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 contents

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[191.] 64. Perſpicuitas medij immoder ata creat errores in ſingulis uiſibilibus ſpeciebus. In diſtãtia: ſitu: figura: magnitudine: diuiſione: continuatione & numero. 16. 44. 97. 28. 109 p 4.
Page: 106 (100)
[192.] 65. In motu: quiete: aſperitate: lenitate: raritate: denſitate: umbra: tenebris: pulchritudine: deformitate: ſimilitudine & dißimilitudine. 138. 141. 144. 147. 150. 153 p 4.
Page: 106 (100)
[193.] 66. Tempus immoderatum creat errores in ſingulis uiſibilibus ſpeciebus. In diſtantia: ſitu: figura: magnitudine. 16. 44. 97. 28 p 4.
Page: 106 (100)
[194.] 67. In diuiſione: continuatione: numero: quiete & motu. 109. 138 p 4.
Page: 106 (100)
[195.] 68. In aſperitate: lenitate: raritate: denſitate: umbra: tenebris: pulchritudine: deformitate: ſimilitudine: dißimilitudine. 141. 144. 147. 150. 153 p 4.
Page: 107 (101)
[196.] 69. Imbecillit{as} uiſus creat errores in ſingulis uiſibilibus ſpeciebus. In diſtantia: ſitu: magni-tudine: figura: diuiſione: continuatione: numero. 16. 44. 28. 97. 109 p 4.
Page: 107 (101)
[197.] 70. In motu & quiete. 138 p 4.
Page: 107 (101)
[198.] 71. In aſperitate: lenitate: raritate: denſitate: umbra: tenebris: pulchritudine: deformitate: ſimilitudine: dißimilitudine. 141. 144. 147. 150. 153 p 4.
Page: 107 (101)
[199.] 72. In uiſione errores creantur aliàs quidem à ſingulis uiſionẽ perficientibus: aliàs uerò à plu-ribus ſimul, quorum nullum per ſe errorem crearet. 154 p 4.
Page: 108 (102)
[200.] ALHAZEN FILII ALHAYZEN OPTICAE LIBER QVARTVS.
Page: 108 (102)
[201.] PROOEMIVM LIBRI. CAP. I. 1. Viſio fit trifariam: rectè: reflexè: & refr actè. In præf. 1. 3. 10 Libr.
Page: 108 (102)
[202.] QVOD LVCI ACCIDAT REFLEXIO À POLITIS corporibus. Cap. II. 2. Lux & color reflectuntur à quolibet politæ ſuperficiei puncto, lineis rectis. 1 p 5.
Page: 108 (102)
[203.] 3. Lux & color à quolibet ſuperficiei coloratæ puncto ad quodlibet ſuperficiei politæ oppoſitæ punctum permixti confluunt. 2 p 5.
Page: 109 (103)
[204.] 4. Reflexio debilit at lucem & colorem: & omnino totam uiſibilis ſpeciem. 3 p 5.
Page: 109 (103)
[205.] 5. Lux & color reflexi ſunt debiliores luce & colore primis: fortiores autem ſecundis, cum quibus ab eodem ortu æquabiliter diſtant. 4 p 5.
Page: 109 (103)
[206.] DE MODO REFLEXIONIS FORMARVM À POLI-tis corporibus. Cap. III. 6. Lenitatis: politæ ſuperficiei: & perpendicularis incidentiæ definitiones. In def. 5 libr.
Page: 110 (104)
[207.] 7. Fabricatio & uſus organi reflexionis. 9 p 5.
Page: 110 (104)
[208.] 8. Fabricatio ſeptem ſpeculorum regularium. 8 p 5.
Page: 112 (106)
[209.] 9. Sit{us} & collocatio ſpeculorum regulariũ in reflexionis organo.10.12.13.14.15.16.17 p 5.
Page: 113 (107)
[210.] 10. Radi{us} ſpeculo plano obliqu{us}, in oppoſitam partem reflectitur: & æquat angulos inci-dentiæ & reflexionis. 10 p 5.
Page: 114 (108)
[211.] 11. Radi{us} ſpeculo perpendicularis, reflectitur in ſeipſum. 11.12 p 5.
Page: 114 (108)
[212.] 12. In ſpeculis, conuexis, cauis: ſphærico, conico cylindraceo, anguli incidentiæ & reflexio-nis æquantur. 12.13.14.15.16.17.20 p 5.
Page: 114 (108)
[213.] 13. Superficies reflexionis eſt perpendicularis plano ſpeculum in reflexionis puncto tan-genti. 25 p 5.
Page: 115 (109)
[214.] 14. Inter uiſibile & ſpeculũ innumer abiles pyramides fiũt alternis baſib. & uerticib{us}. 22 p 5.
Page: 117 (111)
[215.] 15. Lux à ſuperficie polita longinquiore reflexa, trifariam debilitatur.
Page: 117 (111)
[216.] 16. Lux & color reflectuntur per line{as} phyſic{as}, latitudine quadam prędit{as}. 3 p 2.6 p 5.
Page: 118 (112)
[217.] 17. Reflexio lucis & coloris à ſuperficie aſper a facta, plerun fugit uiſum. 1 p 5.
Page: 118 (112)
[218.] 18. Radij incidentiæ & reflexionis, ſit{us} ſimilitudine conueniunt. Ita anguli incidentiæ & reflexionis æquantur. 20 p 5.
Page: 118 (112)
[219.] 19. Colorem luci permiſtum reflecti, reflexionis organo ostenditur. 3 p 5.
Page: 119 (113)
[220.] QVOÒD COMPREHENSIO FORMARVM È CORPORIBVS politis fiat reflexione. Cap. 1111. 20. Falſa eſt utra opinio: & radios à uiſu ad ſpeculum miſſos, inde́ ad uiſibile reflexos, ima ginem percipere: & imaginẽ in ſpeculo iam antè impreſſam inde ad uiſum manare. 23. 24 p 5.
Page: 119 (113)
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            <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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