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
121 115
122 116
123 117
124 118
125 119
126 120
127 121
128 122
129 123
130 124
131 125
132 126
133 127
134 128
135 129
136 130
137 131
138 132
139 133
140 134
141 135
142 136
143 137
144 138
145 139
146 140
147 141
148 142
149 143
150 144
< >
page |< < (136) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div308" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s8012" xml:space="preserve">
              <pb o="136" file="0142" n="142" rhead="ALHAZEN"/>
            per quem ſuperficies his lineis incluſa ſecat ſphæram:</s>
            <s xml:id="echoid-s8013" xml:space="preserve"> erit [per 25 n 4] a b portio apparens ex
              <lb/>
            hoc circulo.</s>
            <s xml:id="echoid-s8014" xml:space="preserve"> Dico ergo, quòd loca imaginum, quæ per reflexiones ab hac portione factas compre-
              <lb/>
            henduntur:</s>
            <s xml:id="echoid-s8015" xml:space="preserve"> quædam ſunt intra ſpeculum:</s>
            <s xml:id="echoid-s8016" xml:space="preserve"> quędam in ſu
              <lb/>
              <figure xlink:label="fig-0142-01" xlink:href="fig-0142-01a" number="50">
                <variables xml:id="echoid-variables40" xml:space="preserve">g m h z p b d a k</variables>
              </figure>
            perficie ſpeculi:</s>
            <s xml:id="echoid-s8017" xml:space="preserve"> quędam extra ſpeculũ.</s>
            <s xml:id="echoid-s8018" xml:space="preserve"> Et unumquod-
              <lb/>
            que horum eſt determinandum.</s>
            <s xml:id="echoid-s8019" xml:space="preserve"> Ducatur à puncto g li-
              <lb/>
            nea ſecans circulum, & pars eius, quæ eſt chorda arcus
              <lb/>
            circuli, ſit æqualis ſemidiametro circuli [id quod per 1
              <lb/>
            p 4 fieri poteſt:</s>
            <s xml:id="echoid-s8020" xml:space="preserve">] ſit linea illa g h k:</s>
            <s xml:id="echoid-s8021" xml:space="preserve"> & chorda æqualis
              <lb/>
            ſemidiametro ſit h k:</s>
            <s xml:id="echoid-s8022" xml:space="preserve"> & producatur à puncto h perpen-
              <lb/>
            dicularis, quæ ſit d h m.</s>
            <s xml:id="echoid-s8023" xml:space="preserve"> Dico, quòd formæ reflexę à pun
              <lb/>
            cto h locus eſt intra ſphęram.</s>
            <s xml:id="echoid-s8024" xml:space="preserve"> Ducatur [per 23 p 1] à pun
              <lb/>
            cto h linea æ qualem renens angulum cum m h, angulo
              <lb/>
            m h g:</s>
            <s xml:id="echoid-s8025" xml:space="preserve"> & ſit p h:</s>
            <s xml:id="echoid-s8026" xml:space="preserve"> reflectentur quidem puncta huius lineæ
              <lb/>
            à puncto h ad uiſum g, & nõ alterius [per 12 n 4.</s>
            <s xml:id="echoid-s8027" xml:space="preserve">] Suma
              <lb/>
            tur ergo aliquod eius punctum:</s>
            <s xml:id="echoid-s8028" xml:space="preserve"> & ſit p:</s>
            <s xml:id="echoid-s8029" xml:space="preserve"> & ducatur ab eo
              <lb/>
            linea ad centrum ſphærę quę ſit p d:</s>
            <s xml:id="echoid-s8030" xml:space="preserve"> erit [ut demonſtra
              <lb/>
            tum eſt 25 n 4] p d perpendicularis ſuper ſuperficiem,
              <lb/>
            contingentem ſphæram ſuper punctum eius, per quod
              <lb/>
            tranſit p d:</s>
            <s xml:id="echoid-s8031" xml:space="preserve"> & coniungatur d k.</s>
            <s xml:id="echoid-s8032" xml:space="preserve"> Verùm angulus p h m eſt
              <lb/>
            æqualis angulo m h g [ex fabricatione.</s>
            <s xml:id="echoid-s8033" xml:space="preserve">] Quare [per 15
              <lb/>
            p 1] ſimiliter æqualis eſt angulo contrapoſito k h d:</s>
            <s xml:id="echoid-s8034" xml:space="preserve"> ſed
              <lb/>
            [per hypotheſim & 5 p 1] k h d eſt æqualis k d h:</s>
            <s xml:id="echoid-s8035" xml:space="preserve"> quoni-
              <lb/>
            am reſpiciunt æqualia latera:</s>
            <s xml:id="echoid-s8036" xml:space="preserve"> Igitur [per 1 ax:</s>
            <s xml:id="echoid-s8037" xml:space="preserve">] angulus
              <lb/>
            p h m æ qualis eſt angulo k d m.</s>
            <s xml:id="echoid-s8038" xml:space="preserve"> Quare [per 28 p 1] lineę
              <lb/>
            k d, p h ſunt ęquidiſtantes:</s>
            <s xml:id="echoid-s8039" xml:space="preserve"> ergo [per 35 def 1] in infi-
              <lb/>
            nitum productę nun quam concurrent:</s>
            <s xml:id="echoid-s8040" xml:space="preserve"> & linea p d ſeca-
              <lb/>
            bit lineam, interiacentem inter k d, & p h [quia ſecat an-
              <lb/>
            gulum h d k ipſi h k ſubtenſum.</s>
            <s xml:id="echoid-s8041" xml:space="preserve">] Et ita quodcunq;</s>
            <s xml:id="echoid-s8042" xml:space="preserve"> pun-
              <lb/>
            ctum ſumatur in linea p h:</s>
            <s xml:id="echoid-s8043" xml:space="preserve"> linea ducta ab illo puncto, ad
              <lb/>
            punctum d, ſecabit lineam reflexionis intra ſphęram:</s>
            <s xml:id="echoid-s8044" xml:space="preserve"> quę quidem linea perpendicularis erit ſuper
              <lb/>
            ſphęram [per 25 n 4] ſicut eſt p d.</s>
            <s xml:id="echoid-s8045" xml:space="preserve"> Quare imago cuiuſcunque puncti lineę p h apparebit intra ſphę
              <lb/>
            ram [per 3 n.</s>
            <s xml:id="echoid-s8046" xml:space="preserve">]</s>
          </p>
        </div>
        <div xml:id="echoid-div310" type="section" level="0" n="0">
          <head xml:id="echoid-head324" xml:space="preserve" style="it">21. Si reflexio fiat à peripheria circuli (qui eſt communis ſectio ſuperficierum, reflexionis &
            <lb/>
          ſpeculi ſphærici conuexi) inter rectam à uiſu ad ſpeculi centrum ductam, & lineam reflexionis,
            <lb/>
          æquantem partem ſuam intra peripheriam, eiuſdem ſemidiametro: imago intra ſpeculum ui-
            <lb/>
          debitur. 25 p 6.</head>
          <p>
            <s xml:id="echoid-s8047" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s8048" xml:space="preserve"> arcus circuli interiacens inter punctum h, & punctum, per quod tranſit perpendi-
              <lb/>
            cularis à centro uiſus ducta:</s>
            <s xml:id="echoid-s8049" xml:space="preserve"> eſto h z.</s>
            <s xml:id="echoid-s8050" xml:space="preserve"> Dico, quod
              <lb/>
              <figure xlink:label="fig-0142-02" xlink:href="fig-0142-02a" number="51">
                <variables xml:id="echoid-variables41" xml:space="preserve">t g p b h i z d a k s</variables>
              </figure>
            à quocunq, puncto huius arcus fiat reflexio:</s>
            <s xml:id="echoid-s8051" xml:space="preserve"> lo-
              <lb/>
            cus imaginis erit intra ſphæram.</s>
            <s xml:id="echoid-s8052" xml:space="preserve"> Sit i punctum ſumptũ:</s>
            <s xml:id="echoid-s8053" xml:space="preserve">
              <lb/>
            & ducatur linea à centro uiſus ſecans cιrculũ ſuper pun-
              <lb/>
            ctum illud, quę ſit g is:</s>
            <s xml:id="echoid-s8054" xml:space="preserve"> & ducatur perpendicularis per
              <lb/>
            punctum hoc, quę ſit d i t:</s>
            <s xml:id="echoid-s8055" xml:space="preserve"> & [per 23 p 1] fiat linea p i, æ-
              <lb/>
            qualem tenens angulum cum it angulo tig.</s>
            <s xml:id="echoid-s8056" xml:space="preserve"> Palàm [per
              <lb/>
            12 n 4] quòd ſola puncta lineę p i reflectuntur à puncto
              <lb/>
            iad uiſum.</s>
            <s xml:id="echoid-s8057" xml:space="preserve"> Palàm etiam [per 15 p 3] quòd linea i s ma-
              <lb/>
            ior eſt linea k h.</s>
            <s xml:id="echoid-s8058" xml:space="preserve"> Quare maior s d [eſt enim h k ex prima
              <lb/>
            hypotheſi ęqualis ſemidiametro s d.</s>
            <s xml:id="echoid-s8059" xml:space="preserve">] Igitur [per 18 p 1]
              <lb/>
            angulus s d i maior eſt angulo s i d:</s>
            <s xml:id="echoid-s8060" xml:space="preserve"> quare [per 15 p 1]
              <lb/>
            eſt maior angulo g i t:</s>
            <s xml:id="echoid-s8061" xml:space="preserve"> quare eſt maior angulo tip.</s>
            <s xml:id="echoid-s8062" xml:space="preserve"> Igitur
              <lb/>
            lineę p i & s d nunquam concurrent [ad partes p & s:</s>
            <s xml:id="echoid-s8063" xml:space="preserve">
              <lb/>
            ſecus ſpatium comprehenderent contra 12 ax.</s>
            <s xml:id="echoid-s8064" xml:space="preserve"> quia con-
              <lb/>
            currunt ad partes i & d per 11 ax.</s>
            <s xml:id="echoid-s8065" xml:space="preserve">] Et linea ducta à pun-
              <lb/>
            cto quocunque p i lineę, ad punctum d, ſecat lineam s i
              <lb/>
            intra ſphęram:</s>
            <s xml:id="echoid-s8066" xml:space="preserve"> quę s i eſt linea reflexionis:</s>
            <s xml:id="echoid-s8067" xml:space="preserve"> & omnis
              <lb/>
            linea ducta à quocunq;</s>
            <s xml:id="echoid-s8068" xml:space="preserve"> puncto p i lineę, ad punctum d:</s>
            <s xml:id="echoid-s8069" xml:space="preserve">
              <lb/>
            erit perpendicularis ſuper ſphęram [ut oſtenſum eſt 25
              <lb/>
            n 4,] ſicut eſt p d.</s>
            <s xml:id="echoid-s8070" xml:space="preserve"> Et cum locus imaginis ſit in concur-
              <lb/>
            ſu perpendicularis à puncto uiſo & lineę reflexionis:</s>
            <s xml:id="echoid-s8071" xml:space="preserve">
              <lb/>
            [per 3n] erit imago cuiuslibet puncti lineę p i intra
              <lb/>
            ſphę
              <gap/>
            a n.</s>
            <s xml:id="echoid-s8072" xml:space="preserve"> Palàm ergo, quòd omnium imaginum arcus
              <lb/>
            hz, locus proprius erit intra ſpeculum:</s>
            <s xml:id="echoid-s8073" xml:space="preserve"> Quod
              <lb/>
            eſt propoſitum.</s>
            <s xml:id="echoid-s8074" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum