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 |< < (450) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div1884" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s50516" xml:space="preserve">
              <pb o="450" file="0752" n="752" rhead="VITELLONIS OPTICAE"/>
            morum tranſcurrimus:</s>
            <s xml:id="echoid-s50517" xml:space="preserve"> reſtat, ut refractiones, quæ in medijs accidunt corporibus, aliqualiter per-
              <lb/>
            tractemus, utpote illas, quę in uaporibus medijs occurrunt.</s>
            <s xml:id="echoid-s50518" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1885" type="section" level="0" n="0">
          <head xml:id="echoid-head1384" xml:space="preserve" style="it">56. Non aggregatis radijs corporis luminoſi in corpore non luminoſo plus, quàm in medio: lu-
            <lb/>
          men ſenſibilius fieriest impoßibile.</head>
          <p>
            <s xml:id="echoid-s50519" xml:space="preserve">Quod hic proponitur, patet:</s>
            <s xml:id="echoid-s50520" xml:space="preserve"> quia lato lumine per aliquã partẽ medij, uniformis erit extenſio ra-
              <lb/>
            dij ſecũdũ lineã rectã per 1 th.</s>
            <s xml:id="echoid-s50521" xml:space="preserve"> 2 huius:</s>
            <s xml:id="echoid-s50522" xml:space="preserve"> unde ſi nõ aggregẽtur radij in corpore aliquo occurrẽre ipſis
              <lb/>
            radijs luminis, nõ erit plus ſenſibile lumẽ in illo corpore ꝗ̃ fuerit in alia parte medij:</s>
            <s xml:id="echoid-s50523" xml:space="preserve"> per quã fereba
              <lb/>
            tur ſecũdũ extẽſionẽ ad modũ linearũ rectarũ.</s>
            <s xml:id="echoid-s50524" xml:space="preserve"> Lumine enim æ qualiter lato ք unũ corpus, & aliud,
              <lb/>
            niſi fiat aliqua diuerſitas ipſius luminis:</s>
            <s xml:id="echoid-s50525" xml:space="preserve"> nõ magis in uno ꝗ̃ in alio corpore ſentietur (alijs circũſtan
              <lb/>
            rijs in uiſu & remotione exiſtentibus æqualibus.</s>
            <s xml:id="echoid-s50526" xml:space="preserve">) Quòd ſi fiat diuerſitas luminis in radijs, reſpectu
              <lb/>
            diuerſorum corporum, ut patet per 4 huius:</s>
            <s xml:id="echoid-s50527" xml:space="preserve"> tunc in eo corpore, in quo magis radij diſgregãtur, mi
              <lb/>
            nus luminis apparet.</s>
            <s xml:id="echoid-s50528" xml:space="preserve"> Si ergo in aliquo corpore plus luminis apparebit:</s>
            <s xml:id="echoid-s50529" xml:space="preserve"> neceſſe eſt in illo corpore
              <lb/>
            radios plus aggregari.</s>
            <s xml:id="echoid-s50530" xml:space="preserve"> Patet ergo quòd nõ aggregatis radijs corporis luminoſi in corpore nõ lumi-
              <lb/>
            noſo plus, quàm in medio, lumẽ ſenſibilius fieri in alio corpore, quàm ſit in medio unius diaphani,
              <lb/>
            impoſsibile eſt.</s>
            <s xml:id="echoid-s50531" xml:space="preserve"> Ex quo patet, quòd ſi radij in aliquo corpore plus aggregẽtur quàm in medio, quòd
              <lb/>
            in illo corpore lumen ſenſibilius quàm in medio apparebit:</s>
            <s xml:id="echoid-s50532" xml:space="preserve"> & ſecundum quantitatem aggregatio,
              <lb/>
            nis radiorum lumen uidebitur intendi.</s>
            <s xml:id="echoid-s50533" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1886" type="section" level="0" n="0">
          <head xml:id="echoid-head1385" xml:space="preserve" style="it">57. Radios corporis luminoſi per reflexionem uel refractionem aggregari palàm eſt.</head>
          <p>
            <s xml:id="echoid-s50534" xml:space="preserve">Iſtud patet per hoc.</s>
            <s xml:id="echoid-s50535" xml:space="preserve"> Quoniã cum radius reuerberatur uel reflectitur ab aliquo corpore:</s>
            <s xml:id="echoid-s50536" xml:space="preserve"> tũc quia
              <lb/>
            ք 20 th.</s>
            <s xml:id="echoid-s50537" xml:space="preserve"> 5 huius angulus incidẽtiæ eſt æqualis angulo reflexionis, & radius incidẽs & reflexus ſunt
              <lb/>
            in eadẽ ſuperficie, ut patet ք 27 th.</s>
            <s xml:id="echoid-s50538" xml:space="preserve"> 5 huius:</s>
            <s xml:id="echoid-s50539" xml:space="preserve"> in ſuperficie ergo eadẽ radij duo ad ęquales angulos inci
              <lb/>
            dentes reflectuntur & uniuntur ſic, ut fiant unum:</s>
            <s xml:id="echoid-s50540" xml:space="preserve"> aggregantur ergo, quia duo obtinẽt unum locũ:</s>
            <s xml:id="echoid-s50541" xml:space="preserve">
              <lb/>
            imò uerius fiunt unũ.</s>
            <s xml:id="echoid-s50542" xml:space="preserve"> Verbi gratia, ſit, ut in ſuperficie una reflexionis, quæ ſit a b c, incidãt duo radij
              <lb/>
            à diuerſis partibus diametri corporis luminoſi, ſcilicet a & c ad unum punctum corporis, à quo fit
              <lb/>
            reflexio:</s>
            <s xml:id="echoid-s50543" xml:space="preserve"> quod ſit b:</s>
            <s xml:id="echoid-s50544" xml:space="preserve"> & ſint anguli incidẽtiæ æquales.</s>
            <s xml:id="echoid-s50545" xml:space="preserve"> Producta ergo à puncto b linea in dicta ſuperfi
              <lb/>
            cie ad utramq;</s>
            <s xml:id="echoid-s50546" xml:space="preserve"> partẽ, ſcilicetea, quæ eſt cõmunis ſectio ſuperficiei reflexionis & ſuperficiei corpo-
              <lb/>
            ris, à quo fit reflexio, quæ ſit d b e:</s>
            <s xml:id="echoid-s50547" xml:space="preserve"> erit angulus incidentiæ, qui eſt a b d, æ qualis angulo reflexionis,
              <lb/>
            qui eſt c b e, per 20 th.</s>
            <s xml:id="echoid-s50548" xml:space="preserve"> 5 huius:</s>
            <s xml:id="echoid-s50549" xml:space="preserve"> ſed & ſecundum angulum incidẽtię, qui eſt c b e fit reflexio radij c b:</s>
            <s xml:id="echoid-s50550" xml:space="preserve">
              <lb/>
            ergo radius b a reflexus & radius b incidens efficiuntur
              <lb/>
            unus radius:</s>
            <s xml:id="echoid-s50551" xml:space="preserve"> & radius b c reflexus, radius quoq;</s>
            <s xml:id="echoid-s50552" xml:space="preserve"> a b inci-
              <lb/>
              <figure xlink:label="fig-0752-01" xlink:href="fig-0752-01a" number="882">
                <variables xml:id="echoid-variables859" xml:space="preserve">a c d b e</variables>
              </figure>
            dens efficiuntur unus.</s>
            <s xml:id="echoid-s50553" xml:space="preserve"> Sic aũt eſt de alijs omnibus, qui
              <lb/>
            incidunt ſecundum pyramidem, cuius conus eſt in ali-
              <lb/>
            quo puncto corporis, à quo fit reflexio, & baſis in corpo
              <lb/>
            reluminoſo.</s>
            <s xml:id="echoid-s50554" xml:space="preserve"> Patet ergo quòd ad minus omnes illi radij
              <lb/>
            in ſe duplicãtur.</s>
            <s xml:id="echoid-s50555" xml:space="preserve"> Vnde cum ipſi ſint infiniti, quoniã ſolũ
              <lb/>
            ſunt entes in potẽtia in cõtinuo, & tales pyramides ſunt
              <lb/>
            tot, quot ſunt puncta in corpore, à quo fit reflexio:</s>
            <s xml:id="echoid-s50556" xml:space="preserve"> patet
              <lb/>
            quòd ipſi ք reflexionẽ aggregãtur.</s>
            <s xml:id="echoid-s50557" xml:space="preserve"> Sed & ք refractionẽ in
              <lb/>
            medio ſecũdi diaphani lumẽ aggregari per experiẽtiã ſenſibiliter ad hibitã patere poteſt.</s>
            <s xml:id="echoid-s50558" xml:space="preserve"> Cũenim
              <lb/>
            oſtẽſum ſit qđ in medio ſecũdi diaphani dẽſioris aere à parte oppoſita ſuperficiei incidẽtię ſemper
              <lb/>
            fit radiorum aggregatio, imò cõcurſus in punctum unum, & ibi lumẽ & calorẽ generant:</s>
            <s xml:id="echoid-s50559" xml:space="preserve"> imò quòd
              <lb/>
            ignitionẽ efficiunt in corpore inflammabili, cui immorãtur, ut patet per 48 huius.</s>
            <s xml:id="echoid-s50560" xml:space="preserve"> Refractio itaque
              <lb/>
            lumen generat, quoniã adunat radios.</s>
            <s xml:id="echoid-s50561" xml:space="preserve"> Sed & in ſuperficie, à qua fit refractio, in proſundum corpo-
              <lb/>
            ris denſioris diaphani radius incidens & refractus (qui in medio unius diaphani producti, eſſent li
              <lb/>
            nea una) angulum refractionis conſtituunt:</s>
            <s xml:id="echoid-s50562" xml:space="preserve"> ſuntq́;</s>
            <s xml:id="echoid-s50563" xml:space="preserve"> per 46 th.</s>
            <s xml:id="echoid-s50564" xml:space="preserve"> 2 huius in una ſuperficie, quæ dicitur
              <lb/>
            ſuperficies refractionis, & eſt ſemք orthogonalis ſuper ſuperficiẽ corporis, à quo fit refractio per 2
              <lb/>
            huius:</s>
            <s xml:id="echoid-s50565" xml:space="preserve"> unde tales radij omnes, ſic ſibijpſis incidentes, quando ſunt refracti, uicinantur & aggregan
              <lb/>
            tur, ſecundum diaphani ſecundi diſpoſitionẽ angulo refractionis ad angulum incidẽtiæ ſuæ uaria-
              <lb/>
            to.</s>
            <s xml:id="echoid-s50566" xml:space="preserve"> In groſsiori enim uel denſiori diaphano radius non perpendicularis magis debilitatur:</s>
            <s xml:id="echoid-s50567" xml:space="preserve"> unde ad
              <lb/>
            perpẽdicularẽ uehemẽtius refringitur, & in uiciniorẽ punctum axis cadit:</s>
            <s xml:id="echoid-s50568" xml:space="preserve"> angulus ergo fit acutior
              <lb/>
            angulo incidẽtiæ ſuæ, reſpectu eius, ſi ſecundum idẽ pũctum radius ſubtiliori diaphano incidiſſet.</s>
            <s xml:id="echoid-s50569" xml:space="preserve">
              <lb/>
            Et ob hoc (quoniã angulus ex omnibus refractis radijs cum linea, quę eſt cõmunis ſectio ſuperfi-
              <lb/>
            ciei refractionis, & ſuperficiei corporis, à quo fit refractio, eſt minor in corporibus dẽſioris diapha-
              <lb/>
            ni quàm minus dẽſi) patet quòd in corporibus dẽſioribus & radij plus aggregãtur ꝗ̃ in minus den
              <lb/>
            ſis per 8 huius.</s>
            <s xml:id="echoid-s50570" xml:space="preserve"> Fit itaq;</s>
            <s xml:id="echoid-s50571" xml:space="preserve"> illorum radiorum aggregatio quandoq;</s>
            <s xml:id="echoid-s50572" xml:space="preserve"> propter lucis reflexionẽ ad punctũ
              <lb/>
            unum mathematicum uel naturalẽ, ut in nono libro huius ſcientiæ per ſpecula comburẽtia oſten-
              <lb/>
            dimus fieri aggregationem radiorum, & in alijs libris ubi de talibus ſermo fuit.</s>
            <s xml:id="echoid-s50573" xml:space="preserve"> Fit etiam hæc aggre
              <lb/>
            gatio quandoq;</s>
            <s xml:id="echoid-s50574" xml:space="preserve"> per refractionem:</s>
            <s xml:id="echoid-s50575" xml:space="preserve"> quoniam radij ſecundum æquales angulos incidentes, per 8 hu-
              <lb/>
            ius ſecundum æquales angulos refringuntur:</s>
            <s xml:id="echoid-s50576" xml:space="preserve"> & quandoque concurrunt in puncto uno, ut patet
              <lb/>
            per 48 th.</s>
            <s xml:id="echoid-s50577" xml:space="preserve"> huius.</s>
            <s xml:id="echoid-s50578" xml:space="preserve"> Semper autem in talibus & radij reflexi & refracti quodammodo in eadem parte
              <lb/>
            medij ſe duplicant:</s>
            <s xml:id="echoid-s50579" xml:space="preserve"> unde faciunt maius lumen.</s>
            <s xml:id="echoid-s50580" xml:space="preserve"> Aggregatis autem per refractionem radijs, ut pa-
              <lb/>
            tet ex præmiſsis:</s>
            <s xml:id="echoid-s50581" xml:space="preserve"> tunc in uiſu exiſtente in loco aggregationis lumen generatur.</s>
            <s xml:id="echoid-s50582" xml:space="preserve"> Et quoniam
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum