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-div149" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s4343" xml:space="preserve">
              <pb o="83" file="0089" n="89" rhead="OPTICAE LIBER III."/>
            ergo àngulus k a q eſt maior angulo k b q.</s>
            <s xml:id="echoid-s4344" xml:space="preserve"> Ergo remotio lineę a k ab axe a q, eſt maior quã rem otio
              <lb/>
            lineæ b k ab axe b q:</s>
            <s xml:id="echoid-s4345" xml:space="preserve">ſed differẽtia inter has duas remotiones eſt modica:</s>
            <s xml:id="echoid-s4346" xml:space="preserve"> differẽtia enim inter duos
              <lb/>
            angulos k a q, k b q eſt parua, & indiuiduum, quod eſt apud punctum k, uidetur ambobus uiſibus u-
              <lb/>
            num, quando axes concurrerint in indiuiduo, quod eſt a pud punctum q.</s>
            <s xml:id="echoid-s4347" xml:space="preserve"> Et duæ lineæ a k, b k, ſunt
              <lb/>
            æ quidiſtantes duobus radijs exeuntibus ad indiuiduũ, quod eſt a pud punctũ k, cum duo axes con-
              <lb/>
            currerint in indiuiduo, quod eſt apud q.</s>
            <s xml:id="echoid-s4348" xml:space="preserve"> Similiter diſpoſitio indiuidui, quod eſt apud punctum r, ſci-
              <lb/>
            tur:</s>
            <s xml:id="echoid-s4349" xml:space="preserve"> quoniam radij exeuntes ad ipſum, erũt in uerticatione duarum linearum a r, b r, & uidebitur u-
              <lb/>
            num:</s>
            <s xml:id="echoid-s4350" xml:space="preserve"> & duo anguli r a q, r b q non maxim è differunt:</s>
            <s xml:id="echoid-s4351" xml:space="preserve"> & angulus k b r non habet ſenſibilem quantita
              <lb/>
            tem, quando punctum r fuerit ualde propinquũ puncto k.</s>
            <s xml:id="echoid-s4352" xml:space="preserve"> Declarabitur igitur ex hac diſpoſitione:</s>
            <s xml:id="echoid-s4353" xml:space="preserve">
              <lb/>
            quòd uiſum, cuius diſpoſitio apud duos axes eſt una poſitio in parte, & remotio radiorum exeun-
              <lb/>
            tium ad ipſum à duobus uiſibus, non eſt maximè differens:</s>
            <s xml:id="echoid-s4354" xml:space="preserve"> illud uiſum uidebitur duobus uiſibus
              <lb/>
            unum.</s>
            <s xml:id="echoid-s4355" xml:space="preserve"> Anguli autem f a q, f b q ſunt diuerſi diuerſitate maxima:</s>
            <s xml:id="echoid-s4356" xml:space="preserve"> & indiuiduum, quod eſt apud pun-
              <lb/>
            ctum f, uidebitur duo:</s>
            <s xml:id="echoid-s4357" xml:space="preserve">quoniã duo axes concurrent in indiuiduo, quod eſt apud punctum q.</s>
            <s xml:id="echoid-s4358" xml:space="preserve"> Decla-
              <lb/>
            rabitur igitur ex hac diſpoſitione, quòd uiſum, ad quod poſitio radiorum exeuntium à duobus uiſi-
              <lb/>
            bus eſt diuerſa in remotione à duobus axibus maxima diuerſitate, uidetur duo:</s>
            <s xml:id="echoid-s4359" xml:space="preserve"> licet poſitio eius in
              <lb/>
            reſpectu duorum axium eadem eſt poſitio in parte.</s>
            <s xml:id="echoid-s4360" xml:space="preserve"> Poſitio autem lineæ h q z in reſpectu axium
              <lb/>
            duorum uiſuum, eſt poſitio diuerſa in parte:</s>
            <s xml:id="echoid-s4361" xml:space="preserve"> radij etenim exeuntes ad partem h q à dextro uiſu,
              <lb/>
            ſunt ſiniſtri ab axe a q:</s>
            <s xml:id="echoid-s4362" xml:space="preserve"> radij autem exeuntes ad hanc partem à ſiniſtro uiſu, ſunt dextri ab axe b q:</s>
            <s xml:id="echoid-s4363" xml:space="preserve">
              <lb/>
            radij uerò exeuntes ad partem q z à dextro uiſu, ſunt dextri ab axe a q:</s>
            <s xml:id="echoid-s4364" xml:space="preserve"> & radij exeuntes ad ipſam à
              <lb/>
            ſiniſtro uiſu, ſunt ſiniſtri ab axe b q:</s>
            <s xml:id="echoid-s4365" xml:space="preserve"> & radij qui exeunt ad ipſum, ſunt diuerſæ poſitionis in parte:</s>
            <s xml:id="echoid-s4366" xml:space="preserve"> &
              <lb/>
            remotio duorum radiorum exeuntium ad quodlibet punctum illius lineæ à duobus uiſibus, à duo-
              <lb/>
            bus axibus eſt æ qualis:</s>
            <s xml:id="echoid-s4367" xml:space="preserve"> & iſta linea, & omnia poſita ſuper ipſam, pręter indiuiduum poſitum in me-
              <lb/>
            dio, ſemper uidentur duo, cum duo axes concurrerint in indiuiduo poſito in medio.</s>
            <s xml:id="echoid-s4368" xml:space="preserve"> Declaratum
              <lb/>
            igitur eſt ex hac diſpoſitione, quòd uiſum, cuius poſitio in reſpectu duorum axium eſt diuerſa in
              <lb/>
            parte, ſemper uidetur duo:</s>
            <s xml:id="echoid-s4369" xml:space="preserve"> quamuis remotiones radiorum exeuntium ad ipſum à duobus uiſibus,
              <lb/>
            à duobus axibus ſint æquales.</s>
            <s xml:id="echoid-s4370" xml:space="preserve"> Remotiones enim quorumlibet duorum radiorum exeuntium à
              <lb/>
            duobus uiſibus ad aliquod punctum eius, erunt in duabus partibus diuerſis.</s>
            <s xml:id="echoid-s4371" xml:space="preserve"> Quapropter duæ for-
              <lb/>
            mæ cuiuslibet puncti eius inſtituentur in duobus punctis concauitatis communis nerui à duobus
              <lb/>
            lateribus centri.</s>
            <s xml:id="echoid-s4372" xml:space="preserve"> Et ſimiliter etiam eſt diſpoſitio utriuſque diametrorum.</s>
            <s xml:id="echoid-s4373" xml:space="preserve"> Quoniam radij exeuntes
              <lb/>
            ad utramlibet earum à uiſu ſequente ipſam, erunt à medio uiſus, & propinqui axi, & ſub axe, & ſu-
              <lb/>
            pra axem:</s>
            <s xml:id="echoid-s4374" xml:space="preserve"> & radij exeuntes ad ipſam à reliquo uiſu, erunt declinantes à reliquo axe:</s>
            <s xml:id="echoid-s4375" xml:space="preserve"> qui uerò à de-
              <lb/>
            xtro uiſu ad ſiniſtram diametrum, erunt ſiniſtri ab axe:</s>
            <s xml:id="echoid-s4376" xml:space="preserve"> qui autem exeunt à ſiniſtro uiſu ad dextram,
              <lb/>
            erunt dextri ab axe.</s>
            <s xml:id="echoid-s4377" xml:space="preserve"> Et formæ diametrorum iſtarum, & omnia puncta, & omnia poſita ſuper i-
              <lb/>
            pſas, uidentur duo, præter indiuiduum poſitum in medio, quando duo axes concurrerint in me-
              <lb/>
            dio indiuiduo.</s>
            <s xml:id="echoid-s4378" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div151" type="section" level="0" n="0">
          <head xml:id="echoid-head175" xml:space="preserve" style="it">13. Viſibile medio unius uiſus rectè, reliquo obliquè oppoſitum, uidetur geminum. 103 p 4.
            <lb/>
          Idem II n.</head>
          <p>
            <s xml:id="echoid-s4379" xml:space="preserve">DEclarabitur igitur exhoc, quòd uiſum, quod in reſpectu alterius uiſus eſt oppoſitum medio
              <lb/>
            eius, in reſpectu autem reliqui eſt obliquum à medio, uidetur duo.</s>
            <s xml:id="echoid-s4380" xml:space="preserve"> Nam formæ puncti, quæ
              <lb/>
            inſtituitur in medio alterius uiſi, ueniet ad centrum:</s>
            <s xml:id="echoid-s4381" xml:space="preserve"> forma uerò puncti obliqui à medio re-
              <lb/>
            liqui uiſus, ueniet ad punctum aliud à centro, & obliquum à centro, ſecundum obliquationem pun
              <lb/>
            cti ſuperficiei uiſus.</s>
            <s xml:id="echoid-s4382" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div152" type="section" level="0" n="0">
          <head xml:id="echoid-head176" xml:space="preserve" style="it">14. Viſibile, in quo concurrunt axes optici, aut radij his propinqui: uidetur unum. 46 p 3.</head>
          <p>
            <s xml:id="echoid-s4383" xml:space="preserve">EX hac igitur experimentatione & expoſitione declaratur bene, quòd uiſum, in quo concur-
              <lb/>
            runt duo axes, ſemper uidetur unum:</s>
            <s xml:id="echoid-s4384" xml:space="preserve"> & quòd unum quod que uiſorum, etiam in quibus con-
              <lb/>
            currunt radij, qui ſunt conſimilis poſitionis in parte, inter quos non eſt maxima diuerſitas in
              <lb/>
            remotione à duobus axibus, uidetur etiam unum:</s>
            <s xml:id="echoid-s4385" xml:space="preserve"> & quòd uiſum, in quo concurrunt radij conſimi-
              <lb/>
            lis poſitionis in parte, & diuerſæ poſitionis in remotione à duobus axibus maxima diuerſitate, uide
              <lb/>
            tur duo:</s>
            <s xml:id="echoid-s4386" xml:space="preserve"> & quòd uiſum, quod comprehen ditur per radios diuerſæ poſitionis in parte, uidetur duo:</s>
            <s xml:id="echoid-s4387" xml:space="preserve">
              <lb/>
            quamuis remotiones radiorum exeuntium ad ipſum à duobus axibus, ſunt ęquales:</s>
            <s xml:id="echoid-s4388" xml:space="preserve"> & quòd omnia
              <lb/>
            iſta erunt ſic:</s>
            <s xml:id="echoid-s4389" xml:space="preserve"> dum duo axes concurrent in uno uiſo.</s>
            <s xml:id="echoid-s4390" xml:space="preserve"> Et omnia uiſa aſſueta ſunt oppoſita ambo-
              <lb/>
            bus uiſibus, & ambo uiſus inſpiciunt ad quodlibet eorum.</s>
            <s xml:id="echoid-s4391" xml:space="preserve"> Ergo duo axes duorum uiſuum ſem-
              <lb/>
            per concurrunt in eis, & poſitio radiorum reſiduorum, qui concurrũt in communi puncto eorum,
              <lb/>
            eſt poſitio conſimilis in parte, & non differt in remotione à duobus axibus maxima differentia.</s>
            <s xml:id="echoid-s4392" xml:space="preserve"> Et
              <lb/>
            ideo quodlibet uiſibilium aſſuetorum uidetur ambobus uiſibus unum:</s>
            <s xml:id="echoid-s4393" xml:space="preserve"> & nullum uiſibilium uide-
              <lb/>
            tur duo, niſi rarò.</s>
            <s xml:id="echoid-s4394" xml:space="preserve"> Nullum enium uiſibiliũ uidetur duo, niſi cum cõpoſitio eius in reſpectu amborũ ui
              <lb/>
            fuũ fuerit diuerſa maxima diuerſitate, aut in parte, aut in remotione, aut in utroq;</s>
            <s xml:id="echoid-s4395" xml:space="preserve">. Et poſitio unius
              <lb/>
            uiſi apud duos uiſus non diuerſatur quidẽ maxima diuerſitate, niſi rarò.</s>
            <s xml:id="echoid-s4396" xml:space="preserve"> Cauſſa igitur propter quã
              <lb/>
            unũquodq;</s>
            <s xml:id="echoid-s4397" xml:space="preserve"> uiſorũ aſſuetorũ uidetur unũ ambobus uiſibus, declarata eſt ratiõe & experientia.</s>
            <s xml:id="echoid-s4398" xml:space="preserve"> Et e-
              <lb/>
            tiã cũ experimẽtator abſtulerit indiuiduũ, quod eſt in medio tabulę, & inſpexerit mediũ ſectionis,
              <lb/>
            quę eſt in medio tabulę:</s>
            <s xml:id="echoid-s4399" xml:space="preserve"> & intuitus fuerit tũc lineas ſcriptas in tabula:</s>
            <s xml:id="echoid-s4400" xml:space="preserve"> inueniet duas diametros qua
              <lb/>
            tuor:</s>
            <s xml:id="echoid-s4401" xml:space="preserve"> & inueniet ſimul duas illarũ quatuor ꝓpinquas ſibi, & duas à ſe remotas:</s>
            <s xml:id="echoid-s4402" xml:space="preserve"> & etiã oẽs ſe ſecãtes
              <lb/>
            ſuperpunctũ mediũ, qđ eſt punctũ ſectiõis duarũ diametrorũ, qđ eſt ſuper axẽ cõmunẽ:</s>
            <s xml:id="echoid-s4403" xml:space="preserve"> & inueniet
              <lb/>
            </s>
          </p>
        </div>
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