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

List of thumbnails

< >
121
121 (115) 		122
122 (116)
123
123 (117) 		124
124 (118)
125
125 (119) 		126
126 (120)
127
127 (121) 		128
128 (122)
129
129 (123) 		130
130 (124)
< >
page |< < (200) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div472" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s13859" xml:space="preserve">
              <pb o="200" file="0206" n="206" rhead="ALHAZEN"/>
            puncto p:</s>
            <s xml:id="echoid-s13860" xml:space="preserve"> & ducatur linea q p:</s>
            <s xml:id="echoid-s13861" xml:space="preserve"> & procedat, donec cadat ſuper e g in pũcto f:</s>
            <s xml:id="echoid-s13862" xml:space="preserve"> & ducatur linea t q uſq;</s>
            <s xml:id="echoid-s13863" xml:space="preserve">
              <lb/>
            ad e g:</s>
            <s xml:id="echoid-s13864" xml:space="preserve"> & cadat in pũctum k.</s>
            <s xml:id="echoid-s13865" xml:space="preserve"> Pa-
              <lb/>
              <figure xlink:label="fig-0206-01" xlink:href="fig-0206-01a" number="167">
                <variables xml:id="echoid-variables157" xml:space="preserve">p o b c e l m t n a q k f d g</variables>
              </figure>
            làm, quòd k erit ſupra f [ꝗa pun-
              <lb/>
            ctum n humilius eſt puncto m.</s>
            <s xml:id="echoid-s13866" xml:space="preserve">]
              <lb/>
            Verùm cũ proportio g c ad c m,
              <lb/>
            ſicut g q ad q m [ut patuit] & à
              <lb/>
            punctis diuiſionũ ducantur tres
              <lb/>
            lineæ concurrẽtes, in aliam par-
              <lb/>
            tem productæ ſecabunt lineam
              <lb/>
            e g ſecundum prædictã propor-
              <lb/>
            tionẽ [per 8 n.</s>
            <s xml:id="echoid-s13867" xml:space="preserve">] Quare propor-
              <lb/>
            tio g e ad e n, ſicut g f ad f n:</s>
            <s xml:id="echoid-s13868" xml:space="preserve"> ſed n
              <lb/>
            eſt finis cõtingentiæ.</s>
            <s xml:id="echoid-s13869" xml:space="preserve"> Quare flo-
              <lb/>
            cus eſt imaginis [per 18 n 5.</s>
            <s xml:id="echoid-s13870" xml:space="preserve">] Igi-
              <lb/>
            tur linea f q t erit imago arcus e
              <lb/>
            c b:</s>
            <s xml:id="echoid-s13871" xml:space="preserve"> & erit linea curua, non recta:</s>
            <s xml:id="echoid-s13872" xml:space="preserve">
              <lb/>
            quoniam t q k eſt recta:</s>
            <s xml:id="echoid-s13873" xml:space="preserve"> & curui-
              <lb/>
            tas lineæ non eſt ex parte ſpecu-
              <lb/>
            li.</s>
            <s xml:id="echoid-s13874" xml:space="preserve"> Similiter ſi perpendicularis à
              <lb/>
            puncto d cadat ex alia parte arcus:</s>
            <s xml:id="echoid-s13875" xml:space="preserve"> ſimilis erit probatio.</s>
            <s xml:id="echoid-s13876" xml:space="preserve"> Si uerò cadat perpendicularis in medium
              <lb/>
            arcus a b:</s>
            <s xml:id="echoid-s13877" xml:space="preserve"> lineæ à puncto d ex diuerſis partibus ad arcum ductæ, æqualiter diſtantes à perpendicu-
              <lb/>
            lari:</s>
            <s xml:id="echoid-s13878" xml:space="preserve"> erunt æquales, & æquales angulos continebunt uerſus g:</s>
            <s xml:id="echoid-s13879" xml:space="preserve"> & imagines à g æqualiter diſtabunt:</s>
            <s xml:id="echoid-s13880" xml:space="preserve">
              <lb/>
            & fines contingentiæ ſimiliter.</s>
            <s xml:id="echoid-s13881" xml:space="preserve"> Et licebit probare prædicto modo de utraq;</s>
            <s xml:id="echoid-s13882" xml:space="preserve"> parte arcus per ſe, ſe-
              <lb/>
            cundum quod diuiditur à perpendiculari:</s>
            <s xml:id="echoid-s13883" xml:space="preserve"> quòd eius imago ſit linea curua modo prædicto.</s>
            <s xml:id="echoid-s13884" xml:space="preserve"> Quod
              <lb/>
            eſt propoſitum.</s>
            <s xml:id="echoid-s13885" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div474" type="section" level="0" n="0">
          <head xml:id="echoid-head426" xml:space="preserve" style="it">13. Si uiſ{us} ſit extra ſuperficiem incidentiæ: imago peripheriæ eccentricæ peripheriæ circuli
            <lb/>
          (qui eſt communis ſectio ſuperficierum, reflex ionis & ſpeculi ſphærici conuexi) uidebitur magis
            <lb/>
          curua, quàm imago peripheriæ concentricæ. 48 p 6.</head>
          <p>
            <s xml:id="echoid-s13886" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s13887" xml:space="preserve"> ſumatur circulus, cuius centrum non ſit centrum ſpeculi, ueruntamen ſit in eadem
              <lb/>
            ſuperficie cum centro ſpeculi.</s>
            <s xml:id="echoid-s13888" xml:space="preserve"> Dico, quòd ſi in hoc circulo
              <lb/>
              <figure xlink:label="fig-0206-02" xlink:href="fig-0206-02a" number="168">
                <variables xml:id="echoid-variables158" xml:space="preserve">b d a e h t z g f</variables>
              </figure>
            exteriore ſumatur arcus ex parte cẽtri ſpeculi, propinquior
              <lb/>
            ei ſecundum medium eius punctum, erit imago eius curua.</s>
            <s xml:id="echoid-s13889" xml:space="preserve"> Dato
              <lb/>
            enim hoc arcu:</s>
            <s xml:id="echoid-s13890" xml:space="preserve"> ducatur linea à centro ſpeculi ad centrum exterio-
              <lb/>
            ris circuli:</s>
            <s xml:id="echoid-s13891" xml:space="preserve"> & producatur hæc linea uſq;</s>
            <s xml:id="echoid-s13892" xml:space="preserve"> ad arcum datum:</s>
            <s xml:id="echoid-s13893" xml:space="preserve"> linea du-
              <lb/>
            cta à centro ſpeculi ad hunc arcum, quæ eſt pars diametri maioris
              <lb/>
            circuli, erit breuior omnibus lineis ductis ab eodem centro ſpecu-
              <lb/>
            li ad illum arcum [per 7 p 3.</s>
            <s xml:id="echoid-s13894" xml:space="preserve">] Et à centro ſpeculi poſſunt duci ad ar-
              <lb/>
            cum datũ duæ lineæ æquales à diuerſis partibus huius breuis [per
              <lb/>
            7 p 3] quæ quidem maiores erũt illa breui.</s>
            <s xml:id="echoid-s13895" xml:space="preserve"> Et ſi ſecundum alteram
              <lb/>
            illarum fiat circulus, cuius centrum ſit ſpeculi centrum:</s>
            <s xml:id="echoid-s13896" xml:space="preserve"> tranſibit
              <lb/>
            per capita harum duarum linearum arcus excedens arcum datum.</s>
            <s xml:id="echoid-s13897" xml:space="preserve">
              <lb/>
            Et palàm, quòd imago huius arcus excedentis, erit linea curua ſe-
              <lb/>
            cundum prædicta [11.</s>
            <s xml:id="echoid-s13898" xml:space="preserve">12 n:</s>
            <s xml:id="echoid-s13899" xml:space="preserve">] Et imagines punctorum huic arcui &
              <lb/>
            arcui dato communium eædem:</s>
            <s xml:id="echoid-s13900" xml:space="preserve"> & medium punctum arcus exce-
              <lb/>
            dentis eſt remotius à centro ſpeculi, quam punctũ arcus dati, quod
              <lb/>
            ipſum reſpicit.</s>
