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-s50837" xml:space="preserve">
              <pb o="455" file="0757" n="757" rhead="LIBER DECIMVS."/>
            ctum a:</s>
            <s xml:id="echoid-s50838" xml:space="preserve"> contingatq́;</s>
            <s xml:id="echoid-s50839" xml:space="preserve"> ipſum ſuperficies plana, quę ſit s p in puncto c:</s>
            <s xml:id="echoid-s50840" xml:space="preserve"> & ſit ſuperficies corporis illumi-
              <lb/>
            nandi à corpore ſphærico, ſuperficies g, quæ eſt ex hypotheſi æquidiſtãs ſuperficiei s p:</s>
            <s xml:id="echoid-s50841" xml:space="preserve"> & ſit linea a
              <lb/>
            c g ducta à centro corporis ſphærici perpendicularis ſuper dicti corporis ſuperficiem:</s>
            <s xml:id="echoid-s50842" xml:space="preserve"> dico quòd ir
              <lb/>
            radiationem illius corporis poſsibile eſt fieri ſecundum pyramidem rotundam, cuius baſis eſt in ſu-
              <lb/>
            perficie corporis g, uertex uerò in puncto a centro corporis luminoſi.</s>
            <s xml:id="echoid-s50843" xml:space="preserve"> Si enim perpendicularis a g
              <lb/>
            in centrum uel in medium ſuperficiei g non ceciderit:</s>
            <s xml:id="echoid-s50844" xml:space="preserve"> ducatur ad ipſius ſuperficiei g breuius extre-
              <lb/>
            mum linea a f:</s>
            <s xml:id="echoid-s50845" xml:space="preserve"> ſuper cuius terminũ in puncto a conſtitua-
              <lb/>
            tur angulus ex 23 p 1 æqualis angulo g a f, qui ſit g a h:</s>
            <s xml:id="echoid-s50846" xml:space="preserve"> pro-
              <lb/>
              <figure xlink:label="fig-0757-01" xlink:href="fig-0757-01a" number="886">
                <variables xml:id="echoid-variables863" xml:space="preserve">d a b p c s k h y f l</variables>
              </figure>
            ducaturq́;</s>
            <s xml:id="echoid-s50847" xml:space="preserve"> linea a h ad ſuperficiem g:</s>
            <s xml:id="echoid-s50848" xml:space="preserve"> & producantur in ſu-
              <lb/>
            perficie g lineę g f, & g h.</s>
            <s xml:id="echoid-s50849" xml:space="preserve"> Et quoniam duorum triangulo-
              <lb/>
            rum a g f & a g h anguli a g f & a g h, qui ſunt ad baſim, ſunt
              <lb/>
            ęquales ex definitione lineæ erectę ſuper ſuperficiẽ, & an-
              <lb/>
            guli g a f & g a h ſunt ęquales, & latus a g commune:</s>
            <s xml:id="echoid-s50850" xml:space="preserve"> patet
              <lb/>
            ex 26 p 1 quia latus a f erit æquale lateri a h, & f g æquale
              <lb/>
            g h.</s>
            <s xml:id="echoid-s50851" xml:space="preserve"> Similiter etiam facto alio angulo æquali g a f & g a h
              <lb/>
            angulis triãgulorum a g f & a g h, qui ſit g a k:</s>
            <s xml:id="echoid-s50852" xml:space="preserve"> productisq́;</s>
            <s xml:id="echoid-s50853" xml:space="preserve">
              <lb/>
            lineis a k & g k:</s>
            <s xml:id="echoid-s50854" xml:space="preserve"> erit, ſicut in præcedentibus, linea a k ęqua
              <lb/>
            lis lineę a f uel a h, & erit linea g k æqualis lineę g f uel g h.</s>
            <s xml:id="echoid-s50855" xml:space="preserve">
              <lb/>
            Cum ergo ex puncto g exeant tres lineæ ęquales & in ea-
              <lb/>
            dem ſuperficie:</s>
            <s xml:id="echoid-s50856" xml:space="preserve"> patet ex 9 p 3 lineam f h k ſecundum quan
              <lb/>
            titatem lineæ g f à puncto g productam eſſe circularem.</s>
            <s xml:id="echoid-s50857" xml:space="preserve">
              <lb/>
            Quia ita que irradiatio fit ſecundum has lineas, ſcilicet a f,
              <lb/>
            a h, a k, & ſecundum alias omnes ducibiles, angulos æqua
              <lb/>
            les cum linea a g prædictorum triangulorum angulis, qui
              <lb/>
            ſunt ad punctum a, continentes, ut eſt linea a l, & aliæ:</s>
            <s xml:id="echoid-s50858" xml:space="preserve"> pa-
              <lb/>
            tet ex definitione pyramidis rotundæ, quoniam fit irradia
              <lb/>
            tio ſecundum pyramidem rotundam.</s>
            <s xml:id="echoid-s50859" xml:space="preserve"> Fit enim ſecundum
              <lb/>
            figuram, quæ deſcribi poſsit per triangulum a g f orthogo
              <lb/>
            nium latere a g fixo manente, & a f & g f lateribus reuolu-
              <lb/>
            tis ad locum, unde inceperant moueri.</s>
            <s xml:id="echoid-s50860" xml:space="preserve"> Et ex pręmiſsis pa-
              <lb/>
            tet quoniam huius irradiatio ſemper fit ſecundum angu-
              <lb/>
            los incidentiæ æquales.</s>
            <s xml:id="echoid-s50861" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s50862" xml:space="preserve"> Si dicatur
              <lb/>
            quòd etiam fit irradiatio extra hanc pyramidem:</s>
            <s xml:id="echoid-s50863" xml:space="preserve"> hoc eſt
              <lb/>
            uerum:</s>
            <s xml:id="echoid-s50864" xml:space="preserve"> ſed quia natura lucis eſt ſemper æqualiter diffundi, ut patet per 20 th.</s>
            <s xml:id="echoid-s50865" xml:space="preserve"> 2 huius:</s>
            <s xml:id="echoid-s50866" xml:space="preserve"> tunc fiet ad
              <lb/>
            omnem partem ſuperficiei g ſecundum pyramidem uel ſecundum partem pyramidis in ipſa rece-
              <lb/>
            ptam irradiatio (parte alia pyramidis ad ſuperficiem corporis non illuminabilis protenſa.</s>
            <s xml:id="echoid-s50867" xml:space="preserve">) Vnde ſi
              <lb/>
            pars illuminata extra ſignatam pyramidem modica fuerit:</s>
            <s xml:id="echoid-s50868" xml:space="preserve"> nó fiet in ea ſenſibilis irradiatio propter
              <lb/>
            radiorum paucitatem:</s>
            <s xml:id="echoid-s50869" xml:space="preserve"> quæ ſi magna fuerit, cum in ipſa ad ęquales angulos multi radij conueniant:</s>
            <s xml:id="echoid-s50870" xml:space="preserve">
              <lb/>
            tunc irradiatio ſenſibilis erit propter multorum radiorum concurſum & æqualitatem angulorum.</s>
            <s xml:id="echoid-s50871" xml:space="preserve">
              <lb/>
            Et ſic eſt poſsibile propter lucis unigenitatem irradiationem fieri ſecũdum lineam circularem, quę
              <lb/>
            ſit terminus baſis pyramidis uel partis baſis.</s>
            <s xml:id="echoid-s50872" xml:space="preserve"> Eodem autem modo demonſtrandum, ſi ſuperficies g
              <lb/>
            æquidiſtet ſuperficiei s p contingenti corpus lumiaoſum in b, d punctis, uel in alijs punctis ſigna-
              <lb/>
            tis.</s>
            <s xml:id="echoid-s50873" xml:space="preserve"> Vniuerſaliter autem corporum, quæ ſplendorem ſenſibilem à corpore aliquo luminoſo acci-
              <lb/>
            piunt, oportet quòd ſit talis aſpectus ad corpus luminoſum, ut theorema ſupponit:</s>
            <s xml:id="echoid-s50874" xml:space="preserve"> ſcilicet æqui-
              <lb/>
            diſtantia ad ſuperficiem planam contingentem corpus lumino ſum in puncto, ubi perpendicularis
              <lb/>
            ducta à centro corporis luminoſi ad ſuperficiem corporis illuminandi ſecat ſuperficiem corporis
              <lb/>
            luminoſi.</s>
            <s xml:id="echoid-s50875" xml:space="preserve"> Et huius ſignum eſt irradiatio lunæ, quæ nunquam, niſi in parte ſoli oppoſita illumina-
              <lb/>
            tur:</s>
            <s xml:id="echoid-s50876" xml:space="preserve"> & ſemper medietas illius, ea ſcilicet, quæ ſolem reſpicit, eſt illuminata neceſſariò propter natu-
              <lb/>
            ram præmiſsi aſpectus:</s>
            <s xml:id="echoid-s50877" xml:space="preserve"> aliam uerò partem irradiatio ſolis, niſi fortè per refractionem, nullatenus
              <lb/>
            attingit.</s>
            <s xml:id="echoid-s50878" xml:space="preserve"> Et quoniam pyramides uerticem habentes in centro corporis luminoſi, ad infinitas ba-
              <lb/>
            ſes in corpore irradiando una baſi alteri inſcripta applicantur:</s>
            <s xml:id="echoid-s50879" xml:space="preserve"> ideo tota ſuperficies irradiati corpo-
              <lb/>
            ris corpus luminoſum aſpiciens multiformiter irradiatur, & augmentatur irradiatio:</s>
            <s xml:id="echoid-s50880" xml:space="preserve"> quoniam o-
              <lb/>
            portet ut tale corpus ſit denſius medio, per quod lumen uenit ad ipſum:</s>
            <s xml:id="echoid-s50881" xml:space="preserve"> oportet enim quòd tale
              <lb/>
            corpus habeat aliquid denſitatis.</s>
            <s xml:id="echoid-s50882" xml:space="preserve"> Vnde ſi lumen nihil haberet reſiſtentiæ, trãſiret, nec corpus per-
              <lb/>
            tranſitum irradiaret:</s>
            <s xml:id="echoid-s50883" xml:space="preserve"> aliter etiam in ipſo non fieret reflexio uel refractio per 58 huius.</s>
            <s xml:id="echoid-s50884" xml:space="preserve"> Et quoniam
              <lb/>
            per reflexionem radij aggregantur, & ſimiliter per refractionem ex 57 huius:</s>
            <s xml:id="echoid-s50885" xml:space="preserve"> tunc per 56 hu-
              <lb/>
            ius radijs non aggregatis plus ſenſibilis non fieret irradiatio quàm in medio:</s>
            <s xml:id="echoid-s50886" xml:space="preserve"> nunc autem irradia-
              <lb/>
            tio in theoremate ſupponitur:</s>
            <s xml:id="echoid-s50887" xml:space="preserve"> patet ergo quòd oportet corpus irradiandum eſſe denſius quàm ſit
              <lb/>
            corpus propinquum corpori luminoſo.</s>
            <s xml:id="echoid-s50888" xml:space="preserve"> Exemplariter uerò id declarari poteſt per hoc, quod
              <lb/>
            in 37 th.</s>
            <s xml:id="echoid-s50889" xml:space="preserve"> 2 huius oſtendimus.</s>
            <s xml:id="echoid-s50890" xml:space="preserve"> Quia ſi per foramen rotundum penetret radius ſolis:</s>
            <s xml:id="echoid-s50891" xml:space="preserve"> ſtatim in cor-
              <lb/>
            pore oppoſito ad baſim applicatur, & in formam pyramidis lumen figuratur.</s>
            <s xml:id="echoid-s50892" xml:space="preserve"> Signum ergo eſt quòd
              <lb/>
            in quolibet radio corporis luminoſi idem fiat, qui cum ſint naturæ homogeneæ, eadem eſt natura
              <lb/>
            in toto & in parte:</s>
            <s xml:id="echoid-s50893" xml:space="preserve"> & ad minus, ſi illud non ſit neceſſarium ſemper fieri:</s>
            <s xml:id="echoid-s50894" xml:space="preserve"> eſt tamen poſsibile fieri, ut
              <lb/>
            proponitur.</s>
            <s xml:id="echoid-s50895" xml:space="preserve"> Patet ergo intentum.</s>
            <s xml:id="echoid-s50896" xml:space="preserve"/>
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