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

Table of figures

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[61] b d a f e g c
[62] q a e g
[63] a z g e b q
[64] d q g h a z b
[65] k t o z m u y f c l z
[66] q d g e a b
[67] q d n e g h a b
[68] d q n g a e h b
[69] a g e b d
[70] h n t f x q c u p m z ſ
[71] q ſ a e z h a t d m c b d g n
[72] ſ a e z h d g c t b q a d n m
[73] d b q a ſ e z h g c a m n d
[74] d a h ſ s u g e z t q
[75] o k f i l n m
[76] d a u m l t z c g s h q
[77] k b d z e i c g x
[78] p n f o m u q ſ
[79] a a n m e z h q ſ b d g d t c
[80] c p r m o f k y s
[81] b f e m h u d a i z q c t y g ſ
[82] c p p m o f k s s
[83] b e n h d a i z q u t y g ſ x
[84] a b c p g l m g h o j k d e f
[85] e g d t m b u k h f q a c
[86] s f h q n x r p l z u t m a b o e g k d
[87] a q k b f l n g c e l d h
[88] a ſ f K b h d z g e s n q o t m i p
[89] f d a e p t m f k h i g z o q n b
[90] l d a e f x u y t k p r c z o h g M n q m i b s
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        <div xml:id="echoid-div449" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s12752" xml:space="preserve">
              <pb o="188" file="0194" n="194" rhead="ALHAZEN"/>
            enim anguli t z f, t f z æquantur angulis z t n & h t n per 12 n 4 æqualibus, cum t ex theſi ſit reflexio
              <lb/>
            nis punctum:</s>
            <s xml:id="echoid-s12753" xml:space="preserve"> ipſi igitur inter ſe æquantur:</s>
            <s xml:id="echoid-s12754" xml:space="preserve"> & anguli ad s recti ſunt:</s>
            <s xml:id="echoid-s12755" xml:space="preserve"> & t s commune latus eſt.</s>
            <s xml:id="echoid-s12756" xml:space="preserve"> Quare
              <lb/>
            per 26 p 1 f s æquatur s z.</s>
            <s xml:id="echoid-s12757" xml:space="preserve">] Sed [per 2 p 6] proportio f s ad s z, ſicut k i ad i z:</s>
            <s xml:id="echoid-s12758" xml:space="preserve"> erit ergo k i ęqualisi z.</s>
            <s xml:id="echoid-s12759" xml:space="preserve"> Du
              <lb/>
            cta autem linea p i:</s>
            <s xml:id="echoid-s12760" xml:space="preserve"> cum ſuperficies a t f ſit orthogonalis ſuper ſuperficiem z k f:</s>
            <s xml:id="echoid-s12761" xml:space="preserve"> erit [per 4 d 11] p i or-
              <lb/>
            thogonalis ſuper z k:</s>
            <s xml:id="echoid-s12762" xml:space="preserve"> & erit [per 4 p 1] angulus p k z æqualis angulo k z p:</s>
            <s xml:id="echoid-s12763" xml:space="preserve"> ſed [ք 29 p 1] angulus e p o
              <lb/>
            æqualis angulo p k z, & angulus o p z æqualis angulo p z k.</s>
            <s xml:id="echoid-s12764" xml:space="preserve"> Quare angulus e p o æqualis eſt angulo
              <lb/>
            o p z.</s>
            <s xml:id="echoid-s12765" xml:space="preserve"> Etita z reflectitur ad e à puncto p [per 12 n 4.</s>
            <s xml:id="echoid-s12766" xml:space="preserve">] Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12767" xml:space="preserve"> Si autem ſumatur aliud
              <lb/>
            punctũ ſn circulo, à quo z reflectatur ad h:</s>
            <s xml:id="echoid-s12768" xml:space="preserve"> probabitur, quòd ab alio puncto pyramidis, quàm p, refle
              <lb/>
            ctetur z ad e.</s>
            <s xml:id="echoid-s12769" xml:space="preserve"> Et ſi reflectatur z ad h à tribus punctis circuli:</s>
            <s xml:id="echoid-s12770" xml:space="preserve"> reflectetur z a d e à tribus pũctis pyrami
              <lb/>
            dis:</s>
            <s xml:id="echoid-s12771" xml:space="preserve"> ſi à quatuor, à quatuor.</s>
            <s xml:id="echoid-s12772" xml:space="preserve"> Si uerò dicatur, quòd à pluribus pũctis pyramidis, ꝗ̃ quatuor, poſsit pun
              <lb/>
            ctũ z reflecti ad e:</s>
            <s xml:id="echoid-s12773" xml:space="preserve"> per cõuerſionẽ prædictæ probatiõis poterit oſtendi, quòd punctũ z reflectitur ad
              <lb/>
            h à pluribus punctis circuli quàm quatuor [contra 86 n.</s>
            <s xml:id="echoid-s12774" xml:space="preserve">] Et ubi accidet punctũ z reflecti ad h ab ali
              <lb/>
            quot punctis circuli, uel ab uno tantùm:</s>
            <s xml:id="echoid-s12775" xml:space="preserve"> accidet punctũ z reflecti ad e à totidem punctis pyramidis,
              <lb/>
            aut ab uno tantùm, aut è contrario.</s>
            <s xml:id="echoid-s12776" xml:space="preserve"> Quòd ſi dicatur contrarium:</s>
            <s xml:id="echoid-s12777" xml:space="preserve"> poterit improbari prædicto modo.</s>
            <s xml:id="echoid-s12778" xml:space="preserve">
              <lb/>
            Palàm ergo, quòd punctorũ quædam unicã habent imaginẽ:</s>
            <s xml:id="echoid-s12779" xml:space="preserve"> quędam duas:</s>
            <s xml:id="echoid-s12780" xml:space="preserve"> quædã tres:</s>
            <s xml:id="echoid-s12781" xml:space="preserve"> quædã qua-
              <lb/>
            tuor:</s>
            <s xml:id="echoid-s12782" xml:space="preserve"> ſed nõ poſsibile plures.</s>
            <s xml:id="echoid-s12783" xml:space="preserve"> Verùm duplici uiſu adhibito, ſpeculo:</s>
            <s xml:id="echoid-s12784" xml:space="preserve"> eiuſdem imaginis diuerſa erunt
              <lb/>
            loca:</s>
            <s xml:id="echoid-s12785" xml:space="preserve"> quæ diuerſitas propter ſuam imperceptibilitatem non inducit errorem.</s>
            <s xml:id="echoid-s12786" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div451" type="section" level="0" n="0">
          <head xml:id="echoid-head405" xml:space="preserve" style="it">102. Viſu & uiſibili datis, in ſpeculo conico cauo punctum reflexionis inuenire. 21 p 9.</head>
          <p>
            <s xml:id="echoid-s12787" xml:space="preserve">PVnctum autem reflexionis, à quo z reflectitur ad e, facile eſt inuenire:</s>
            <s xml:id="echoid-s12788" xml:space="preserve"> inuento puncto circuli,
              <lb/>
            à quo punctum z reflectitur ad h.</s>
            <s xml:id="echoid-s12789" xml:space="preserve"> Et erit inuentio modo prædicto.</s>
            <s xml:id="echoid-s12790" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div452" type="section" level="0" n="0">
          <head xml:id="echoid-head406" xml:space="preserve">ALHAZEN FILII</head>
          <head xml:id="echoid-head407" xml:space="preserve">ALHAYZEN OPTICAE</head>
          <head xml:id="echoid-head408" xml:space="preserve">LIBER SEXTVS.</head>
          <p style="it">
            <s xml:id="echoid-s12791" xml:space="preserve">Llber ſextus in nouẽ partes diuiditur.</s>
            <s xml:id="echoid-s12792" xml:space="preserve"> Pars prima eſt titulus libri.</s>
            <s xml:id="echoid-s12793" xml:space="preserve"> Secunda, quòd er-
              <lb/>
            ror accidat uiſui propter reflexionem.</s>
            <s xml:id="echoid-s12794" xml:space="preserve"> Tertia de errore eueniente in ſpeculis planis.</s>
            <s xml:id="echoid-s12795" xml:space="preserve">
              <lb/>
            Quarta de errore, qui oritur in ſpeculis ſphæricis exteriorib.</s>
            <s xml:id="echoid-s12796" xml:space="preserve"> Quinta de errore in ſpeculis
              <lb/>
            columnaribus exterioribus.</s>
            <s xml:id="echoid-s12797" xml:space="preserve"> Sexta de errore in pyramidalibus exterioribus.</s>
            <s xml:id="echoid-s12798" xml:space="preserve"> Septima de
              <lb/>
            errore in ſphæricis concauis.</s>
            <s xml:id="echoid-s12799" xml:space="preserve"> Octaua de errore in columnaribus concauis.</s>
            <s xml:id="echoid-s12800" xml:space="preserve"> Nona de errore
              <lb/>
            in pyramidalibus concauis.</s>
            <s xml:id="echoid-s12801" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div453" type="section" level="0" n="0">
          <head xml:id="echoid-head409" xml:space="preserve">PROOEMIVM LIBRI. CAP. I.</head>
          <p>
            <s xml:id="echoid-s12802" xml:space="preserve">PAtuit ex ſuperioribus libris modus acquiſitionis formarum in ſpeculis per uiſum, ſitus
              <lb/>
            linearum reflexionis & acceſſus, ſitus imaginum:</s>
            <s xml:id="echoid-s12803" xml:space="preserve"> & loca ipſarũ.</s>
            <s xml:id="echoid-s12804" xml:space="preserve"> Verùm per reflexionẽ
              <lb/>
            non ſemper comprehenditur formæ ueritas.</s>
            <s xml:id="echoid-s12805" xml:space="preserve"> In ſpeculis enim concauis apparet imago
              <lb/>
            faciei diſtorta, & occultatur uiſui diſpoſitio eius uera.</s>
            <s xml:id="echoid-s12806" xml:space="preserve"> Vnde planum eſt, errorẽ incide.</s>
            <s xml:id="echoid-s12807" xml:space="preserve">
              <lb/>
            re in comprehenſione formarum propter reflexionem.</s>
            <s xml:id="echoid-s12808" xml:space="preserve"> Huius erroris modum, & modi
              <lb/>
            cauſſam, propoſitum eſt in libro præſente explanare, & ſecundum diuerſitates ſpeculorum diſcurre
              <lb/>
            re uarietates errorum.</s>
            <s xml:id="echoid-s12809" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div454" type="section" level="0" n="0">
          <head xml:id="echoid-head410" xml:space="preserve">QVO'D ERROR ACCIDAT VISVI PROPTER RE-
            <lb/>
          flexionem. Cap. II.</head>
          <head xml:id="echoid-head411" xml:space="preserve" style="it">1. Viſus reflexus ſimiliter allucinatur, ut directus: ſed uebementius & frequentius. 7 p 5.</head>
          <p>
            <s xml:id="echoid-s12810" xml:space="preserve">COmprehenſionem formarũ in uiſu directo liber ſecundus docuit:</s>
            <s xml:id="echoid-s12811" xml:space="preserve"> & ſingula, quę propter e-
              <lb/>
            greſſum à tẽperantia in uiſu illo errorẽ inducũt, liber tertius diligẽter expoſuit.</s>
            <s xml:id="echoid-s12812" xml:space="preserve"> Fit aũt com-
              <lb/>
            prehenſio formarũ per reflexionẽ, ſicut & directè:</s>
            <s xml:id="echoid-s12813" xml:space="preserve"> & quorũ fit acquiſitio in directione, fit eriã
              <lb/>
            in reflexione, utpote lucis, coloris, figurę, magnitudinis, diſtantiæ, & ſimiliũ.</s>
            <s xml:id="echoid-s12814" xml:space="preserve"> Et quemadmodũ in di
              <lb/>
            rectione rerum præfixarũ & cognitarũ ad alias fit collatio, & inde oritur cõiecturatio, & ſumitur iu-
              <lb/>
            diciũ in anima:</s>
            <s xml:id="echoid-s12815" xml:space="preserve"> ſimiliter accidit in reflexione.</s>
            <s xml:id="echoid-s12816" xml:space="preserve"> Vnde quæcunq;</s>
            <s xml:id="echoid-s12817" xml:space="preserve"> temperamentũ egreſſa, in uiſu dire-
              <lb/>
            cto errorẽ efficiunt, in reflexione ſimiliter inducunt.</s>
            <s xml:id="echoid-s12818" xml:space="preserve"> Et ſecundũ ſingula maior accidit error in refle
              <lb/>
            xione, propter lucẽ debilem, quã debilitat ipſa reflexio.</s>
            <s xml:id="echoid-s12819" xml:space="preserve"> Vt aũt generaliter loquamur, nõ poteſt in re
              <lb/>
            flexione coprehendi ueritas formę, ſicut in directione, propter triplex impedιmentũ reflexioni ſpe-
              <lb/>
            ciale.</s>
            <s xml:id="echoid-s12820" xml:space="preserve"> Primũ eſt, quòd in reflexione apparet rei forma præ oculis uiſui oppoſita, cum non ſit reuera.</s>
            <s xml:id="echoid-s12821" xml:space="preserve">
              <lb/>
            Secundũ, quòd lux & color corporis uiſi miſcentur cum colore ſpeculi, quã mixturã uiſus percipit,
              <lb/>
            nõ uerũ rei uiſę colorẽ uel lucem.</s>
            <s xml:id="echoid-s12822" xml:space="preserve"> Tertiũ, quòd ipſa reflexio, ut in ſuperioribus [4 n 4] eſt aſsignatũ,
              <lb/>
            lucẽ & colorẽ debilitat.</s>
            <s xml:id="echoid-s12823" xml:space="preserve"> Quare in reflexione latebit uiſum ueritas lucis & coloris plus, ꝗ̃ in directio-
              <lb/>
            ne.</s>
            <s xml:id="echoid-s12824" xml:space="preserve"> Amplius:</s>
            <s xml:id="echoid-s12825" xml:space="preserve"> ſuperiorà docuerunt, quòd quantitas temperamenti eorũ, quę in uiſu directo errorem
              <lb/>
            inducunt, fortitudinẽ lucis & coloris reſpicit:</s>
            <s xml:id="echoid-s12826" xml:space="preserve"> fortiore enim luce uel colore erit maior, debiliore mi-
              <lb/>
            hor.</s>
            <s xml:id="echoid-s12827" xml:space="preserve"> Cum autem per reflexionem debilitentur lux & color:</s>
            <s xml:id="echoid-s12828" xml:space="preserve"> erit latitudo temperamenti ſingulorum
              <lb/>
            errorẽ inducentium minor in reflexione, quàm in directione:</s>
            <s xml:id="echoid-s12829" xml:space="preserve"> & temperantiæ diminuta latitudo plu
              <lb/>
              <gap/>
            alitatem erroris inducit.</s>
            <s xml:id="echoid-s12830" xml:space="preserve"> Præterea quædam minutiæ corporum comprehendi poterunt per dire-
              <lb/>
            </s>
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