            <s xml:id="echoid-s13901" xml:space="preserve"> Quare eius imago propinquior eſt centro, quã ima-
              <lb/>
            go puncti arcus dati illum reſpicientis.</s>
            <s xml:id="echoid-s13902" xml:space="preserve"> Et ita cuiuslibet puncti ar-
              <lb/>
            cus exterioris imago propinquior eſt cẽtro, imagine puncti arcus
              <lb/>
            dati, quod ipſum reſpicit.</s>
            <s xml:id="echoid-s13903" xml:space="preserve"> Quare imago arcus dati curuior, quã imago arcus exterioris.</s>
            <s xml:id="echoid-s13904" xml:space="preserve"> Quare ima-
              <lb/>
            go arcus dati curua eſt.</s>
            <s xml:id="echoid-s13905" xml:space="preserve"> Quod eſt propoſitum.</s>
            <s xml:id="echoid-s13906" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div476" type="section" level="0" n="0">
          <head xml:id="echoid-head427" xml:space="preserve" style="it">14. Si uiſ{us} ſit extra ſuperficiem incidentiæ: imago lineæ rectæ, parallelæ rectæ tangẽti peri-
            <lb/>
          pheriam circuli (qui eſt communis ſectio ſuperficierum, reflexionis & ſpeculi ſphærici conuexi)
            <lb/>
          uidebitur curua. 49 p 6.</head>
          <p>
            <s xml:id="echoid-s13907" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s13908" xml:space="preserve"> quòd lineę rectæ imago in his ſpeculis ſit curua, probatur ſic.</s>
            <s xml:id="echoid-s13909" xml:space="preserve"> Sit a b linea uiſa:</s>
            <s xml:id="echoid-s13910" xml:space="preserve"> g cen
              <lb/>
            trum ſpeculi:</s>
            <s xml:id="echoid-s13911" xml:space="preserve"> ducantur lineæ a g, b g.</s>
            <s xml:id="echoid-s13912" xml:space="preserve"> Hæ aut ſunt æquales:</s>
            <s xml:id="echoid-s13913" xml:space="preserve"> aut non.</s>
            <s xml:id="echoid-s13914" xml:space="preserve"> Si æquales:</s>
            <s xml:id="echoid-s13915" xml:space="preserve"> fiat circulus,
              <lb/>
            cuius g centrum, ſecundum quantitatem illarum:</s>
            <s xml:id="echoid-s13916" xml:space="preserve"> qui ſit a e b:</s>
            <s xml:id="echoid-s13917" xml:space="preserve"> cadet quidem linea a b intra
              <lb/>
            circulum.</s>
            <s xml:id="echoid-s13918" xml:space="preserve"> Palàm ex prædictis [11.</s>
            <s xml:id="echoid-s13919" xml:space="preserve">12 n] quòd imago arcus a e b erit curua.</s>
            <s xml:id="echoid-s13920" xml:space="preserve"> Sit igitur imago eius z t h:</s>
            <s xml:id="echoid-s13921" xml:space="preserve">
              <lb/>
            imago a ſit z:</s>
            <s xml:id="echoid-s13922" xml:space="preserve"> imago b ſit h:</s>
            <s xml:id="echoid-s13923" xml:space="preserve"> imago e ſit t:</s>
            <s xml:id="echoid-s13924" xml:space="preserve"> & ducatur g e ſecans a b in puncto f.</s>
            <s xml:id="echoid-s13925" xml:space="preserve"> Palàm, quòd e eſt in ea-
              <lb/>
            dem linea cum f, remotior à centro g.</s>
            <s xml:id="echoid-s13926" xml:space="preserve"> Erit ergo eius imago propinquior centro, quàm fimago [per
              <lb/>
            30 n 5.</s>
            <s xml:id="echoid-s13927" xml:space="preserve">] Sit ergo m.</s>
            <s xml:id="echoid-s13928" xml:space="preserve"> Palàm ergo, quòd linea z m h eſt imago lineæ a b:</s>
            <s xml:id="echoid-s13929" xml:space="preserve"> [imagines enim punctorum a
              <lb/>
            & b communium eædem permanent] & eſt linea curua.</s>
            <s xml:id="echoid-s13930" xml:space="preserve"> Quod eſt propoſitum.</s>
            <s xml:id="echoid-s13931" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum