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

Page concordance

< >
Scan Original
191 185
192 186
193 187
194 188
195 189
196 190
197 191
198 192
199 193
200 194
201 195
202 196
203 197
204 198
205 199
206 200
207 201
208 202
209 203
210 204
211 205
212 206
213 207
214 208
215 209
216 210
217 211
218 212
219 213
220 214
< >
page |< < (188) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <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>
          </p>
        </div>
      </text>
    </echo>
Impressum