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

List of thumbnails

< >
751
751 (449) 		752
752 (450)
753
753 (451) 		754
754 (452)
755
755 (453) 		756
756 (454)
757
757 (455) 		758
758 (456)
759
759 (457) 		760
760 (458)
< >
page |< < (456) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div1895" type="section" level="0" n="0">
          <pb o="456" file="0758" n="758" rhead="VITELLONIS OPTICAE"/>
        </div>
        <div xml:id="echoid-div1897" type="section" level="0" n="0">
          <head xml:id="echoid-head1392" xml:space="preserve" style="it">64. Si ad idem cẽtrum uiſus ab aliqua ſuperficie fiat luminis refractio uel reflexio: neceſſe eſt
            <lb/>
          extremum illius luminis ſuperficiei uiſus circulariter ſecundum rotundam pyramidem incide-
            <lb/>
          re. Ex quo patet tunc centrum corporis irr adiantis, & centrum uiſus, centrũ́ circuli baſis py-
            <lb/>
          ramidis irradiationis refractæ uel reflexæ in eadem recta linea conſistere oportere.</head>
          <p>
            <s xml:id="echoid-s50897" xml:space="preserve">Suppoſito quòd aliquod corpus irradiatum ſit inter uiſum & inter corpus luminoſum irradiãs:</s>
            <s xml:id="echoid-s50898" xml:space="preserve">
              <lb/>
            & ſit illud medium corpus diaphanum, ita quòd radij refracti in centro uiſus ualeant aggregari:</s>
            <s xml:id="echoid-s50899" xml:space="preserve"> ali-
              <lb/>
            ter enim non uideretur irradiatio.</s>
            <s xml:id="echoid-s50900" xml:space="preserve"> Sit quo que centrum corporis irradiantis a:</s>
            <s xml:id="echoid-s50901" xml:space="preserve"> ſuperficiesq́;</s>
            <s xml:id="echoid-s50902" xml:space="preserve"> corpo-
              <lb/>
            ris irradiati ſit f h i k:</s>
            <s xml:id="echoid-s50903" xml:space="preserve"> perpendicularis ducta à centro corporis luminoſi ſuper illam ſuperficiem ſit
              <lb/>
            a g:</s>
            <s xml:id="echoid-s50904" xml:space="preserve"> & ducantur lineæ a f, a h, a i, a k:</s>
            <s xml:id="echoid-s50905" xml:space="preserve"> & lineę g f, g h, g i, g k:</s>
            <s xml:id="echoid-s50906" xml:space="preserve"> & ſit centrum uiſus b:</s>
            <s xml:id="echoid-s50907" xml:space="preserve"> ducanturq́;</s>
            <s xml:id="echoid-s50908" xml:space="preserve"> lineæ b f,
              <lb/>
            b h, b i, b k, b g.</s>
            <s xml:id="echoid-s50909" xml:space="preserve"> Quoniã itaque, ut patet ex hypotheſi, lumẽ corporis irradiantis per refractionem ui
              <lb/>
            detur in puncto b:</s>
            <s xml:id="echoid-s50910" xml:space="preserve"> & per 3 huius perpendicularis non refringitur, ſed trãſit ad angulos rectos, ut in-
              <lb/>
            cidebat ad lineas f g, h g, i g, k g, & in uno puncto, ut in centro oculi, concurrunt plures radij refra-
              <lb/>
            cti, qui obliquè incidunt illi ſuperficiei ex hypotheſi:</s>
            <s xml:id="echoid-s50911" xml:space="preserve"> qua autẽ ratione aliquis radius refractus per-
              <lb/>
            uenit ad centrum uiſus, eadem ratione omnes radij incidentes ſuperficiei corporis f h i k, ſecundũ
              <lb/>
            circulum (cuius centrum eſt punctum g) refracti perueniunt ad centrum uiſus, ut patuit in 48 hu-
              <lb/>
            ius:</s>
            <s xml:id="echoid-s50912" xml:space="preserve"> ſunt enim illi anguli incidentiæ omnes æquales, ut patet per præmiſſam:</s>
            <s xml:id="echoid-s50913" xml:space="preserve"> ergo & anguli refra-
              <lb/>
            ctionis omnes erunt æquales per 8 huius.</s>
            <s xml:id="echoid-s50914" xml:space="preserve"> In centro ergo unius ui-
              <lb/>
              <figure xlink:label="fig-0758-01" xlink:href="fig-0758-01a" number="887">
                <variables xml:id="echoid-variables864" xml:space="preserve">a f h g k i b</variables>
              </figure>
            ſus nulli radij extremi concurrunt, niſi qui refringuntur ſecundum
              <lb/>
            angulos æquales.</s>
            <s xml:id="echoid-s50915" xml:space="preserve"> Sit ergo, ut ſit illa refractio ſecundum aliquos an
              <lb/>
            gulos extremos, qui ſint b f g, b h g, b k g, b i g:</s>
            <s xml:id="echoid-s50916" xml:space="preserve"> erunt ergo illi anguli
              <lb/>
            æquales:</s>
            <s xml:id="echoid-s50917" xml:space="preserve"> ſed & anguli ad punctum g ſub linea b g & ſub lineis f g,
              <lb/>
            h g, k g, i g, ſuntæ quales:</s>
            <s xml:id="echoid-s50918" xml:space="preserve"> quia ſunt recti.</s>
            <s xml:id="echoid-s50919" xml:space="preserve"> Sunt ergo trigona b g f, b g
              <lb/>
            h, b g k, b g i æquiãgula per 32 p1:</s>
            <s xml:id="echoid-s50920" xml:space="preserve"> ergo per 4 p 6 ipſorum latera ſunt
              <lb/>
            proportionalia:</s>
            <s xml:id="echoid-s50921" xml:space="preserve"> ſed latus b g eſt æ quale ſibijpſi, cum omnib.</s>
            <s xml:id="echoid-s50922" xml:space="preserve"> ſit illis
              <lb/>
            trigonis commune:</s>
            <s xml:id="echoid-s50923" xml:space="preserve"> latera ergo b f, b h, b k, b i ſunt æqualia inter ſe,
              <lb/>
            & latera g f, g h, g k, g i ſunt inter ſe æqualia.</s>
            <s xml:id="echoid-s50924" xml:space="preserve"> Ergo per 9 p 3 linea h f
              <lb/>
            i k eſt perpheria circuli, cuius centrum eſt punctum g:</s>
            <s xml:id="echoid-s50925" xml:space="preserve"> & ſic deſcri-
              <lb/>
            bitur in oculi ſuperficie.</s>
            <s xml:id="echoid-s50926" xml:space="preserve"> Fit ergo pyramis refracta, cuius uertex eſt
              <lb/>
            in puncto b centro uiſus, & eius baſis eſt in illuminata ſuperficie:</s>
            <s xml:id="echoid-s50927" xml:space="preserve">
              <lb/>
            eſtq́;</s>
            <s xml:id="echoid-s50928" xml:space="preserve"> alia pyramis illuminationis, cuius uertex eſt in puncto a cen-
              <lb/>
            tro luminoſi, & eius baſis eſt etiam circulus f h i k.</s>
            <s xml:id="echoid-s50929" xml:space="preserve"> Patet ergo quòd
              <lb/>
            iſtarum duarum pyramidum lineæ g f, g h, g i, g k ſunt in eadem ſu-
              <lb/>
            perficie, ut prius:</s>
            <s xml:id="echoid-s50930" xml:space="preserve"> quoniam ab eiſdem lineis, in quas radius incidit,
              <lb/>
            etiam refringitur.</s>
            <s xml:id="echoid-s50931" xml:space="preserve"> Vna eſt ergo ſuperficies communis terminans i-
              <lb/>
            ſtas duas pyramides, quæ eſt circulus f h i k:</s>
            <s xml:id="echoid-s50932" xml:space="preserve"> & eſt baſis ambarum il
              <lb/>
            larum pyramidum.</s>
            <s xml:id="echoid-s50933" xml:space="preserve"> Patet etiam hoc ex 5 p 11:</s>
            <s xml:id="echoid-s50934" xml:space="preserve"> quia illæ lineæ ſecun-
              <lb/>
            dum unum punctum, qui eſt g, cum linea b a angulos rectos faciũt.</s>
            <s xml:id="echoid-s50935" xml:space="preserve">
              <lb/>
            Angulus enim f g b eſt æqualis angulo f g a:</s>
            <s xml:id="echoid-s50936" xml:space="preserve"> quoniam uterque ipſo-
              <lb/>
            rum eſt rectus, ex eo quòd ſuppoſitum eſt angulum a g f eſſe rectũ:</s>
            <s xml:id="echoid-s50937" xml:space="preserve">
              <lb/>
            eritq́ue ſuperficies, in qua ſunt lineę f g, h g, i g, k g orthogonalis ſu-
              <lb/>
            per ſuperficies omnes refractionis.</s>
            <s xml:id="echoid-s50938" xml:space="preserve"> Patet ergo unum propoſitorũ.</s>
            <s xml:id="echoid-s50939" xml:space="preserve">
              <lb/>
            Quòd ſi centrum uiſus fuerit inter corpus irradiatum, & corpus ir-
