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-div1886" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s50582" xml:space="preserve">
              <pb o="451" file="0753" n="753" rhead="LIBER DECIMVS."/>
            in corporibus diaphanis ſuperficiem lenem habentibus, denſioribus aere propter lenitatem ſuper-
              <lb/>
            ficiei lumen incidens ab ipſis reflectitur, ut oſtendimus per 1 th.</s>
            <s xml:id="echoid-s50583" xml:space="preserve"> 5 huius:</s>
            <s xml:id="echoid-s50584" xml:space="preserve"> tunc patet quòd propterre
              <lb/>
            flexionem lumen aggregatur:</s>
            <s xml:id="echoid-s50585" xml:space="preserve"> & item quia in illis corporibus propter diuerſitatem dẽſioris diapha
              <lb/>
            ni fit luminis refractio ad perpendicularem intra corpus, ut patet per 4 huius:</s>
            <s xml:id="echoid-s50586" xml:space="preserve"> tunc in peripheria cu
              <lb/>
            iuslibet ſuperficiei refraction is propter acutum angulum refractionis ipſis adinuicem radijs uici-
              <lb/>
            natis fortificatur ſenſibilitas luminis.</s>
            <s xml:id="echoid-s50587" xml:space="preserve"> Quando ergo ſuperficies talium corporum ſunt lenes, ut po-
              <lb/>
            litæ per naturam:</s>
            <s xml:id="echoid-s50588" xml:space="preserve"> tunc licet in ipſis fiat refractio:</s>
            <s xml:id="echoid-s50589" xml:space="preserve"> ab eorum tamen ſuperficie fit etiam reflexio radio
              <lb/>
            rum, licet debiliter.</s>
            <s xml:id="echoid-s50590" xml:space="preserve"> Et propter hoc duabus his cauſsis concurrentibus, in ſuperficie corporũ taliũ
              <lb/>
            lumẽ aggregatur, & apparẽt corpora plurimũ luminoſa:</s>
            <s xml:id="echoid-s50591" xml:space="preserve"> quáuis magis dẽſa magis appareát lumino
              <lb/>
            ſa.</s>
            <s xml:id="echoid-s50592" xml:space="preserve"> Non ſunt aũt modi alij aggregationis radiorum, quá reflexio & refractio:</s>
            <s xml:id="echoid-s50593" xml:space="preserve"> ad hos enim, ut ad pri-
              <lb/>
            mos, ſi qui alij modi apparuerint, radicaliter reducuntur.</s>
            <s xml:id="echoid-s50594" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s50595" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1888" type="section" level="0" n="0">
          <head xml:id="echoid-head1386" xml:space="preserve" style="it">58. Sine oppoſitione corporis denſioris, quàm ſit medium proximum radijs corporis lumino-
            <lb/>
          ſi: ipſorum radiorum reflexionem uel refractionem uel maiorem ſenſibιlitatem impoßibile
            <lb/>
          eſt fieri.</head>
          <p>
            <s xml:id="echoid-s50596" xml:space="preserve">Iſtud patet per hoc.</s>
            <s xml:id="echoid-s50597" xml:space="preserve"> Quoniá enim radij cuiuslibet corporis radioſi ſunt in ſe ſemper luminoſi &
              <lb/>
            uniformes:</s>
            <s xml:id="echoid-s50598" xml:space="preserve"> ſi ergo medium, per quod feruntur, ſit uniforme:</s>
            <s xml:id="echoid-s50599" xml:space="preserve"> nunquá reflectentur uel refringentur,
              <lb/>
            ſed ſemper ferentur in continuum & directum, ut patet per 1 th.</s>
            <s xml:id="echoid-s50600" xml:space="preserve"> 2 huius:</s>
            <s xml:id="echoid-s50601" xml:space="preserve"> nec lumen propter eorum
              <lb/>
            diſperſionem aggregabitur, ut uincat lumen, quod ex æquali diffuſione luminis receptum eſt in o-
              <lb/>
            culo uidentis.</s>
            <s xml:id="echoid-s50602" xml:space="preserve"> Nec etiam ad uiſum fiet reflexio, nec refractio in partem oppoſitam ad axem pyrami
              <lb/>
            dis uiſualis:</s>
            <s xml:id="echoid-s50603" xml:space="preserve"> nec lumen uel ſenſibilitas luminis maior efficietur.</s>
            <s xml:id="echoid-s50604" xml:space="preserve"> Patet ergo propoſitum, quòd ſine
              <lb/>
            oppoſitione corporis denſioris, quá ſit primũ medium, per quod fertur radius corporis luminoſi, i-
              <lb/>
            pſorum radiorum reflexionem uel refractionem fieri nõ eſt poſsibile:</s>
            <s xml:id="echoid-s50605" xml:space="preserve"> quoniam omnis reflexio uel
              <lb/>
            refractio ſemper fit ab aliquo talium corporum, ut eſt habitum expræmiſsis.</s>
            <s xml:id="echoid-s50606" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1889" type="section" level="0" n="0">
          <head xml:id="echoid-head1387" xml:space="preserve" style="it">59. Quantitatem arcus circuli magniterræ, ſecundum quem illuminatur à ſole, poßibile est
            <lb/>
          declarari. Alhazen 5 n libride crepuſculis.</head>
          <p>
            <s xml:id="echoid-s50607" xml:space="preserve">Suppoſito ex his, quę alibi declarata ſunt per antiquos & nos, quòd corpus ſolis ſit maius corpo
              <lb/>
            re terræ:</s>
            <s xml:id="echoid-s50608" xml:space="preserve"> palàm per 27 th.</s>
            <s xml:id="echoid-s50609" xml:space="preserve"> 2 huius quoniam ſol
              <lb/>
            aſpicit terram ſecundum ſuperficiẽ terræ maio-
              <lb/>
            rem medietate ſuperficiei ipſius terrę.</s>
            <s xml:id="echoid-s50610" xml:space="preserve"> Sit itaq;</s>
            <s xml:id="echoid-s50611" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0753-01" xlink:href="fig-0753-01a" number="883">
                <variables xml:id="echoid-variables860" xml:space="preserve">g f k h d c e a b</variables>
              </figure>
            circulus, ſecundum quem terra illuminatur à ſo
              <lb/>
            le, qui b c d e, cuius centrum ſit a:</s>
            <s xml:id="echoid-s50612" xml:space="preserve"> & ſit circulus
              <lb/>
            maior ſolaris corporis, qui g h:</s>
            <s xml:id="echoid-s50613" xml:space="preserve"> cuius centrum
              <lb/>
            ſit f:</s>
            <s xml:id="echoid-s50614" xml:space="preserve"> ducanturq́;</s>
            <s xml:id="echoid-s50615" xml:space="preserve"> lineæ contingentes utrunq;</s>
            <s xml:id="echoid-s50616" xml:space="preserve"> ho
              <lb/>
            rum circulorum:</s>
            <s xml:id="echoid-s50617" xml:space="preserve"> quę ſint b h & e g.</s>
            <s xml:id="echoid-s50618" xml:space="preserve"> Portio itaq;</s>
            <s xml:id="echoid-s50619" xml:space="preserve">
              <lb/>
            b c d e terræ eſt illuminata à ſole, quæ eſt maior
              <lb/>
            hemiſphærio.</s>
            <s xml:id="echoid-s50620" xml:space="preserve"> Ducantur itaq;</s>
            <s xml:id="echoid-s50621" xml:space="preserve"> lineæ a b & f h:</s>
            <s xml:id="echoid-s50622" xml:space="preserve">
              <lb/>
            quæ erunt ęquidiſtantes per 28 p 1:</s>
            <s xml:id="echoid-s50623" xml:space="preserve"> quoniam u-
              <lb/>
            traq;</s>
            <s xml:id="echoid-s50624" xml:space="preserve"> ipſarum eſt perpendicularis ſuper lineam
              <lb/>
            b h utroſque circulos contingentem per 18 p 3.</s>
            <s xml:id="echoid-s50625" xml:space="preserve">
              <lb/>
            Et quoniá linea h f eſt maior quàm linea b a (ut
              <lb/>
            patet ex ſuppoſitis) reſecetur à linea f h ęqualis
              <lb/>
            lineæ a b per 3 p 1:</s>
            <s xml:id="echoid-s50626" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s50627" xml:space="preserve"> h k æqualis ipſi a b:</s>
            <s xml:id="echoid-s50628" xml:space="preserve"> & du
              <lb/>
            catur linea a k:</s>
            <s xml:id="echoid-s50629" xml:space="preserve"> eritq́ue per 33 p 1 linea a k æqui-
              <lb/>
            diſtans lineæ h b:</s>
            <s xml:id="echoid-s50630" xml:space="preserve">ergo linea a k eſt perpendicu-
              <lb/>
            laris ſuper lineam f h.</s>
            <s xml:id="echoid-s50631" xml:space="preserve"> Et quia linea f h eſt 5 par-
              <lb/>
            tes & medietas partis ferè, ſecundũ quod linea
              <lb/>
            a b eſt pars una, ut demonſtratum eſt in Aſtro-
              <lb/>
            nomicis:</s>
            <s xml:id="echoid-s50632" xml:space="preserve"> remanet linea k f 4 partes & media.</s>
            <s xml:id="echoid-s50633" xml:space="preserve">
              <lb/>
            Per eandem quoq;</s>
            <s xml:id="echoid-s50634" xml:space="preserve"> uiam aſtronomicam oſten-
              <lb/>
            ſum eſt, quòd ſecundum quantitatem, qua ſemi
              <lb/>
            diameter terræ eſt pars una, linea a f eſt partes
              <lb/>
            12 10:</s>
            <s xml:id="echoid-s50635" xml:space="preserve"> cum ſit diftantia ſolis à terra in medijs lon
              <lb/>
            gitudinibus eius.</s>
            <s xml:id="echoid-s50636" xml:space="preserve"> Si ergo ſecundum quantita-
              <lb/>
            tem, qua linea a f eſt 12 10 partes, linea f k eſt 4
              <lb/>
            partes, & medietas partis:</s>
            <s xml:id="echoid-s50637" xml:space="preserve"> erit ſecundum quan-
              <lb/>
            titatem, qua linea a f eſt 120 partes, linea f k 29
              <lb/>
            minuta, 12 ſecunda:</s>
            <s xml:id="echoid-s50638" xml:space="preserve"> & ſecundũ quantitatẽ qua
              <lb/>
            linea a f eſt 60 partes, linea f k eſt 14 minuta,
              <lb/>
            & 36 ſecunda.</s>
            <s xml:id="echoid-s50639" xml:space="preserve"> Circumſcripto ergo circulo illi
              <lb/>
            trigono orthogonio, qui eſt f k a, per 5 p 4:</s>
            <s xml:id="echoid-s50640" xml:space="preserve"> erit
              <lb/>
            arcus, quem ſubtendit chorda f k quaſi 13 minuta, & 56 ſecunda:</s>
            <s xml:id="echoid-s50641" xml:space="preserve"> ergo per 33 p 6 erit angulus k a f 13
              <lb/>
            minuta, & 56 ſecunda, ſecundum quòd angulus rectus eſt 90 partes:</s>
            <s xml:id="echoid-s50642" xml:space="preserve"> arcus ergo c d erit 13 minuta,
              <lb/>
            </s>
          </p>
        </div>
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