, in qua ſuperficie de-
              <lb/>
            ducatur perpendicularis ſuper lineã longitudinis in puncto illo:</s>
            <s xml:id="echoid-s7147" xml:space="preserve"> con
              <lb/>
            curret hæc quidem perpendicularis cum axe:</s>
            <s xml:id="echoid-s7148" xml:space="preserve"> [per 11 ax] & ex ea, &
              <lb/>
            axe, & linea longitudinis efficietur triangulum.</s>
            <s xml:id="echoid-s7149" xml:space="preserve"> Super punctũ illud
              <lb/>
            intelligatur linea contingens, & ſuper diametrum circuli, quem feci
              <lb/>
            mus, intelligatur diameter alia orthogonalis ſuper ipſam:</s>
            <s xml:id="echoid-s7150" xml:space="preserve"> quæ erit
              <lb/>
            orthogonalis ſuper ipſum axem:</s>
            <s xml:id="echoid-s7151" xml:space="preserve"> & ſuper ſuperficiem, in qua eſt axis,
              <lb/>
            & diameter prima [per 4 p 11] & hæc diameter ſecunda eſt æquidi-
              <lb/>
            ſtans contingenti [per 28 p 1] quoniam contingens perpendicularis
              <lb/>
            eſt ſuper diametrum primam [per 18 p 3] & ita linea contingens or-
              <lb/>
            thogonalis eſt ſuper ſuperficiem, in qua ſunt axis & diameter prima
              <lb/>
            [per 8 p 11.</s>
            <s xml:id="echoid-s7152" xml:space="preserve">] Quare erit perpendicularis ſuper perpendicularẽ, quam
              <lb/>
            primo fecimus [per 3 d 11] & ita illa prima perpendicularis orthogonaliter cadit ſuper ſuperficiem,
              <lb/>
            contingẽtem pyramidem, in qua punctum eſt ſumptum.</s>
            <s xml:id="echoid-s7153" xml:space="preserve"> Igitur ſi linea uiſualis, cadens in punctum
              <lb/>
            ſumptum, trãſeat ſecundũ proceſſum perpendicularis:</s>
            <s xml:id="echoid-s7154" xml:space="preserve"> erit quidẽ orthogonalis ſuper ſuperficiem,
              <lb/>
            </s>
          </p>
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