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-div222" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s6259" xml:space="preserve">
              <pb o="108" file="0114" n="114" rhead="ALHAZEN"/>
            menſuram, ut in eo deſcendat acumen:</s>
            <s xml:id="echoid-s6260" xml:space="preserve"> donec acuitas lineæ adhibitæ, cõtingat punctũ lineæ diui-
              <lb/>
            dentis triangulum primò ſignatũ:</s>
            <s xml:id="echoid-s6261" xml:space="preserve"> quod cum fuerit:</s>
            <s xml:id="echoid-s6262" xml:space="preserve"> erit quidem acumen tabulæ æneæ in eadem ſu
              <lb/>
            perficie cũ termino axis ſpeculi:</s>
            <s xml:id="echoid-s6263" xml:space="preserve"> quæ ſuperficies eſt æquidiſtãs ſuperficiei regulę:</s>
            <s xml:id="echoid-s6264" xml:space="preserve"> & erit linea à ter-
              <lb/>
            mino axis ad acumen ducta, perpendicularis ſuper ſuperficiẽ tabulæ æneæ.</s>
            <s xml:id="echoid-s6265" xml:space="preserve"> Axis aũt ſpeculi in ea-
              <lb/>
            dem erit ſuperficie cũ centris foraminũ:</s>
            <s xml:id="echoid-s6266" xml:space="preserve"> quoniam diſtantia eorũ à ſuperficie annuli duorum eſt di-
              <lb/>
            gitorum, & terminus axis ſimiliter.</s>
            <s xml:id="echoid-s6267" xml:space="preserve"> His cum diligentia præparatis, poterit uĩderi, quod ꝓmiſimus.</s>
            <s xml:id="echoid-s6268" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div223" type="section" level="0" n="0">
          <head xml:id="echoid-head255" xml:space="preserve" style="it">10. Radi{us} ſpeculo plano obliqu{us}, in oppoſitam partem reflectitur: & æquat angulos inci-
            <lb/>
          dentiæ & reflexionis. 10 p 5.</head>
          <p>
            <s xml:id="echoid-s6269" xml:space="preserve">IMmittatur annulo regula, ſuper quã eſt ſpeculum planũ, donec acumen tabulæ æneæ cadat ſu-
              <lb/>
            per ſpeculũ, & ſit infixa regula quadrato concauo:</s>
            <s xml:id="echoid-s6270" xml:space="preserve"> & in eo ſubtus regulã aliquid appoǹatur, qđ
              <lb/>
            ei cõferat firmitatẽ, ne uacillet:</s>
            <s xml:id="echoid-s6271" xml:space="preserve"> deinde opponatur pergamenũ foraminibus, & cũ digito fiat im
              <lb/>
            preſsio, ut obturentur, & impreſsionẽ percipere poſsis, & ſignum foraminis fiat in pergameno cũ
              <lb/>
            in cauſto uel aliquo alio:</s>
            <s xml:id="echoid-s6272" xml:space="preserve"> Vnum autem foraminum relinquatur apertum, declinatũ non ſuper me-
              <lb/>
            diam regulam, & adhibeatur radio ſolis foramen apertum:</s>
            <s xml:id="echoid-s6273" xml:space="preserve"> certior autem erit huius rei comprehen
              <lb/>
            ſio, ſi adhibeatur radio ſolis per foramen domus intranti.</s>
            <s xml:id="echoid-s6274" xml:space="preserve"> Cum igitur radius foramẽ intrans ad ſpe
              <lb/>
            culum peruenerit, uidebis ipſum reflecti ad foramen illud, reſpiciens ſuper lineam tabulæ æneę æ-
              <lb/>
            qualem angulum continentem cum linea triangulum per æqua diuidente, ei angulo, quem tenet li
              <lb/>
            nea à foramine diſcooperto cum eadem tabulæ ſemidiametro.</s>
            <s xml:id="echoid-s6275" xml:space="preserve"> Siuerò foramẽ, in quod fit reflexio,
              <lb/>
            diſcoopertum opponas radio, priore cooperto:</s>
            <s xml:id="echoid-s6276" xml:space="preserve"> uidebis radium reflecti in coopertum.</s>
            <s xml:id="echoid-s6277" xml:space="preserve"> Si uerò fora
              <lb/>
            mini imponatur columna ferrea concaua, quam ad quantitatem foraminum fieri pręcepimus:</s>
            <s xml:id="echoid-s6278" xml:space="preserve"> quę
              <lb/>
            ut firmius ſtet, modicum ceræ circa eam apponatur:</s>
            <s xml:id="echoid-s6279" xml:space="preserve"> deſcendet lux per columnæ concauitatem, ſi-
              <lb/>
            cut deſcendit per foramen, & reflectetur in foramen ſibi reſpondens, & ſuper lineas tabulæ æneæ
              <lb/>
            erit deſcenſus & reflexio pari modo, ut prius.</s>
            <s xml:id="echoid-s6280" xml:space="preserve"> Et ſi ad ſecundum foramen columnã tranſtulerimus:</s>
            <s xml:id="echoid-s6281" xml:space="preserve">
              <lb/>
            in primum lucem reflexam uidebimus.</s>
            <s xml:id="echoid-s6282" xml:space="preserve"> Erit autem debilior lux per columnam deſcendens, quàm
              <lb/>
            ſine columna per foramen.</s>
            <s xml:id="echoid-s6283" xml:space="preserve"> Erit autem uιdere eundem reflectendi modum in debiliore luce.</s>
            <s xml:id="echoid-s6284" xml:space="preserve"> Obtu
              <lb/>
            retur foramen cum cera, ut modicum circa centrum ei reſtet uacuum:</s>
            <s xml:id="echoid-s6285" xml:space="preserve"> & uidebitur lucis reflexio in
              <lb/>
            foramine ſimili circa centrum.</s>
            <s xml:id="echoid-s6286" xml:space="preserve"> Pari modo, ſi concauitatem columnæ cum cera obturaueris, ut re-
              <lb/>
            maneat quaſi terminus ſolius axis:</s>
            <s xml:id="echoid-s6287" xml:space="preserve"> deſcen det lux ſuper axem columnæ, & reflectetur ad centrum
              <lb/>
            foraminis ſimilis.</s>
            <s xml:id="echoid-s6288" xml:space="preserve"> Eodem modo altera columna impoſita, cũ deſcen derit lux ſuper axem unius fo-
              <lb/>
            raminis:</s>
            <s xml:id="echoid-s6289" xml:space="preserve"> reflectetur ſuper axem ſimilis.</s>
            <s xml:id="echoid-s6290" xml:space="preserve"> Centrum enim foraminis directè axi opponitur:</s>
            <s xml:id="echoid-s6291" xml:space="preserve"> & cũ lucis
              <lb/>
            reflexio cadat in centrũ, nec moueatur, niſi per lineam rectã, oportet, ut procedat ſecundum axem.</s>
            <s xml:id="echoid-s6292" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div224" type="section" level="0" n="0">
          <head xml:id="echoid-head256" xml:space="preserve" style="it">11. Radi{us} ſpeculo perpendicularis, reflectitur in ſeipſum. 11.12 p 5.</head>
          <p>
            <s xml:id="echoid-s6293" xml:space="preserve">OBturatis autem foraminibus ſingulis, præter medium, quod directè ſuper tabulam æneam
              <lb/>
            incidit:</s>
            <s xml:id="echoid-s6294" xml:space="preserve"> fiat baculus columnaris ad quantitatẽ foraminis, & extremitas eius acuatur, ut re-
              <lb/>
            maneat ſolus terminus axis eius, & deſcẽdat per foramen ad ſpeculũ, & ſignetur punctum,
              <lb/>
            in quod ceciderit:</s>
            <s xml:id="echoid-s6295" xml:space="preserve"> deinde deſcen dat radius ſolis per foramen illud:</s>
            <s xml:id="echoid-s6296" xml:space="preserve"> cadet quidẽ ſuper punctũ ſigna
              <lb/>
            tum, & circa ipſum efficiet circulum.</s>
            <s xml:id="echoid-s6297" xml:space="preserve"> Signetur igitur in fine huius lucis circularis punctũ, & ſecun-
              <lb/>
            dum quantitatẽ lineæ interiacentis puncta ſignata, fiat circulus:</s>
            <s xml:id="echoid-s6298" xml:space="preserve"> erit quidẽ circulus iſte maior circu
              <lb/>
            lo foraminis:</s>
            <s xml:id="echoid-s6299" xml:space="preserve"> quoniam proceſſus lucis perforamen ingredientis, eſt per modum pyramidis.</s>
            <s xml:id="echoid-s6300" xml:space="preserve"> Vnde
              <lb/>
            palàm, quòd lux deſcendens per axem, reflectitur ſuper eundem.</s>
            <s xml:id="echoid-s6301" xml:space="preserve"> Veruntamen apparebit lux circu
              <lb/>
            laris circa baſim interiorem foraminis, maioris quidem capacitatis luce incidente uel radio, & ma-
              <lb/>
            ioris etiã lucis, interioris lucis circulo:</s>
            <s xml:id="echoid-s6302" xml:space="preserve"> & palã eſt, hãc lucẽ eſſe per reflexionẽ:</s>
            <s xml:id="echoid-s6303" xml:space="preserve"> uerùm nõ per reflexi
              <lb/>
            onem lucis ſuper axem deſcendentis:</s>
            <s xml:id="echoid-s6304" xml:space="preserve"> quod ex hoc poterit patére.</s>
            <s xml:id="echoid-s6305" xml:space="preserve"> Obturata utraq;</s>
            <s xml:id="echoid-s6306" xml:space="preserve"> foraminis baſi,
              <lb/>
            ut quaſi ſola remaneat axis uia, & radio ſolis per uiam axis deſcendente:</s>
            <s xml:id="echoid-s6307" xml:space="preserve"> nõ apparebit lux illa circu
              <lb/>
            laris, circa interiorẽ baſim foraminis.</s>
            <s xml:id="echoid-s6308" xml:space="preserve"> Quare nõ procedebat ex reflexa lúcis axe.</s>
            <s xml:id="echoid-s6309" xml:space="preserve"> Amplius:</s>
            <s xml:id="echoid-s6310" xml:space="preserve"> ut ſuprà
              <lb/>
            quidẽ ſuppoſuimus, ut regula orthogonaliter caderet in quadratũ concauũ;</s>
            <s xml:id="echoid-s6311" xml:space="preserve">
              <unsure/>
            ſi aliquantulũ inde au
              <lb/>
            feratur, ut regula declinetur, ita, ut extremitas à quadrato remotior, ſit demiſsior radio deſcen-
              <lb/>
            dente ſuper foramen mediũ:</s>
            <s xml:id="echoid-s6312" xml:space="preserve"> non cadet perpen diculariter ſuper ſpeculũ:</s>
            <s xml:id="echoid-s6313" xml:space="preserve"> & apparebit lux reflexa à
              <lb/>
            foramine medio remota:</s>
            <s xml:id="echoid-s6314" xml:space="preserve"> & quantò maior erit declinatio, tantò maior erit lucis reflexæ à foramine
              <lb/>
            remotio.</s>
            <s xml:id="echoid-s6315" xml:space="preserve"> Si uerò ad rectitudinẽ regula reducatur, lux reflexa circa interiorẽ foraminis baſim, ut pri
              <lb/>
            us, uidebitur.</s>
            <s xml:id="echoid-s6316" xml:space="preserve"> Palã igitur, quòd luce ſuper ſpeculũ perpendiculariter cadẽte, regreditur ad foramẽ,
              <lb/>
            per quod ingreſſa eſt.</s>
            <s xml:id="echoid-s6317" xml:space="preserve"> Cũ uerò lux axis declinata ceciderit, nõ reflectetur ad foramen, per quod in-
              <lb/>
            greſſa eſt, ſed tamẽ apparebit centrum lucis ſemper ſuper lineam ſuperficiei concauæ annuli, per-
              <lb/>
            pendicularem ſuper tabulam æneam, & deſcendentem per centrum foraminis medij.</s>
            <s xml:id="echoid-s6318" xml:space="preserve"> Quæcun-
              <lb/>
            que autem dicta ſunt in duobus foraminibus primis declinatis:</s>
            <s xml:id="echoid-s6319" xml:space="preserve"> intellige in ſingulis:</s>
            <s xml:id="echoid-s6320" xml:space="preserve"> & quod dictũ
              <lb/>
            eſt in ſpeculo plano, de luce per foramen ſeu declinatum ſeu medium deſcendente:</s>
            <s xml:id="echoid-s6321" xml:space="preserve"> regula ſeu recta
              <lb/>
            ſeu declanata:</s>
            <s xml:id="echoid-s6322" xml:space="preserve"> in alijs ſpeculis intellige.</s>
            <s xml:id="echoid-s6323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div225" type="section" level="0" n="0">
          <head xml:id="echoid-head257" xml:space="preserve" style="it">12. In ſpeculis, conuexis, cauis: ſphærico, conico cylindraceo, anguli incidentiæ & reflexio-
            <lb/>
          nis æquantur. 12.13.14.15.16.17.20 p 5.</head>
          <p>
            <s xml:id="echoid-s6324" xml:space="preserve">SIautẽ regula, in qua fuerit ſpeculũ columnare extrà politũ, declinetur in quadrato, ita ut non
              <lb/>
            orthogonaliter cadat ſuper quadratum, ſed declinetur ſuper partem dextram uel ſiniſtram:</s>
            <s xml:id="echoid-s6325" xml:space="preserve">
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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