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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            <s xml:id="echoid-s18260" xml:space="preserve">
              <pb o="262" file="0268" n="268" rhead="ALHAZEN"/>
            uiſus non uidebit niſi unam ſolam imaginem.</s>
            <s xml:id="echoid-s18261" xml:space="preserve"> Nam tunc uiſus erit ut b:</s>
            <s xml:id="echoid-s18262" xml:space="preserve"> & res uiſa ut a.</s>
            <s xml:id="echoid-s18263" xml:space="preserve"> Et cum for-
              <lb/>
            ma a refringetur ad b:</s>
            <s xml:id="echoid-s18264" xml:space="preserve"> refractio erit in ſuperficie perpendiculari ſuper ſuperficiem corporis diapha
              <lb/>
            ni [per 9 n] & erit differentia communis inter illam ſuperficiem & ſuperficiem corporis diaphani
              <lb/>
            circulus [per 1 th 1 ſphæricorum,] ut circulus c e d:</s>
            <s xml:id="echoid-s18265" xml:space="preserve"> & erit punctum refractionis, ut e:</s>
            <s xml:id="echoid-s18266" xml:space="preserve"> & erit linea re
              <lb/>
            fracta, ut a e k.</s>
            <s xml:id="echoid-s18267" xml:space="preserve"> Sequitur ergo, ut forma, quę extendetur per lineam a e, & refringetur per b e:</s>
            <s xml:id="echoid-s18268" xml:space="preserve"> exten-
              <lb/>
            datur ex b per lineam b e, & refringatur per lineam a e.</s>
            <s xml:id="echoid-s18269" xml:space="preserve"> Si ergo forma a refringitur ad b ex alio pun-
              <lb/>
            cto quàm ex e:</s>
            <s xml:id="echoid-s18270" xml:space="preserve"> ſequetur quòd forma b refringetur ad a ex illo puncto.</s>
            <s xml:id="echoid-s18271" xml:space="preserve"> [Quia lineæ incidentiæ &
              <lb/>
            refractionis eædem permanent, nominibus tantùm mutatis.</s>
            <s xml:id="echoid-s18272" xml:space="preserve">] Sed iam declaratum eſt [ſuperiore
              <lb/>
            numero] quòd cum forma extenſa fuerit per lineam b e, & refracta per lineam a e:</s>
            <s xml:id="echoid-s18273" xml:space="preserve"> nunquam refrin
              <lb/>
            getur, niſi ex puncto uno, nec habebit niſi unam imaginem.</s>
            <s xml:id="echoid-s18274" xml:space="preserve"> Et ſi a fuerit in perpendiculari exeunte
              <lb/>
            ex b ad centrum ſphæræ:</s>
            <s xml:id="echoid-s18275" xml:space="preserve"> tunc b comprehendet a in rectitudine perpendicularis [per 13 n] & patet,
              <lb/>
            quòd forma a non refringetur ad b.</s>
            <s xml:id="echoid-s18276" xml:space="preserve"> Ex quo patuit, quòd forma b, cum fuerit in perpendiculari, nõ
              <lb/>
            refringetur ad a.</s>
            <s xml:id="echoid-s18277" xml:space="preserve"> Cum ergo groſsius corpus fuerit ex parte uiſus, & ſubtilius ex parte rei uiſæ:</s>
            <s xml:id="echoid-s18278" xml:space="preserve"> tunc
              <lb/>
            res uiſa non habebit, niſi unam imaginem & unam formam tantùm.</s>
            <s xml:id="echoid-s18279" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div595" type="section" level="0" n="0">
          <head xml:id="echoid-head512" xml:space="preserve" style="it">29. Si uiſ{us} ſit extra circulum (qui eſt communis ſectio ſuperficierum, refractionis & re-
            <lb/>
          fractiui ſphærici conuexi denſioris) linea recta in definito ſitu poteſt à ſegmento peripheriæ nõ
            <lb/>
          magnæ refringi: & aliquod ei{us} punctum rectè: è reliquis plura refractè uideri: & locus to-
            <lb/>
          ti{us} imaginis est in ipſo uiſu. 25 p 10.</head>
          <p>
            <s xml:id="echoid-s18280" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s18281" xml:space="preserve"> iteremus figuram ponentes in circumferentia g e d, punctum ex parte g:</s>
            <s xml:id="echoid-s18282" xml:space="preserve"> & ſit e:</s>
            <s xml:id="echoid-s18283" xml:space="preserve"> ex quo
              <lb/>
            extrahamus lineam æquidiſtantem lineæ a b [per 31 p 1:</s>
            <s xml:id="echoid-s18284" xml:space="preserve">] & ſit linea e t:</s>
            <s xml:id="echoid-s18285" xml:space="preserve"> & continuemus z e, &
              <lb/>
            extrahamus illam uſque ad h:</s>
            <s xml:id="echoid-s18286" xml:space="preserve"> & ſit proportio anguli z e k ad angulum k e t duplicatum maxima
              <lb/>
            proportio, quam angulus, quem continet linea, per quam extenditur forma cum perpendiculari,
              <lb/>
            poſsit habere ad angulum refractionis, quem exigit ille angulus, quò ad ſenſum.</s>
            <s xml:id="echoid-s18287" xml:space="preserve"> [Id autem per 10.</s>
            <s xml:id="echoid-s18288" xml:space="preserve">
              <lb/>
            11.</s>
            <s xml:id="echoid-s18289" xml:space="preserve"> 12 n præſtari poteſt, quibus anguli refractionum à medio craſsiore ad ſubtilius & contrà, inuen-
              <lb/>
            ti ſunt.</s>
            <s xml:id="echoid-s18290" xml:space="preserve">] Anguli enim refractionis, qui fuerint inter duo corpora diuerſa in diaphanitate, à luce
              <lb/>
            tranſeunte per illa diuerſantur:</s>
            <s xml:id="echoid-s18291" xml:space="preserve"> quorum diuerſitas, quò ad ſenſum, habet finem:</s>
            <s xml:id="echoid-s18292" xml:space="preserve"> quem ſi exceſſerit:</s>
            <s xml:id="echoid-s18293" xml:space="preserve">
              <lb/>
            ſenſus non comprehendet quantitatem refractionis:</s>
            <s xml:id="echoid-s18294" xml:space="preserve"> comprehendet enim centrum lucis in rectitu
              <lb/>
            dine lineæ, per quam lux extenditur, cum uidelicet experimentatus fuerit hoc per inſtrumentum.</s>
            <s xml:id="echoid-s18295" xml:space="preserve">
              <lb/>
            Et ponamus angulum d z t æqualem angulo k e t [per 23 p 1] erit ergo angulus z k e duplus ad an-
              <lb/>
            gulum k e t.</s>
            <s xml:id="echoid-s18296" xml:space="preserve"> [Quia enim e t, z b ſunt parallelæ per fabricationem:</s>
            <s xml:id="echoid-s18297" xml:space="preserve"> æquatur angulus k b z angulo
              <lb/>
            k e t per 29 p 1:</s>
            <s xml:id="echoid-s18298" xml:space="preserve"> cui iam æquatus eſt k z b:</s>
            <s xml:id="echoid-s18299" xml:space="preserve"> anguli igitur k b z, k z b ſunt æquales:</s>
            <s xml:id="echoid-s18300" xml:space="preserve"> quibus cum æque-
              <lb/>
            tur z k e per 32 p 1:</s>
            <s xml:id="echoid-s18301" xml:space="preserve"> erit duplus ad utrumlibet:</s>
            <s xml:id="echoid-s18302" xml:space="preserve"> itaque duplus ad ęqua-
              <lb/>
              <figure xlink:label="fig-0268-01" xlink:href="fig-0268-01a" number="230">
                <variables xml:id="echoid-variables217" xml:space="preserve">a l g h e z d k b t</variables>
              </figure>
            lẽ k e t] & ſic proportio anguli z e k ad angulũ z k e erit maxima pro-
              <lb/>
            portio inter angulum, quem continet prima linea & perpendicula-
              <lb/>
            ris, exiens à puncto refractionis, & inter angulum refractionis.</s>
            <s xml:id="echoid-s18303" xml:space="preserve"> Sed
              <lb/>
            linea e k concurret cum linea a d:</s>
            <s xml:id="echoid-s18304" xml:space="preserve"> [per lemma Procli ad 29 p 1] con-
              <lb/>
            currant ergo in b:</s>
            <s xml:id="echoid-s18305" xml:space="preserve"> & extrahamus ex e lineam æquidiſtantem t z:</s>
            <s xml:id="echoid-s18306" xml:space="preserve"> con
              <lb/>
            curret ergo [ut antè] cum z g extra circulum ex parte g:</s>
            <s xml:id="echoid-s18307" xml:space="preserve"> ſit concur-
              <lb/>
            ſus in a:</s>
            <s xml:id="echoid-s18308" xml:space="preserve"> & extrahamus b e uſq;</s>
            <s xml:id="echoid-s18309" xml:space="preserve"> ad l:</s>
            <s xml:id="echoid-s18310" xml:space="preserve"> erit ergo [per 29 p 1] angulus l
              <lb/>
            e a æqualis angulo z k e:</s>
            <s xml:id="echoid-s18311" xml:space="preserve"> & [per 15 p 1] angulus l e h æqualis angulo
              <lb/>
            z e k.</s>
            <s xml:id="echoid-s18312" xml:space="preserve"> Erit ergo angulus l e a angulus refractionis, quẽ exigit angulus
              <lb/>
            l e h [angulus enim z e k, qui ք 15 p 1 æquatur angulo l e h, talis eſt ex
              <lb/>
            theſi.</s>
            <s xml:id="echoid-s18313" xml:space="preserve">] Si ergo b fuerit in aliquo uiſo:</s>
            <s xml:id="echoid-s18314" xml:space="preserve"> & corpus diaphanũ, cuius con
              <lb/>
            uexum eſt ex parte a, fuerit continuatum ex e uſque ad b, & nõ fue-
              <lb/>
            rit diſtinctum apud circum ferentiam g e d ex parte b:</s>
            <s xml:id="echoid-s18315" xml:space="preserve"> tunc forma b
              <lb/>
            extendetur per lineam b e, & refringetur per lineam e a, & compre-
              <lb/>
            hendetur à uiſu a peruerticationem a e.</s>
            <s xml:id="echoid-s18316" xml:space="preserve"> Et quia angulus a e h poteſt
              <lb/>
            diuidi pluribus proportionibus earum, quæ fuerint inter angulos re
              <lb/>
            fractionis, & angulos, quos continent perpendiculares cum primis
              <lb/>
            lincis, quæ fuerint inter duo corpora diaphana:</s>
            <s xml:id="echoid-s18317" xml:space="preserve"> ſic ergo in linea d b
              <lb/>
            erunt plura puncta, quorum formæ extenduntur ad arcum e g, & re-
              <lb/>
            fringuntur ad a:</s>
            <s xml:id="echoid-s18318" xml:space="preserve"> & forma totius lineæ, in qua ſunt illa puncta, refrin-
              <lb/>
            getur ad a ex arcu g e.</s>
            <s xml:id="echoid-s18319" xml:space="preserve"> Cum ergo uiſus fuerit in corpore diaphano,
              <lb/>
            & res uiſa fuerit in alio diaphano groſsiore, & fuerit ſuperficies dia-
              <lb/>
            phani groſsioris, quæ eſt ex parte uiſus, ſphærica conuexa, & uiſus
              <lb/>
            fuerit extra circulum, cuius conuexum eſt ex parte uiſus, & fuerit il-
              <lb/>
            le circulus remotior à uiſu, quàm punctum remotius ex duobus pun
              <lb/>
            ctis, ſectionis factæ inter perpendicularem & circumferentiam, &
              <lb/>
            corpus diaphanum groſſum, quod eſt ex parte uiſus, fuerit conti-
              <lb/>
            nuum uſque ad locum, in quo eſt res uiſa, & non fuerit deciſum a-
              <lb/>
            pud circulum, qui eſt ex parte rei uiſæ:</s>
            <s xml:id="echoid-s18320" xml:space="preserve"> tunc uiſus poterit comprehendere illam rem uiſam & re-
              <lb/>
            </s>
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