              <lb/>
            radians conſtitutum:</s>
            <s xml:id="echoid-s50940" xml:space="preserve"> tunc eadem diſpoſitione manente, niſi ſolo
              <lb/>
            puncto b inter a & g puncta conſtituto, patet propoſitum ex eo:</s>
            <s xml:id="echoid-s50941" xml:space="preserve">
              <lb/>
            quòd tunc corpus irradiatum non uidetur niſi per reflexionem lu-
              <lb/>
            minis recepti à corpore luminoſo:</s>
            <s xml:id="echoid-s50942" xml:space="preserve"> & ſemper angulus incidentiæ
              <lb/>
            erit æqualis angulo reflexionis per 20th.</s>
            <s xml:id="echoid-s50943" xml:space="preserve"> 5 huius:</s>
            <s xml:id="echoid-s50944" xml:space="preserve"> quia angulus extrinſecus angulo a g fin triangu-
              <lb/>
            lo a g f pyramidis illuminationis erit æqualis angulo b f g, qui fit ad baſim trianguli b f g pyrami-
              <lb/>
            dis reflexionis:</s>
            <s xml:id="echoid-s50945" xml:space="preserve"> nec erit poſsibilis uiſio irradiationis niſi in puncto axis pyramidis illuminationis:</s>
            <s xml:id="echoid-s50946" xml:space="preserve">
              <lb/>
            ubi ſecundum æquales angulos reflexi radij à tota ſuperficie illuminati corporis concurrunt:</s>
            <s xml:id="echoid-s50947" xml:space="preserve"> e-
              <lb/>
            runtq́ue omnes anguli triangulorum pyramidis reflexionis, qui ſunt ad baſim, æquales inter ſe per
              <lb/>
            20th.</s>
            <s xml:id="echoid-s50948" xml:space="preserve"> 5 huius:</s>
            <s xml:id="echoid-s50949" xml:space="preserve"> quoniam anguli extrinſeci pyramidis irradiationis, qui ſunt anguli incidentiæ, o-
              <lb/>
            mnes ſunt æquales inter ſe.</s>
            <s xml:id="echoid-s50950" xml:space="preserve"> Omnes ita que radij ad uiſum reflexi, qui ſunt in eadem ſuperficie, per
              <lb/>
            6 p 1 erunt æquales.</s>
            <s xml:id="echoid-s50951" xml:space="preserve"> Et quoniam lineæ f g, h g, i g, i g, k g ſunt æquales:</s>
            <s xml:id="echoid-s50952" xml:space="preserve"> patet per 9 p 3 lineam f h i k eſſe
              <lb/>
            peripheriam circuli:</s>
            <s xml:id="echoid-s50953" xml:space="preserve"> quod eſt ſecundum propoſitum.</s>
            <s xml:id="echoid-s50954" xml:space="preserve"> Et quoniam linea b g, quæ eſt perpendicula-
              <lb/>
            ris ſuper illam ſuperficiem, omnibus illis trigonis eſt communis, & angulus cuiuslibet triangulo-
              <lb/>
            rum, qui ſunt ad baſim, æqualis eſt alteri ſibi correſpondenti per 4 p 1, cum lineæ f g, h g, i g, k g ſint
              <lb/>
            adinuicem æquales, ut declaratum eſt prius, & ab ipſis fiat reflexio ad uiſum:</s>
            <s xml:id="echoid-s50955" xml:space="preserve"> patet per 106 th.</s>
            <s xml:id="echoid-s50956" xml:space="preserve"> 1 hu-
              <lb/>
            ius quia erit per radios ab ipſis reflexos pyramis inſcripta pyramidi ad eandem baſim, ſed diuerſæ
              <lb/>
            altitudinis:</s>
            <s xml:id="echoid-s50957" xml:space="preserve"> quoniam punctus b, qui eſt centrum uiſus, poſitus eſt eſſe inter corpus irradians &
              <lb/>
            corpus irradiatum:</s>
            <s xml:id="echoid-s50958" xml:space="preserve"> & erit illa baſis communis duabus pyramidibus, ſcilicet pyramidi irradiatio-
              <lb/>
            nis & pyramidi reflexionis orthogonalis ſuper omnes ſuperficies reflexionis.</s>
            <s xml:id="echoid-s50959" xml:space="preserve"> Patet ergo, quod co-
              <lb/>
            rollario proponebatur per 107 th.</s>
            <s xml:id="echoid-s50960" xml:space="preserve"> 1 huius.</s>
            <s xml:id="echoid-s50961" xml:space="preserve"> Viſum eſt etiam quibuſdam ad propoſitam uiſorum
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum