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-s6552" xml:space="preserve">
              <pb o="112" file="0118" n="118" rhead="ALHAZEN"/>
            ex illis ſumptæ uenit etiã pyramis à luminoſo, quæ quidẽ pyramis cum ſimilibus excluditur in ha
              <gap/>
              <lb/>
            conſideratione.</s>
            <s xml:id="echoid-s6553" xml:space="preserve"> Si uerò elongatio ponderet ſuper aggregationem:</s>
            <s xml:id="echoid-s6554" xml:space="preserve"> erit lux puncti politi minor luce
              <lb/>
            ſola unius lineæ ſumpta:</s>
            <s xml:id="echoid-s6555" xml:space="preserve"> & ſi aggre gatio plus ponderet elongatione:</s>
            <s xml:id="echoid-s6556" xml:space="preserve"> erit fortior.</s>
            <s xml:id="echoid-s6557" xml:space="preserve"> Luces aũt, quę à lu
              <lb/>
            minoſo ad ſpeculũ accedunt ſuper lineas æquidiſtantes:</s>
            <s xml:id="echoid-s6558" xml:space="preserve"> erunt debiliores, quàm modo alio acceden
              <lb/>
            tes:</s>
            <s xml:id="echoid-s6559" xml:space="preserve"> quoniã debilitatę propter elon gationẽ non aggregantur in ſpeculũ, ſed in reflexione per lineas
              <lb/>
            æquidiſtantes mouentur:</s>
            <s xml:id="echoid-s6560" xml:space="preserve"> unde per reflexionẽ & elongationẽ debilitantur.</s>
            <s xml:id="echoid-s6561" xml:space="preserve"> Et ſi aggregentur in re-
              <lb/>
            flexione:</s>
            <s xml:id="echoid-s6562" xml:space="preserve"> conferetur eis fortitudo comparata ad fortitudinem, quam habuerunt in ſpeculo, ſecun-
              <lb/>
            dum poſſe aggregans ſuper reflexionem & elongationem.</s>
            <s xml:id="echoid-s6563" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div230" type="section" level="0" n="0">
          <head xml:id="echoid-head261" xml:space="preserve" style="it">16. Lux & color reflectuntur per line{as} phyſic{as}, latitudine quadam prędit{as}. 3 p 2.6 p 5.</head>
          <p>
            <s xml:id="echoid-s6564" xml:space="preserve">AMplius.</s>
            <s xml:id="echoid-s6565" xml:space="preserve"> Omnis linea, per quã mouetur lux à corpore luminoſo ad corpus oppoſitũ, eſt linea
              <lb/>
            ſenſualis, non ſine latitudine.</s>
            <s xml:id="echoid-s6566" xml:space="preserve"> Lux enim nõ procedit, niſi à corpore, quoniã non eſt, niſi in cor
              <lb/>
            pore:</s>
            <s xml:id="echoid-s6567" xml:space="preserve"> ſed in minore luce, quæ ſumi poteſt, eſt latitudo, & in linea proceſſus eius eſt latitudo:</s>
            <s xml:id="echoid-s6568" xml:space="preserve">
              <lb/>
            & in medio illius lineæ ſenſualis, eſt linea intellectualis, & aliæ eius lineæ ſunt æquidιſtantes illi.</s>
            <s xml:id="echoid-s6569" xml:space="preserve"> Et
              <lb/>
            ſi diuidatur minor ex lucibus:</s>
            <s xml:id="echoid-s6570" xml:space="preserve"> neutra eius pars erit lux, ſed utraq, extinguetur, nec apparebit.</s>
            <s xml:id="echoid-s6571" xml:space="preserve"> Si aũt
              <lb/>
            lux minima doplicetur, aut amplius multiplicetur, & cõpacta per æqualιa diuidatur:</s>
            <s xml:id="echoid-s6572" xml:space="preserve"> erit lux utraq;</s>
            <s xml:id="echoid-s6573" xml:space="preserve">
              <lb/>
            pars eius:</s>
            <s xml:id="echoid-s6574" xml:space="preserve"> Si uerò per inæqualia fiat diuiſio:</s>
            <s xml:id="echoid-s6575" xml:space="preserve"> erit altera pars eius lux, altera minime.</s>
            <s xml:id="echoid-s6576" xml:space="preserve"> Lux aũt minima
              <lb/>
            procedit in minimã corporis partem, quã lux occupare poſsit, & proceſſus eius eſt ſecundum lineã
              <lb/>
            intellectualem, lineæ ſenſualis mediam, & extremitates ei æquidiſtantes.</s>
            <s xml:id="echoid-s6577" xml:space="preserve"> Et cadit lux minima non
              <lb/>
            in punctũ corporis intelligibile, ſed ſenſibile, & reflectitur per lineam ſenſibilem, cuius latitudo eſt
              <lb/>
            æqualis latitudini lineę ſenſibilis ueniẽtis.</s>
            <s xml:id="echoid-s6578" xml:space="preserve"> Et ſi intelligatur in linea ſinſibili, linea reflexa intellectua
              <lb/>
            lis media:</s>
            <s xml:id="echoid-s6579" xml:space="preserve"> eundẽ habebit ſitũ ſuper reflexiõis locũ, quẽ habet linea intelligιbιlis media, lineę ſenſibi-
              <lb/>
            lis ueniẽtis.</s>
            <s xml:id="echoid-s6580" xml:space="preserve"> Et quęlibet linea intellectualis in linea reflexa ſenſibili eundẽ penitus obſeruat ſitũ cũ li
              <lb/>
            nea intell gibili alterius lineę ſenſibilis, ipſã reſpiciẽte.</s>
            <s xml:id="echoid-s6581" xml:space="preserve"> Obſeruatur ergo in omniluce ratio linearũ
              <lb/>
            & punctorũ intellectorũ, licet ab eis aut per ipſas nõ procedat lux:</s>
            <s xml:id="echoid-s6582" xml:space="preserve"> & in hũc modũ erit reflexio lucis.</s>
            <s xml:id="echoid-s6583" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div231" type="section" level="0" n="0">
          <head xml:id="echoid-head262" xml:space="preserve" style="it">17. Reflexio lucis & coloris à ſuperficie aſper a facta, plerun fugit uiſum. 1 p 5.</head>
          <p>
            <s xml:id="echoid-s6584" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s6585" xml:space="preserve"> quare ex politis corporibus, non ex aſperis fiat reflexio:</s>
            <s xml:id="echoid-s6586" xml:space="preserve"> eſt:</s>
            <s xml:id="echoid-s6587" xml:space="preserve"> Quoniã lux, ut diximus,
              <lb/>
            non accedit ad corpus, niſi per motum citiſsimũ, & cum peruenerit ad politũ:</s>
            <s xml:id="echoid-s6588" xml:space="preserve"> eijcit eam po-
              <lb/>
            litum à ſe:</s>
            <s xml:id="echoid-s6589" xml:space="preserve"> corpus uerò aſperum non poteſt eam eijcere:</s>
            <s xml:id="echoid-s6590" xml:space="preserve"> quoniã in corpore aſpero ſunt pori,
              <lb/>
            quos lux ſubintrat:</s>
            <s xml:id="echoid-s6591" xml:space="preserve"> in polιtis aũt non inuenit poros, nec accidit eiectio hæc, propter corporis forti-
              <lb/>
            tudinẽ uel duriciem, quia uidemus in aqua reflexionẽ:</s>
            <s xml:id="echoid-s6592" xml:space="preserve"> ſed eſt hæc repulſio propria politurę:</s>
            <s xml:id="echoid-s6593" xml:space="preserve"> ſicut de
              <lb/>
            natura accidit, quod aliquid poroſum cadens ab alto ſuper lapidẽ durum, reuertitur in altũ:</s>
            <s xml:id="echoid-s6594" xml:space="preserve"> & quan
              <lb/>
            tò minor fuerit duricies lapidis, in quẽ ceciderit, tantò regreſsio cadentis debilior erit:</s>
            <s xml:id="echoid-s6595" xml:space="preserve"> & ſemper re
              <lb/>
            greditur cadens uerſus partẽ, à qua proceſsit:</s>
            <s xml:id="echoid-s6596" xml:space="preserve"> Verũ in arena propter eius mollitiẽ non fit regreſsio,
              <lb/>
            quæ accidit in corpore duro.</s>
            <s xml:id="echoid-s6597" xml:space="preserve"> Si aũt in poris aſperi corporis ſit politio:</s>
            <s xml:id="echoid-s6598" xml:space="preserve"> tamen lux intrans poros nõ
              <lb/>
            reflectitur:</s>
            <s xml:id="echoid-s6599" xml:space="preserve"> & ſi eam reflecti acciderit, diſpergitur, & propter diſperſionem à uiſu nõ percιpitur.</s>
            <s xml:id="echoid-s6600" xml:space="preserve"> Pari
              <lb/>
            modo ſi in aſpero corpore partes elatiores fuerint politæ:</s>
            <s xml:id="echoid-s6601" xml:space="preserve"> fiet reflexa diſperſio:</s>
            <s xml:id="echoid-s6602" xml:space="preserve"> & ob hoc occultabi-
              <lb/>
            tur uiſui.</s>
            <s xml:id="echoid-s6603" xml:space="preserve"> Si uerò eminentia partiũ adeò ſit modica, ut eius quaſi ſit idem ſitus cũ depreſsis:</s>
            <s xml:id="echoid-s6604" xml:space="preserve"> compre-
              <lb/>
            hendetur eius reflexio tan quam in polito, non aſpero, licet minus perfectè.</s>
            <s xml:id="echoid-s6605" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div232" type="section" level="0" n="0">
          <head xml:id="echoid-head263" xml:space="preserve" style="it">18. Radij incidentiæ & reflexionis, ſit{us} ſimilitudine conueniunt. Ita anguli incidentiæ &
            <lb/>
          reflexionis æquantur. 20 p 5.</head>
          <p>
            <s xml:id="echoid-s6606" xml:space="preserve">QVare aũt fiat reflexio lucis ſecundum lineam eiuſdem ſitus cum linea, per quã accedit ad ſpe
              <lb/>
            culũ ipſa lux:</s>
            <s xml:id="echoid-s6607" xml:space="preserve"> eſt:</s>
            <s xml:id="echoid-s6608" xml:space="preserve"> Quoniã lux motu citiſsimo mouetur:</s>
            <s xml:id="echoid-s6609" xml:space="preserve"> & quando cadit in ſpeculũ, nõ recipi
              <lb/>
            tur:</s>
            <s xml:id="echoid-s6610" xml:space="preserve"> ſed ei fixio in corpore illo negatur:</s>
            <s xml:id="echoid-s6611" xml:space="preserve"> & cũ in ea perſeueret adhuc prioris motus uis & na-
              <lb/>
            tura, reflectitur ad partẽ, à qua proceſsit, & ſecundũ lineas eundẽ ſitũ cũ prioribus habentes.</s>
            <s xml:id="echoid-s6612" xml:space="preserve"> Huius
              <lb/>
            aũt rei ſimile in naturalibus motibus uidere poſſumus, & etiã in accidentalibus.</s>
            <s xml:id="echoid-s6613" xml:space="preserve"> Si corpus ſphæricũ
              <lb/>
            ponderoſum ab aliqua altitudine deſcendere permittamus perpendiculariter ſuper politũ corpus:</s>
            <s xml:id="echoid-s6614" xml:space="preserve">
              <lb/>
            uide bimus ipſum ſuper perpendicularẽ reflecti, per quã deſcenderat.</s>
            <s xml:id="echoid-s6615" xml:space="preserve"> In accidentali motu.</s>
            <s xml:id="echoid-s6616" xml:space="preserve"> Si eleue-
              <lb/>
            tur aliquod ſpeculum ſecundum aliquã altitudinẽ hominis, & firmiter in pariete figatur:</s>
            <s xml:id="echoid-s6617" xml:space="preserve"> & in acu-
              <lb/>
            mine ſagittæ cõſolidetur corpus ſphæricũ:</s>
            <s xml:id="echoid-s6618" xml:space="preserve"> & proijciatur ſagitta per arcum in ſpeculũ hoc modo, ut
              <lb/>
            eleuatio ſagittę ſit æqualis eleuationi ſpeculi, & ſit ſagitta æquidiſtans horizonti:</s>
            <s xml:id="echoid-s6619" xml:space="preserve"> planũ, quòd ſuper
              <lb/>
            perpendicularẽ accedit ſagitta ad ſpeculũ, & uidebitur ſuper eandẽ perpendicularẽ eius regreſſus.</s>
            <s xml:id="echoid-s6620" xml:space="preserve">
              <lb/>
            Si uerò motus ſagittæ fuerit ſuper lineam declinatã in ipſum, uidebitur reflecti non per lineam, per
              <lb/>
            quam uenerat, ſed per lineam æquidiſtantẽ horizonti, ſicut & alia erat, & eiuſdẽ ſitus, reſpectu ſpe-
              <lb/>
            culi cum ea, & reſpectu' perpendicularis in ſpeculo.</s>
            <s xml:id="echoid-s6621" xml:space="preserve"> Quòd aũt ex prohibitione corporis politi acci-
              <lb/>
            dat luci motus reflexionis, palàm:</s>
            <s xml:id="echoid-s6622" xml:space="preserve"> quia cum fortior fuerit repulſio uel prohibitio, fortior erit lucis re
              <lb/>
            flexio.</s>
            <s xml:id="echoid-s6623" xml:space="preserve"> Quare aũt accidat idem motus reflexionis & eius acceſſus, hæc eſt ratio.</s>
            <s xml:id="echoid-s6624" xml:space="preserve"> Cum deſcendit cor
              <lb/>
            pus ponderoſum ſuper perpendicularẽ:</s>
            <s xml:id="echoid-s6625" xml:space="preserve"> repulſio corporis politi, & motus deſcendentis ponderoſi
              <lb/>
            directè ſibi ſunt oppoſiti, nec eſt ibi motus, niſi perpendicularis:</s>
            <s xml:id="echoid-s6626" xml:space="preserve"> & prohibitio fit per perpendicula-
              <lb/>
            rem:</s>
            <s xml:id="echoid-s6627" xml:space="preserve"> quare repellitur corpus ſecundum perpendicularẽ.</s>
            <s xml:id="echoid-s6628" xml:space="preserve"> Vnde perpendiculariter regreditur.</s>
            <s xml:id="echoid-s6629" xml:space="preserve"> Cum
              <lb/>
            uerò deſcenderit corpus ſuper lineam declinatã:</s>
            <s xml:id="echoid-s6630" xml:space="preserve"> cadit quidem linea deſcenſus inter perpendicula-
              <lb/>
            rem ſuperficiei politi, per ipſum politum tranſeuntẽ, & lineam ſuperficiei eius orthogonalem ſuper
              <lb/>
            </s>
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