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-s7454" xml:space="preserve">
              <pb o="127" file="0133" n="133" rhead="OPTICAE LIBER V."/>
            comprehendetur imago uerticis in cõcurſu lineæ reflexionis, & perpendicularis à uertice ad ſphæ-
              <lb/>
            ram ductæ, ſiue ad contingentem, circulum communem ſuperficiei ſphæræ & ſuperficiei reflexio-
              <lb/>
            nis.</s>
            <s xml:id="echoid-s7455" xml:space="preserve"> Sumpto autem quocunque puncto huic ſpeculo oppoſito, eſt intelligere pyramidem ſuper
              <lb/>
            ſuperficiem ſpeculi orthogonalem, aut ſuper continuam ei, cuius uertex ſit punctũ ſumptum:</s>
            <s xml:id="echoid-s7456" xml:space="preserve"> [per
              <lb/>
            14 n 4] & linea ab illo puncto ad imaginẽ puncti illius, erit in ſuperficie reflexionis, & perpendicu-
              <lb/>
            laris ſuper ſuperficiem ſpeculi, uel ei continuam modo prædicto:</s>
            <s xml:id="echoid-s7457" xml:space="preserve"> quoniam punctum uiſum & ima-
              <lb/>
            go ſemper ſunt ſimul in ſuperficie reflexionis [per 23 n 4.</s>
            <s xml:id="echoid-s7458" xml:space="preserve">] Quare & linea à puncto uiſo ad eius
              <lb/>
            imaginem ducta.</s>
            <s xml:id="echoid-s7459" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div282" type="section" level="0" n="0">
          <head xml:id="echoid-head307" xml:space="preserve" style="it">4. In ſpeculis conuexis cylindraceo, conico, imago uidetur in concurſu perpendicularis inci-
            <lb/>
          dentiæ & lineæ reflexionis. 37 p 5.</head>
          <p>
            <s xml:id="echoid-s7460" xml:space="preserve">IN ſpeculis columnaribus exterius politis non apparent, quæ in ligno & pyramide diximus:</s>
            <s xml:id="echoid-s7461" xml:space="preserve">
              <lb/>
            quoniam recta in his ſpeculis uidetur non recta:</s>
            <s xml:id="echoid-s7462" xml:space="preserve"> & eſt error uiſus communis, cuius poſtea cauſ-
              <lb/>
            ſam aſsignabimus.</s>
            <s xml:id="echoid-s7463" xml:space="preserve"> Accidit tamen in ſolo corporis puncto uidere locum imaginis prædictum,
              <lb/>
            hoc modo.</s>
            <s xml:id="echoid-s7464" xml:space="preserve"> Adhibito præcedentis libri inſtrumento, immittatur regula, cui ſit infixum columnare
              <lb/>
            ſpeculum, ut media portionis ſpeculi linea ſit in ſuperficie regulæ, & non tranſeat hæc regula tabu-
              <lb/>
            lam æneam, ſed ſuper ipſam cadat orthogonaliter, ita ut altitudo regulæ ſit ſuper lineam, diuidentẽ
              <lb/>
            triangulum tabulæ æneæ.</s>
            <s xml:id="echoid-s7465" xml:space="preserve"> Erectione facta in hac tabula, impleatur cera, & inducatur ei planities, ut
              <lb/>
            ſit in eadem ſuperficie cum tabula:</s>
            <s xml:id="echoid-s7466" xml:space="preserve"> & eſt;</s>
            <s xml:id="echoid-s7467" xml:space="preserve"> ut certior fiat orthogonalis regulę directio ſuper tabulam.</s>
            <s xml:id="echoid-s7468" xml:space="preserve">
              <lb/>
            Deinde quæratur regula acuta, & acuatur extremitas, & applicetur huius regulæ acuitas mediæ ſu
              <lb/>
            perficiei annuli lineæ, & deſcendat ſecundum lineam hanc, & ubi ceciderit ſuper regulam, fiat ſi-
              <lb/>
            gnum.</s>
            <s xml:id="echoid-s7469" xml:space="preserve"> Poſtea acus deſcendat, in qua infixum ſit modicũ corpus album:</s>
            <s xml:id="echoid-s7470" xml:space="preserve"> & hoc in termino, ne de-
              <lb/>
            icendat acus uſq;</s>
            <s xml:id="echoid-s7471" xml:space="preserve"> ad regulam.</s>
            <s xml:id="echoid-s7472" xml:space="preserve"> Adhibeatur autem uiſus, ut ſit in ſuperficie regulæ, & claudatur unus
              <lb/>
            uiſuum:</s>
            <s xml:id="echoid-s7473" xml:space="preserve"> uidebitur quidem imago corporis ſuper lineam, à puncto ſignato ad acumen acus protra-
              <lb/>
            ctam:</s>
            <s xml:id="echoid-s7474" xml:space="preserve"> quæ quidem linea perpendicularis eſt ſuper ſuperficiem regulæ;</s>
            <s xml:id="echoid-s7475" xml:space="preserve"> quæ ſuperficies tangit colu-
              <lb/>
            mnam in linea longitudinis:</s>
            <s xml:id="echoid-s7476" xml:space="preserve"> & eſt perpendicularis ſuper lineam longitudinis columnæ, quæ eſt in
              <lb/>
            ſuperficie regulæ:</s>
            <s xml:id="echoid-s7477" xml:space="preserve"> & eſt linea cõmunis ſuperficiei regulæ & ſuperficiei reflexionis:</s>
            <s xml:id="echoid-s7478" xml:space="preserve"> & in ſuperficie re
              <lb/>
            flexionis ſunt linea longitudinis & linea perpendicularis.</s>
            <s xml:id="echoid-s7479" xml:space="preserve"> Et ſi ſitus uiſus mutetur, & circa annuli ſu
              <lb/>
            perficiem uiſus uoluatur:</s>
            <s xml:id="echoid-s7480" xml:space="preserve"> apparebunt ſicut prius, & in eadem linea corpus, & imago corporis, & a-
              <lb/>
            cus.</s>
            <s xml:id="echoid-s7481" xml:space="preserve"> Et eſt linea illa perpendicularis ſuper mediam longitudinis columnæ lineam:</s>
            <s xml:id="echoid-s7482" xml:space="preserve"> & hæc eſt per-
              <lb/>
            pendicularis in ſuperficie reflexionis:</s>
            <s xml:id="echoid-s7483" xml:space="preserve"> quoniam ſuperficies annuli ſecat columnam ſuper circulum,
              <lb/>
            æquidiſtantem baſi columnæ:</s>
            <s xml:id="echoid-s7484" xml:space="preserve"> & in hac ſuperficie eſt uiſus.</s>
            <s xml:id="echoid-s7485" xml:space="preserve"> Et nos probabimus poſtea, quòd quan-
              <lb/>
            do uiſus, & uiſum corpus fuerint in ſuperficie, æquidiſtante baſi columnæ, illa eſt ſuperficies refle-
              <lb/>
            xionis.</s>
            <s xml:id="echoid-s7486" xml:space="preserve"> In hoc autem ſitu, linea communis ſuperficiei columnæ, & ſuperficiei reflexionis, eſt circu-
              <lb/>
            lus:</s>
            <s xml:id="echoid-s7487" xml:space="preserve"> & perpendicularis, in qua uidetur imago & corpus, orthogonaliter cadunt ſuper lineam, hunc
              <lb/>
            circulum contingentem.</s>
            <s xml:id="echoid-s7488" xml:space="preserve"> His peractis auferatur acus à loco ſuo, & ponatur regula acuta ſuper li-
              <lb/>
            neam annuli mediam, ita ut cadat ſuper mediam longitudinis regulæ lineam, & adhibeatur regula
              <lb/>
            acuta ſuperficiei annuli cera firmiter.</s>
            <s xml:id="echoid-s7489" xml:space="preserve"> Poſtea auferatur regula, in qua eſt ſpeculum, & accipiatur
              <lb/>
            regula acuta, & applicetur eius acuitas mediæ longitudinis regulæ lineæ, & ſecundum proceſſum
              <lb/>
            acuitatis fiat cum incanſto ſuper ſpeculum protractio.</s>
            <s xml:id="echoid-s7490" xml:space="preserve"> Pòſt ſumatur triangulum cereum modi-
              <lb/>
            cum, cuius unum latus ſit æquale altitudini regulæ, in qua eſt ſpeculum, & ſit ſpiſsitudo huius tri-
              <lb/>
            anguli moderata, & ſuperficies huius trianguli ſint planæ pro poſſe:</s>
            <s xml:id="echoid-s7491" xml:space="preserve"> & adhibeatur columnæ re-
              <lb/>
            gulæ triangulum firmiter ſub baſi regulæ, & latus eius æquale altitudini regulæ ponatur ſuper la-
              <lb/>
            tus baſis regulæ.</s>
            <s xml:id="echoid-s7492" xml:space="preserve"> Cum ita fuerit, erit huius trianguli altitudo ſuper baſim columnæ æqualem regu-
              <lb/>
            læ.</s>
            <s xml:id="echoid-s7493" xml:space="preserve"> Et ut efficiatur ſuperficies plana ad modum ſuperficiei regulæ, includatur triangulum inter
              <lb/>
            regulam & ſuperficiem planam, & comprimatur, donec ſit bene complanatum, & ſuper ſuperfi-
              <lb/>
            ciem huius trianguli ponatur regula acuta, & ſecetur finis huius trianguli cum acuitate regulæ, &
              <lb/>
            erit finis eius linea recta, & erit linea hæc baſis regulæ, in qua eſt ſpeculum.</s>
            <s xml:id="echoid-s7494" xml:space="preserve"> Poſtea ponatur regu-
              <lb/>
            la ſuper ſuperficiem tabulæ, quæ eſt in inſtrumento, & ponatur finis eius baſis, quæ eſt in longitu-
              <lb/>
            dine, quæ eſt latus trianguli cerei, ſuper lineam, quę eſt in longitudine tabulę, ſicut factum eſt prius:</s>
            <s xml:id="echoid-s7495" xml:space="preserve">
              <lb/>
            & erit ſuperficies regulæ, in qua eſt ſpeculum, orthogonalis ſuper tabulam æneam:</s>
            <s xml:id="echoid-s7496" xml:space="preserve"> & hæc ſuperfi-
              <lb/>
            cies ſecat tabulam æneam ſuper lineam, quæ eſt in longitudine eius:</s>
            <s xml:id="echoid-s7497" xml:space="preserve"> & hæc ſuperficies tangit ſu-
              <lb/>
            perficiem ſpeculi ſuper lineam, quæ eſt in ſuperficie ſpeculi:</s>
            <s xml:id="echoid-s7498" xml:space="preserve"> & hæc eſt ſuperficies regulæ, in qua eſt
              <lb/>
            ſpeculum:</s>
            <s xml:id="echoid-s7499" xml:space="preserve"> & erit angulus regulæ acutæ, adhærentis in media linea ſuperficiei annuli, in qua ſuper-
              <lb/>
            ficie erit ſpeculum, declinatus in partem, in qua eſt caput trianguli:</s>
            <s xml:id="echoid-s7500" xml:space="preserve"> quia regula exaltauit unam
              <lb/>
            partem eius cum corpore trianguli, & alia pars, quæ eſt poſt caput trianguli, eſt ſuperficies tabulæ
              <lb/>
            æneæ:</s>
            <s xml:id="echoid-s7501" xml:space="preserve"> & erit linea, quæ eſt in medietate ſpeculi, declinata.</s>
            <s xml:id="echoid-s7502" xml:space="preserve"> Et quando fuerit latus trianguli cerei ſu-
              <lb/>
            per lineam, quæ eſt in longitudine æneæ tabulæ:</s>
            <s xml:id="echoid-s7503" xml:space="preserve"> mouebitur regula, in qua eſt ſpeculum:</s>
            <s xml:id="echoid-s7504" xml:space="preserve"> & latus
              <lb/>
            trianguli in hoc motu, ſi ſit ſuper lineam longitudinis tabulę æneæ, & procedat uel retrocedat, do-
              <lb/>
            nec concurrat angulus regulæ acutę cum puncto aliquo lineę ſuperficiei ſpeculi, donec firmetur re
              <lb/>
            gula acuta, & auferatur linea in ſpeculo cum incauſto facta:</s>
            <s xml:id="echoid-s7505" xml:space="preserve"> & fiat punctum in ſuperficie ſpecu-
              <lb/>
            li in directo capitis regulæ acutę, & auferatur regula acuta, & apponatur acus, & ſit acus ſuper li-
              <lb/>
            neam mediam ſuperficiei annuli, & adhærere cogatur cum cera:</s>
            <s xml:id="echoid-s7506" xml:space="preserve"> erit linea intellectualis ab acu in
              <lb/>
            punctum ſignatum in ſuperficie ſpeculi, perpendicularis ſuper ſuperficiem regulæ, quæ tangit ſu-
              <lb/>
            </s>
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