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-s18825" xml:space="preserve">
              <pb o="271" file="0277" n="277" rhead="OPTICAE LIBER VII."/>
            cias & cauſſas earum:</s>
            <s xml:id="echoid-s18826" xml:space="preserve"> & quę ſunt etiam cauſſæ iſtarum:</s>
            <s xml:id="echoid-s18827" xml:space="preserve"> ſed in his accidit magis, & citius propter de-
              <lb/>
            bilitatem harum formarum.</s>
            <s xml:id="echoid-s18828" xml:space="preserve"> Particulares autem deceptiones, quæ accidunt propter figuras ſuper-
              <lb/>
            ficierum corporum diaphanorum, ſunt multimodæ, ſed accidunt rarò uiſui.</s>
            <s xml:id="echoid-s18829" xml:space="preserve"> Ea enim, quę compre-
              <lb/>
            henduntur ultra corpora diaphana, diuerſa ab aere, ſunt ſtellæ, & ea, quæ ſunt in aqua:</s>
            <s xml:id="echoid-s18830" xml:space="preserve"> illa autem,
              <lb/>
            quæ ſunt ultra ultrum, & lapides diaphanos diuerſarum figurarum rarò comprehenduntur à uiſu:</s>
            <s xml:id="echoid-s18831" xml:space="preserve">
              <lb/>
            & non eſt ita de iſtis corporibus diaphanis, ut de ſpeculis:</s>
            <s xml:id="echoid-s18832" xml:space="preserve"> ſpecula enim ſæpius aſpiciuntur ab homi
              <lb/>
            nibus, ut uideant in eis ſuas formas, & habentur in domibus.</s>
            <s xml:id="echoid-s18833" xml:space="preserve"> Et ſimiliter quando homo inſpexerit
              <lb/>
            in quodlibet corpus terſum:</s>
            <s xml:id="echoid-s18834" xml:space="preserve"> etiam uidebit formam eorum, quæ ſunt in oppoſitione.</s>
            <s xml:id="echoid-s18835" xml:space="preserve"> Et ſimiliter ſi
              <lb/>
            aſpexerit a quam:</s>
            <s xml:id="echoid-s18836" xml:space="preserve"> uidebit formam ſuam in ea, & uidebit, quæ ſunt in oppoſitione.</s>
            <s xml:id="echoid-s18837" xml:space="preserve"> Et non eſt ita il-
              <lb/>
            lud, quod uidebit ultra uitrum, & lapides diaphanos:</s>
            <s xml:id="echoid-s18838" xml:space="preserve"> quia homines rarò aſpiciunt ad illud, quod eſt
              <lb/>
            ultra uitrum, & lapides diaphanos.</s>
            <s xml:id="echoid-s18839" xml:space="preserve"> Et quia ita eſt, dicamus de deceptionibus refractionis particu-
              <lb/>
            laribus, quæ ſemper accidunt & ſine difficultate, ſcilicet quæ accidunt in eis, quę uidentur in cœlo,
              <lb/>
            & in aqua:</s>
            <s xml:id="echoid-s18840" xml:space="preserve"> & dicemus parum de his, quæ uidentur ultra uitrũ, & lapides.</s>
            <s xml:id="echoid-s18841" xml:space="preserve"> Dicamus ergo, quòd ſemք
              <lb/>
            uiſus fallitur in eis, quæ comprehen duntur ultra corpus diaphanum, diuerſum ab aere, præſertim
              <lb/>
            in poſitione & remotione, in coloribus & lucibus eorum, & in magnitudine eorum & figuris quo-
              <lb/>
            rundam.</s>
            <s xml:id="echoid-s18842" xml:space="preserve"> Ea enim, quæ uidentur in aqua, & ultra uitrum, & lapides diaphanos, uidẽtur maiora:</s>
            <s xml:id="echoid-s18843" xml:space="preserve"> ſtel-
              <lb/>
            læ autem, & diſtantiæ inter ſtellas, quandoq;</s>
            <s xml:id="echoid-s18844" xml:space="preserve"> uidentur maiores, quandoque minores.</s>
            <s xml:id="echoid-s18845" xml:space="preserve"/>
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        <div xml:id="echoid-div607" type="section" level="0" n="0">
          <head xml:id="echoid-head524" xml:space="preserve" style="it">39. Si communis ſectio ſuperficierum, refractionis & refractiui fuerit linea recta, & uiſ{us}
            <lb/>
          ſit in perpendiculari duct a à medio uiſibilis par alleli communi ſectioni: imago maior uidebitur
            <lb/>
          uiſibili. 31 p 10.</head>
          <p>
            <s xml:id="echoid-s18846" xml:space="preserve">SIt ergo uiſus a:</s>
            <s xml:id="echoid-s18847" xml:space="preserve"> & ſit b c ultra corpus diaphanum, groſsius aere:</s>
            <s xml:id="echoid-s18848" xml:space="preserve"> Dico, quòd b cuidetur maior,
              <lb/>
            quàm ſit.</s>
            <s xml:id="echoid-s18849" xml:space="preserve"> Sit ergo primò ſuperficies corporis diaphani plana.</s>
            <s xml:id="echoid-s18850" xml:space="preserve"> A aut eſt in perpendiculari, exe-
              <lb/>
            unte à medio b c ſuper ſuperficiem corporis:</s>
            <s xml:id="echoid-s18851" xml:space="preserve"> aut extra.</s>
            <s xml:id="echoid-s18852" xml:space="preserve"> Sit ergo in primis, in ipſa:</s>
            <s xml:id="echoid-s18853" xml:space="preserve"> & [per 12 p 1]
              <lb/>
            ſit illa perpendicularis a m z:</s>
            <s xml:id="echoid-s18854" xml:space="preserve"> & extrahamus ſuperficiem, in qua ſunt lineæ a z, b c:</s>
            <s xml:id="echoid-s18855" xml:space="preserve"> & faciet in ſuperfi
              <lb/>
            cie corporis diaphani lineam d m e [per 3 p 11:</s>
            <s xml:id="echoid-s18856" xml:space="preserve">] & [per 9 n] ſuperficies, in qua ſunt duæ lineę a z, b c,
              <lb/>
            crit perpendicularis ſuper ſuperficiem corporis diaphani.</s>
            <s xml:id="echoid-s18857" xml:space="preserve"> Et non tranſit per a & per aliquod pun-
              <lb/>
            ctum lineæ b c ſuperficies, quæ ſit perpendicularis ſuper ſuperficiem corporis diaphani, niſi illa, in
              <lb/>
            qua ſunt lineæ a z, b c.</s>
            <s xml:id="echoid-s18858" xml:space="preserve"> Non enim tranſit per a ſuperficies perpendicularis ſuper ſuperficiem corpo-
              <lb/>
            ris diaphani, niſi illa, quæ tranſit per a z:</s>
            <s xml:id="echoid-s18859" xml:space="preserve"> quæ linea eſt perpendicularis ſuper ſuperficiem corporis:</s>
            <s xml:id="echoid-s18860" xml:space="preserve">
              <lb/>
            [per 9 n & conuerſionem 4 d 11] nec exit ex a perpendicularis ſuper ſuperficiem corporis diapha-
              <lb/>
            ni, niſi linea a z.</s>
            <s xml:id="echoid-s18861" xml:space="preserve"> Non ergo per a tranſit ſuperficies, quæ ſit perpendicularis ſuper ſuperficiem corpo
              <lb/>
            ris diaphani, niſi illa, quæ tranſit per lineam a z:</s>
            <s xml:id="echoid-s18862" xml:space="preserve"> & non tranſit per aliquod punctum lineæ b c & per
              <lb/>
            lineam a z, niſi illa ſuperficies, in qua ſunt duæ lineæ a z, b c.</s>
            <s xml:id="echoid-s18863" xml:space="preserve"> Non ergo tranſit per a & per aliquod
              <lb/>
            punctum lineæ b c ſuperficies perpen dicularis ſuper ſu-
              <lb/>
              <figure xlink:label="fig-0277-01" xlink:href="fig-0277-01a" number="235">
                <variables xml:id="echoid-variables222" xml:space="preserve">a
                  <unsure/>
                d m
                  <gap/>
                g p h l k q bn
                  <unsure/>
                z c</variables>
              </figure>
            perficiẽ corporis diaphani, niſi illa, in qua ſunt lineæ a z,
              <lb/>
            b c.</s>
            <s xml:id="echoid-s18864" xml:space="preserve"> Non ergo refringetur forma alicuius puncti eorum,
              <lb/>
            quæ ſunt in b c, niſi ex linea d e.</s>
            <s xml:id="echoid-s18865" xml:space="preserve"> Et [per 11 p 1] extraha-
              <lb/>
            mus ex b & c duas perpendiculares:</s>
            <s xml:id="echoid-s18866" xml:space="preserve"> cadent ergo in lineã
              <lb/>
            d e in duobus punctis d e, [per lemma Procli ad 29 p 1:</s>
            <s xml:id="echoid-s18867" xml:space="preserve">
              <lb/>
            quia b c, d e ſunt parallelæ ex theſi] ſcilicet b d, c e.</s>
            <s xml:id="echoid-s18868" xml:space="preserve"> Et ſit
              <lb/>
            b c in primis æ quidiſtans lineę d e:</s>
            <s xml:id="echoid-s18869" xml:space="preserve"> & refringatur forma
              <lb/>
            b ad a ex p:</s>
            <s xml:id="echoid-s18870" xml:space="preserve"> & forma c ad a ex h:</s>
            <s xml:id="echoid-s18871" xml:space="preserve"> & cõtinuemus lineas b p,
              <lb/>
            p a, c h, h a:</s>
            <s xml:id="echoid-s18872" xml:space="preserve"> item a b, a c:</s>
            <s xml:id="echoid-s18873" xml:space="preserve"> & extrahamus a p ad l, & a h ad k.</s>
            <s xml:id="echoid-s18874" xml:space="preserve">
              <lb/>
            [Nam quòd a p, a h concurrant cum b d, c e patet per lem
              <lb/>
            ma Procli ad 29 p 1.</s>
            <s xml:id="echoid-s18875" xml:space="preserve">] Quia ergo z poſitum fuit in medio
              <lb/>
            lineæ b c, poſitio b ex a erit ęqualis poſitioni c exa:</s>
            <s xml:id="echoid-s18876" xml:space="preserve"> & ſic
              <lb/>
            diſtantia p ex a erit ſicut diſtantia h ex a.</s>
            <s xml:id="echoid-s18877" xml:space="preserve"> [Quia enim a z
              <lb/>
            bifariam ſecans b c, eſt ad eandem perpendicularis per
              <lb/>
            theſin, ipſaq́;</s>
            <s xml:id="echoid-s18878" xml:space="preserve"> a z communis, æquatur ſibijpſi:</s>
            <s xml:id="echoid-s18879" xml:space="preserve"> erit per 4 p 1
              <lb/>
            a b æqualis a c.</s>
            <s xml:id="echoid-s18880" xml:space="preserve"> Itaque cum b c, d e ſint parallelæ ex theſi,
              <lb/>
            & puncta b & c à uiſu a æ quabiliter diſtent:</s>
            <s xml:id="echoid-s18881" xml:space="preserve"> ab eodem æ-
              <lb/>
            quabiliter diſtabuntrefractionum puncta p & h, propter
              <lb/>
            æquabilem in eodem & æquabili medio punctorum o-
              <lb/>
            mnium diffuſionem.</s>
            <s xml:id="echoid-s18882" xml:space="preserve"> Quare a p æquatur ipſi h a:</s>
            <s xml:id="echoid-s18883" xml:space="preserve">] & ſic
              <lb/>
            [per 5.</s>
            <s xml:id="echoid-s18884" xml:space="preserve"> 15 p 1] angulus d p l erit æqualis angulo e h k, ſed
              <lb/>
            [per 29 p 1] duo anguli d, e ſunt recti:</s>
            <s xml:id="echoid-s18885" xml:space="preserve"> & linea d p eſt æqua
              <lb/>
            lis lineæ e h:</s>
            <s xml:id="echoid-s18886" xml:space="preserve"> quia p m eſt ęqualis m h.</s>
            <s xml:id="echoid-s18887" xml:space="preserve"> [Nam quia per the
              <lb/>
            ſin, fabricationem & 34 p 1 tota m d ęquatur toti m e:</s>
            <s xml:id="echoid-s18888" xml:space="preserve"> & an
              <lb/>
            guli ad m deinceps recti per 29 p 1, & ad p & h ęquales per
              <lb/>
            concluſionem, latusq́;</s>
            <s xml:id="echoid-s18889" xml:space="preserve"> a m commune:</s>
            <s xml:id="echoid-s18890" xml:space="preserve"> æquabitur per 26
              <lb/>
            p 1 m p ipſim h.</s>
            <s xml:id="echoid-s18891" xml:space="preserve"> Quare reliqua d p æ quabitur reliquæ e h per 19 p 5] ergo [per 26 p 1] d l eſt æqualis
              <lb/>
            e k:</s>
            <s xml:id="echoid-s18892" xml:space="preserve"> & continuemus l k:</s>
            <s xml:id="echoid-s18893" xml:space="preserve"> erit ergo [per 33 p 1] æqualis lineæ b c:</s>
            <s xml:id="echoid-s18894" xml:space="preserve"> angulus ergo c a b erit minor angu-
              <lb/>
            lo k a l.</s>
            <s xml:id="echoid-s18895" xml:space="preserve"> [Nam recta l k ſecãs latera a b, a c, facit duos angulos exteriores, maiores interioribus oppo
              <lb/>
            </s>
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