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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        <div xml:id="echoid-div1897" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s50961" xml:space="preserve">
              <pb o="457" file="0759" n="759" rhead="LIBER DECIMVS."/>
            circulationem coadunare circulationem foraminis uueæ, ac ſi ad peripheriam foraminis ſolùm ra-
              <lb/>
            dij incidant:</s>
            <s xml:id="echoid-s50962" xml:space="preserve"> & ſic in ſuperficie uiſus rotundentur.</s>
            <s xml:id="echoid-s50963" xml:space="preserve"> Quòd etſi ſit aliquando poſsibile, non tamen eſt
              <lb/>
            uniuerſaliter neceſſarium:</s>
            <s xml:id="echoid-s50964" xml:space="preserve"> quia etiam cuicunq;</s>
            <s xml:id="echoid-s50965" xml:space="preserve"> parti ſuperficiei uiſus radij incidant ſecundum an-
              <lb/>
            gulos æquales:</s>
            <s xml:id="echoid-s50966" xml:space="preserve"> ſemper accidet neceſſario figuram uideri circula-
              <lb/>
            rem.</s>
            <s xml:id="echoid-s50967" xml:space="preserve"> Ex iſtis itaq, manifeſtè patet, quia etſi tota ſuperficies alicu-
              <lb/>
              <figure xlink:label="fig-0759-01" xlink:href="fig-0759-01a" number="888">
                <variables xml:id="echoid-variables865" xml:space="preserve">a g f y h k i</variables>
              </figure>
            ius corporis irregularis uel regularis, rectilinea uel circularis ſit
              <lb/>
            irradiata:</s>
            <s xml:id="echoid-s50968" xml:space="preserve"> non tamen uidebitur niſi circularis pars eius irradiata,
              <lb/>
            quando per reflexionem uel refractionem uidetur.</s>
            <s xml:id="echoid-s50969" xml:space="preserve"> Quia oportet
              <lb/>
            ad hoc, quòd uiſus ipſum iudicet irradiatum, radios plures in cen
              <lb/>
            tro oculi aggregari:</s>
            <s xml:id="echoid-s50970" xml:space="preserve"> non autem concurrunt niſi illi, qui inci dentes
              <lb/>
            ad ſuperficiem corporis irradiati & reflexi ad centrũ oculi omnes
              <lb/>
            æquales angulos conſtituunt:</s>
            <s xml:id="echoid-s50971" xml:space="preserve"> tales autem in cidunt ſecundum cir
              <lb/>
            culum:</s>
            <s xml:id="echoid-s50972" xml:space="preserve"> faciunt enim pyramidem, ut patet ex præmiſſa, & refle-
              <lb/>
            ctuntur uel refringuntur neceſſariò ſecundũ circulum eundem.</s>
            <s xml:id="echoid-s50973" xml:space="preserve">
              <lb/>
            Ergo ſuperficies illius corporis ſemper uidebitur circulariter irra
              <lb/>
            diata:</s>
            <s xml:id="echoid-s50974" xml:space="preserve"> nec uidebit uiſus illam irradiationem, niſi fuerit in puncto
              <lb/>
            concurſus linearum taliter reflexarũ conſtitutus.</s>
            <s xml:id="echoid-s50975" xml:space="preserve"> Et propter hoc
              <lb/>
            in eadem ſuperficie irràdiati corporis diuerſis uiſibus diuerſi ap-
              <lb/>
            parebunt circuli:</s>
            <s xml:id="echoid-s50976" xml:space="preserve"> quia eæ dem lineæ in diuerſis punctis non con-
              <lb/>
            currunt, ſed in uno tantùm:</s>
            <s xml:id="echoid-s50977" xml:space="preserve"> & remotioribus maiores apparebunt
              <lb/>
            circuli:</s>
            <s xml:id="echoid-s50978" xml:space="preserve"> ſcllicet illi, quibus ad maiores angulos incidebant radij, &
              <lb/>
            ad maiores reflectuntur uel refringuntur:</s>
            <s xml:id="echoid-s50979" xml:space="preserve"> & ſunt exteriores in pe
              <lb/>
            ripheria baſis.</s>
            <s xml:id="echoid-s50980" xml:space="preserve"> Sic ergo pyramis interior, ſcilicet reflexionis uel re
              <lb/>
            fractionis inſcribitur pyramidi alteri reflexionis uel refractionis
              <lb/>
            minorẽ exterius ambienti:</s>
            <s xml:id="echoid-s50981" xml:space="preserve"> centrumq́;</s>
            <s xml:id="echoid-s50982" xml:space="preserve"> uiſus propinquius ſuperfi-
              <lb/>
            ciei irradiatæ minorẽ uidebit circulũ, ꝗ̃ uiſus remotior:</s>
            <s xml:id="echoid-s50983" xml:space="preserve"> quoniã ra
              <lb/>
            dij in minori circulo ſecundũ angulos minores incidunt, & ſecun
              <lb/>
            dum angulos minores reflectuntur per 20th.</s>
            <s xml:id="echoid-s50984" xml:space="preserve"> 5 huius, uel ſecundũ
              <lb/>
            minores angulos refringuntur per 8 huius.</s>
            <s xml:id="echoid-s50985" xml:space="preserve"> Patet aũt ք 106 th.</s>
            <s xml:id="echoid-s50986" xml:space="preserve"> 1 hu
              <lb/>
            ius quia ſecundũ quòd angulus refractionis uel reflexionis plus
              <lb/>
            minuitur, ſecundum hoc angulus in uiſu contentus augmenta-
              <lb/>
            tur.</s>
            <s xml:id="echoid-s50987" xml:space="preserve"> Et quia angulus refractionis uel reflexionis ſemper eſt acutus
              <lb/>
            rectilineus diuiſibilis:</s>
            <s xml:id="echoid-s50988" xml:space="preserve"> propter hoc angulus in oculo ſemper eſt acutus, nec ad rectum poteſt excre
              <lb/>
            ſcere, ut quartã partẽ circuli altitudinis ſibi faciat reſpõdere:</s>
            <s xml:id="echoid-s50989" xml:space="preserve"> quoniã inter angulos cauſſantes pyra
              <lb/>
            midem ille angulus in oculo & angulus reflexionis uel refractionis ualent unũ rectũ:</s>
            <s xml:id="echoid-s50990" xml:space="preserve"> cum angulus
              <lb/>
            ad axẽ ſemper ſit rectus per 89 primi huius.</s>
            <s xml:id="echoid-s50991" xml:space="preserve"> Ex præmiſsis quoq;</s>
            <s xml:id="echoid-s50992" xml:space="preserve"> patet corollariũ perpulchrũ auxi-
              <lb/>
            lio 12 huius.</s>
            <s xml:id="echoid-s50993" xml:space="preserve"> Quoniam enim in pyramide orthogonia centrum circuli baſis & conus ſemper ſunt in
              <lb/>
            eadem linea (ut in axe) in propoſito erunt a & g in axe a g:</s>
            <s xml:id="echoid-s50994" xml:space="preserve"> ſed eadem ratione erunt b & g in eadem
              <lb/>
            linea:</s>
            <s xml:id="echoid-s50995" xml:space="preserve"> lineæ uerò b g & g a coniunctæ ſunt linea una:</s>
            <s xml:id="echoid-s50996" xml:space="preserve"> eò quòd f g à termino ipſarum exiens cum am
              <lb/>
            babus facit angulos rectos.</s>
            <s xml:id="echoid-s50997" xml:space="preserve"> Quo modocunq;</s>
            <s xml:id="echoid-s50998" xml:space="preserve"> ergo ſe habeat uiſus ad corpus irradiatum, dummo-
              <lb/>
            do ad ipſum fiat reflexio uel refractio:</s>
            <s xml:id="echoid-s50999" xml:space="preserve"> patet propoſitum quoniã ſemper centrum corporis irradian
              <lb/>
            tis & centrum oculi & centrũ circuli baſis utriuſq;</s>
            <s xml:id="echoid-s51000" xml:space="preserve"> pyramidis, irradiationis ſcilicet & uiſionis ſunt
              <lb/>
            in eadem linea, ſcilicet axe pyramidis irradiationis:</s>
            <s xml:id="echoid-s51001" xml:space="preserve"> nec aliter eſt poſsibile uideri irradiationem.</s>
            <s xml:id="echoid-s51002" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1899" type="section" level="0" n="0">
          <head xml:id="echoid-head1393" xml:space="preserve" style="it">65. Iridem ex reflexione & refractione radiorum corporis luminoſi uideri neceſſe ect.</head>
          <p>
            <s xml:id="echoid-s51003" xml:space="preserve">Locuturi de iride, de illa principaliter intendimus, quæ interſecans horizontem ad diuerſas par
              <lb/>
            tes mundi protenditur:</s>
            <s xml:id="echoid-s51004" xml:space="preserve"> quamuis etiam de alijs, quæ illi iridi ſimiles uidentur, intentionem non
              <lb/>
            principaliter facturi ſimus.</s>
            <s xml:id="echoid-s51005" xml:space="preserve"> Quòd uerò iris fiat ex multitudine luminis corporis luminoſi in uiſu re
              <lb/>
            cepti, hoc patet ſenſui:</s>
            <s xml:id="echoid-s51006" xml:space="preserve"> quòd autem (non aggregatis radijs corporis luminoſi) lumen ſenſibilius
              <lb/>
            poſsit fieri in corpore non luminoſo, quàm in medio, per quod prius lumen ferebatur, oſtenſum
              <lb/>
            eſt per 56 huius impoſsibile eſſe.</s>
            <s xml:id="echoid-s51007" xml:space="preserve"> Vnde patet ex hoc quòd lumẽ uigoratur ex aggregatione radio-
              <lb/>
            rum corporis luminoſi, ut ſenſibilius fiat in aliquo corpore quàm in medio.</s>
            <s xml:id="echoid-s51008" xml:space="preserve"> Quod uerò aggregatio
              <lb/>
            radiorum corporis luminoſi fiat per reflexionem uel per refractionem, quæ fit in corpore denſio-
              <lb/>
            ris diaphani quàm medium, per quod antea ferebatur, declaratum eſt per 57 huius.</s>
            <s xml:id="echoid-s51009" xml:space="preserve"> Patet itaq;</s>
            <s xml:id="echoid-s51010" xml:space="preserve"> ge-
              <lb/>
            neraliter quòd luminis maior ſenſibilitas per reflexionẽ uel per refractionem in omnibus uiſibili-
              <lb/>
            bus cauſſatur.</s>
            <s xml:id="echoid-s51011" xml:space="preserve"> Quòd uerò iris ſpecialiter ex reflexione fiat:</s>
            <s xml:id="echoid-s51012" xml:space="preserve"> patet per hoc:</s>
            <s xml:id="echoid-s51013" xml:space="preserve"> quia lumen eius ſenſibile
              <lb/>
            peruenit ad uiſum, ut ſuppoſitũ eſt in 2 petitione libri huius.</s>
            <s xml:id="echoid-s51014" xml:space="preserve"> Oſtenſum eſt quoq;</s>
            <s xml:id="echoid-s51015" xml:space="preserve"> per 20 th.</s>
            <s xml:id="echoid-s51016" xml:space="preserve"> 5 huius
              <lb/>
            quòd omne, quod uidetur per reflexionem, ſic uidetur, quòd angulus, ſecundum quẽ forina ſpecu
              <lb/>
            lo uel alteri corpori polito incidit, fit æqualis angulo, ſecundũ quẽ illa forma reflectitur ad uiſum:</s>
            <s xml:id="echoid-s51017" xml:space="preserve">
              <lb/>
            quod etiam patet per 26 th.</s>
            <s xml:id="echoid-s51018" xml:space="preserve"> 5 huius ducta perpendiculari à puncto incidentiæ ſuper ſuperficiem
              <lb/>
            corporis politi, ad quam reflexionis anguli referuntur:</s>
            <s xml:id="echoid-s51019" xml:space="preserve"> continet enim radius incidens & radius re-
              <lb/>
            flexus cum eadem perpendiculari angulos æquales.</s>
            <s xml:id="echoid-s51020" xml:space="preserve"> Cum itaq;</s>
            <s xml:id="echoid-s51021" xml:space="preserve"> forma iridis fiat in uiſu:</s>
            <s xml:id="echoid-s51022" xml:space="preserve"> patet iri-
              <lb/>
            dem per reflexionẽ radiorũ corporis luminoſi ad uiſum cauſſari.</s>
            <s xml:id="echoid-s51023" xml:space="preserve"> Quòd uerò iris per refractionem
              <lb/>
            </s>
          </p>
        </div>
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    </echo>
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