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-div226" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s6462" xml:space="preserve">
              <pb o="111" file="0117" n="117" rhead="OPTICAE LIBER IIII."/>
            per ipſum:</s>
            <s xml:id="echoid-s6463" xml:space="preserve"> & declinato capite regulæ:</s>
            <s xml:id="echoid-s6464" xml:space="preserve"> erit reflexio ſuper perpendicularẽ annuli, ſicut dictũ eſt in pla
              <lb/>
            no.</s>
            <s xml:id="echoid-s6465" xml:space="preserve"> In ſpeculo pyramidali concauo eadẽ in omnibus probatio.</s>
            <s xml:id="echoid-s6466" xml:space="preserve"> In ſpeculo ſphęrico exteriori palàm,
              <lb/>
            quòd mediũ eius punctũ eſt in ſuperficie regulæ, & axis cadit in punctũ illud:</s>
            <s xml:id="echoid-s6467" xml:space="preserve"> & erit in eo idẽ ſitus li
              <lb/>
            nearum & aliorũ penitus, qui in plano:</s>
            <s xml:id="echoid-s6468" xml:space="preserve"> & eadem demonſtratio.</s>
            <s xml:id="echoid-s6469" xml:space="preserve"> In ſpeculo ſphærico cõcauo iam de-
              <lb/>
            claratum eſt, [9 n] quòd axis foraminis deſcendat ad punctum eius mediũ, & acumen tabulæ æneę
              <lb/>
            tranſeat per foramẽ in ſpeculo iam factũ, uſq;</s>
            <s xml:id="echoid-s6470" xml:space="preserve"> dum ſit in eadem ſuperficie cum puncto illo medio:</s>
            <s xml:id="echoid-s6471" xml:space="preserve"> &
              <lb/>
            linea à puncto illo ad acumen protracta, eſt æquidiſtans mediæ lineę longitudinis regulæ.</s>
            <s xml:id="echoid-s6472" xml:space="preserve"> Et ita de-
              <lb/>
            ſcenſus & reflexio ſunt in eadẽ ſuperficie, orthogonali ſuper ſuperficiem contingentẽ ſpeculũ in illo
              <lb/>
            puncto mediò, & æquidiſtantẽ ſuperficiei regulę.</s>
            <s xml:id="echoid-s6473" xml:space="preserve"> Et eadem probatio penitus, quę in alijs.</s>
            <s xml:id="echoid-s6474" xml:space="preserve"> Planũ er-
              <lb/>
            go, quòd omnis lux, in quodcunq;</s>
            <s xml:id="echoid-s6475" xml:space="preserve"> horum ſpeculorũ ceciderit, reflexio & deſcenſus ſunt in eadẽ ſu-
              <lb/>
            perficie orthogonali.</s>
            <s xml:id="echoid-s6476" xml:space="preserve"> Hic aũt modus reflexionis non accidit ex proprietate axis uel puncti, in quod
              <lb/>
            cadit:</s>
            <s xml:id="echoid-s6477" xml:space="preserve"> uel foraminis, per quod intrat:</s>
            <s xml:id="echoid-s6478" xml:space="preserve"> uel ꝓprietate ſpeculi.</s>
            <s xml:id="echoid-s6479" xml:space="preserve"> Accidit enim in quolibet foramine, quæ-
              <lb/>
            cunq;</s>
            <s xml:id="echoid-s6480" xml:space="preserve"> ſit lux, & per quamcunq;</s>
            <s xml:id="echoid-s6481" xml:space="preserve"> lineã deſcendat, & in quodcunq;</s>
            <s xml:id="echoid-s6482" xml:space="preserve"> ſpeculi punctũ cadat.</s>
            <s xml:id="echoid-s6483" xml:space="preserve"> Quoniã quo-
              <lb/>
            cunq;</s>
            <s xml:id="echoid-s6484" xml:space="preserve"> puncto ſpeculi ſumpto, ſi lux in ipſum deſcendat, cũ idem ſit ei ſitus, reſpectu longitudinis ſpe
              <lb/>
            culi, & cuicunq;</s>
            <s xml:id="echoid-s6485" xml:space="preserve"> alij:</s>
            <s xml:id="echoid-s6486" xml:space="preserve"> erunt ſimiliter ijdem reſpectu linearũ ab eo protractarũ, quæ eiuſdẽ ſunt decli-
              <lb/>
            nationis cũ lineis à puncto priore intellectis, ſicut puncto priori uel cuicunq;</s>
            <s xml:id="echoid-s6487" xml:space="preserve"> alij.</s>
            <s xml:id="echoid-s6488" xml:space="preserve"> Et generaliter idẽ
              <lb/>
            eſt ſitus cuilibet puncto, in quod cadit lux, qui & in priore ſumpto, & reſpectu axis & reſpectu acu-
              <lb/>
            minis tabulæ æneę:</s>
            <s xml:id="echoid-s6489" xml:space="preserve"> & eadem in omnibus probatio, & ſimilis demonſtratio.</s>
            <s xml:id="echoid-s6490" xml:space="preserve"> Vnde eſt certũ, non eſſe
              <lb/>
            hoc ex proprietate lucis uel figura alicuius ſpeculi, ſed ex proprietate quadam communi rei politæ
              <lb/>
            & cuilibet luci.</s>
            <s xml:id="echoid-s6491" xml:space="preserve"> Si autem per diuerſa in quodcunq;</s>
            <s xml:id="echoid-s6492" xml:space="preserve"> punctum deſcenderit lux foramina, uidebitur re
              <lb/>
            flexio diuerſa, & angulorum diuerſitas ſuo deſcenſui conſona:</s>
            <s xml:id="echoid-s6493" xml:space="preserve"> & ſic in omnibus.</s>
            <s xml:id="echoid-s6494" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div228" type="section" level="0" n="0">
          <head xml:id="echoid-head259" xml:space="preserve" style="it">14. Inter uiſibile & ſpeculũ innumer abiles pyramides fiũt alternis baſib. & uerticib{us}. 22 p 5.</head>
          <p>
            <s xml:id="echoid-s6495" xml:space="preserve">MAnifeſtũ aũt ex ſuperioribus [2.</s>
            <s xml:id="echoid-s6496" xml:space="preserve">3 n] quòd ſi corpus politum opponatur corpori luminoſo:</s>
            <s xml:id="echoid-s6497" xml:space="preserve">
              <lb/>
            cadet in quodlibet punctũ eius lux à quolibet puncto luminoſi:</s>
            <s xml:id="echoid-s6498" xml:space="preserve"> unde ſuper quodlibet politi
              <lb/>
            punctũ cadit pyramis, cuius acumẽ in eo, & ſuperficies luminoſi eſt baſis:</s>
            <s xml:id="echoid-s6499" xml:space="preserve"> & à quolibet pun
              <lb/>
            cto luminoſi procedit pyramis, cuius acumẽ in eo, & baſis ſuperficies politi.</s>
            <s xml:id="echoid-s6500" xml:space="preserve"> Si aũt inter luminoſum
              <lb/>
            & politũ intelligatur punctũ aliquod:</s>
            <s xml:id="echoid-s6501" xml:space="preserve"> ueniet quidẽ ad illud punctũ lux luminoſi, in modum pyrami
              <lb/>
            dis, cuius acumen in puncto, & latera huius pyramidis procedentia, uſq;</s>
            <s xml:id="echoid-s6502" xml:space="preserve"> dum cadant in ſuperficiem
              <lb/>
            politi, pyramidẽ efficiunt.</s>
            <s xml:id="echoid-s6503" xml:space="preserve"> Vnde in puncto intellecto erunt acumina duarũ pyramidũ, quarũ baſes
              <lb/>
            ſunt ſuperficies luminoſi & politi.</s>
            <s xml:id="echoid-s6504" xml:space="preserve"> Et ſi ad punctũ quodcũq;</s>
            <s xml:id="echoid-s6505" xml:space="preserve"> intermediũ intelligatur pyramis, cuius
              <lb/>
            baſis ſuperficies politi, & procedant huius pyramidis lineę:</s>
            <s xml:id="echoid-s6506" xml:space="preserve"> illud, quod occupabunt ex ſuperficie lu
              <lb/>
            minoſi, hoc eſt, à quo procedebat lux ad politũ:</s>
            <s xml:id="echoid-s6507" xml:space="preserve"> erit ſecun dũ duas pyramides, quarũ acumina ſunt in
              <lb/>
            puncto intellecto:</s>
            <s xml:id="echoid-s6508" xml:space="preserve"> & quicquid procedit lucis in his duabus pyramidibus, procedit & includitur in
              <lb/>
            duabus primis pyramidibus.</s>
            <s xml:id="echoid-s6509" xml:space="preserve"> Et à luminoſo ſecundũ lineas æquidiſtantes procedit lux ad ſpeculũ:</s>
            <s xml:id="echoid-s6510" xml:space="preserve">
              <lb/>
            ſed hæ lineę includuntur in duabus primis pyramidibus:</s>
            <s xml:id="echoid-s6511" xml:space="preserve"> & per quaſcũq;</s>
            <s xml:id="echoid-s6512" xml:space="preserve"> lineas mouetur lux ad ſpe
              <lb/>
            culũ:</s>
            <s xml:id="echoid-s6513" xml:space="preserve"> obſeruant lineę reflexionis eundẽ penitus ſitum, quẽ habebant lineæ motus lucis.</s>
            <s xml:id="echoid-s6514" xml:space="preserve"> Vnde ſi mo
              <lb/>
            ueatur lux per æquidiſtantes, reflectitur per æquidiſtantes:</s>
            <s xml:id="echoid-s6515" xml:space="preserve"> & lux cadẽs in politũ, ad modũ pyrami-
              <lb/>
            dis reflectitur, obſeruãs modũ eiuſdem pyramidis.</s>
            <s xml:id="echoid-s6516" xml:space="preserve"> Et cũ deſcendit lux à corpore luminoſo per fora
              <lb/>
            men aliquod ad corpus politũ:</s>
            <s xml:id="echoid-s6517" xml:space="preserve"> ſi in ſuperficie foraminis ex parte luminoſi intelligatur pũctũ, à quo
              <lb/>
            puncto intelligãtur duę pyramides, baſis unius in luminoſo, alterius in polito:</s>
            <s xml:id="echoid-s6518" xml:space="preserve"> à ſola baſi pyramidis,
              <lb/>
            cuius luminoſum baſis:</s>
            <s xml:id="echoid-s6519" xml:space="preserve"> uenit lux ad politũ ſuper illud punctũ.</s>
            <s xml:id="echoid-s6520" xml:space="preserve"> Similiter ſi in ſuperficie foraminis
              <lb/>
            ex parte politi intelligatur punctũ, in quo acumina duarũ pyramidum, unius ad ſpeculũ, alterius ad
              <lb/>
            luminoſum:</s>
            <s xml:id="echoid-s6521" xml:space="preserve"> à ſola baſi pyramidis, quę baſis eſt in luminoſo, accedit lux ad ſpeculum ſuper hoc pun-
              <lb/>
            ctum:</s>
            <s xml:id="echoid-s6522" xml:space="preserve"> & à parte luminoſi his duabus pyramidibus cõmunis, accedit lux ad partẽ ſpeculi communẽ
              <lb/>
            duabus pyramidibus.</s>
            <s xml:id="echoid-s6523" xml:space="preserve"> Venit etiã lux à luminoſo ad ſpeculũ per lineas ęquidiſtãtes:</s>
            <s xml:id="echoid-s6524" xml:space="preserve"> ſed per quaſcũq;</s>
            <s xml:id="echoid-s6525" xml:space="preserve">
              <lb/>
            accedat:</s>
            <s xml:id="echoid-s6526" xml:space="preserve"> fit reflexio modo prædicto:</s>
            <s xml:id="echoid-s6527" xml:space="preserve"> & quælibet lineę reflexionis obſeruant ſitum linearum deſcen
              <lb/>
            ſus lucis eas reſpicientium:</s>
            <s xml:id="echoid-s6528" xml:space="preserve"> & in omni reflexione obſeruatur identitas formę lucis, quę fuerit in po-
              <lb/>
            lito corpore:</s>
            <s xml:id="echoid-s6529" xml:space="preserve"> & hæc deinceps explanabimus explanatione euidenti.</s>
            <s xml:id="echoid-s6530" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div229" type="section" level="0" n="0">
          <head xml:id="echoid-head260" xml:space="preserve" style="it">15. Lux à ſuperficie polita longinquiore reflexa, trifariam debilitatur.</head>
          <p>
            <s xml:id="echoid-s6531" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s6532" xml:space="preserve"> Patuit [4.</s>
            <s xml:id="echoid-s6533" xml:space="preserve">5 n] quòd lux quanto plus ab ortu ſuo elongatur, tantò plus debilitatur:</s>
            <s xml:id="echoid-s6534" xml:space="preserve">
              <lb/>
            patuit etiã, quòd lux cõtinua fortior eſt diſgregata.</s>
            <s xml:id="echoid-s6535" xml:space="preserve"> Cũ igitur ab aliquo puncto luminoſi pro
              <lb/>
            cedit lux ad ſuperficiẽ ſpeculi in modũ pyramidis, quãto magis elongatur ab illo puncto:</s>
            <s xml:id="echoid-s6536" xml:space="preserve"> tan
              <lb/>
            tò maior erit eius debilitas duplici de cauſſa:</s>
            <s xml:id="echoid-s6537" xml:space="preserve"> & propter elongationẽ ab ortu ſuo, & propter diſgre-
              <lb/>
            gationẽ.</s>
            <s xml:id="echoid-s6538" xml:space="preserve"> Cum aũt ab aliquo ſpeculi puncto reflectitur lux iſta, fit debilior tripliciter:</s>
            <s xml:id="echoid-s6539" xml:space="preserve"> & propter refle
              <lb/>
            xionẽ, quæ debilitat, & propter elongationẽ à loco reflexionis, & propter diſgregationẽ.</s>
            <s xml:id="echoid-s6540" xml:space="preserve"> Si uerò lux
              <lb/>
            reflexa à ſpeculo aggregetur in punctũ aliquod:</s>
            <s xml:id="echoid-s6541" xml:space="preserve"> fiet quidẽ fortior propter aggregationẽ, ſed debilita
              <lb/>
            bitur propter reflexionẽ & elongationẽ.</s>
            <s xml:id="echoid-s6542" xml:space="preserve"> Si igitur aggregatio lucis tantũ reddit ei fortitudinis, quan
              <lb/>
            tum ſubtrahunt reflexio & elongatio:</s>
            <s xml:id="echoid-s6543" xml:space="preserve"> erit lux reflexa aggregata eiuſdẽ fortitudinis, cuius eſt in ſu-
              <lb/>
            perficie ſpeculi:</s>
            <s xml:id="echoid-s6544" xml:space="preserve"> ſi uerò aggre gatio minus addat fortitudinis, quàm diminuũt illa duo:</s>
            <s xml:id="echoid-s6545" xml:space="preserve"> erit debilior:</s>
            <s xml:id="echoid-s6546" xml:space="preserve">
              <lb/>
            & ſi plus addat, erit fortior.</s>
            <s xml:id="echoid-s6547" xml:space="preserve"> Sumiliter ſi à ſuperficie luminoſi procedat pyramis ad aliquod punctum
              <lb/>
            ſpeculi:</s>
            <s xml:id="echoid-s6548" xml:space="preserve"> erit lux procedẽs ſecundum hanc pyramidalitatẽ debilior propter elongationẽ, ſed fortior
              <lb/>
            propter aggregationẽ.</s>
            <s xml:id="echoid-s6549" xml:space="preserve"> Si aũt aggregatio poteſt ſuper elongationẽ:</s>
            <s xml:id="echoid-s6550" xml:space="preserve"> erit lux in pũcto ſpeculi aggrega
              <lb/>
            ta fortior luce unica à luminoſo ueniente per lineã unã:</s>
            <s xml:id="echoid-s6551" xml:space="preserve"> unica dico:</s>
            <s xml:id="echoid-s6552" xml:space="preserve"> quia ad quodlibet punctũ lineæ
              <lb/>
            </s>
          </p>
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