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

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        <div xml:id="echoid-div294" type="section" level="0" n="0">
          <pb o="133" file="0139" n="139" rhead="OPTICAE LIBER V."/>
        </div>
        <div xml:id="echoid-div296" type="section" level="0" n="0">
          <head xml:id="echoid-head317" xml:space="preserve" style="it">14. Ab uno ſpeculi plani puncto, unum uiſibilis punctũ ad unũ uiſum reflectitur. 45 p 5.</head>
          <p>
            <s xml:id="echoid-s7847" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s7848" xml:space="preserve"> forma puncti uiſi in ſpeculo plano non reflectitur ad eundẽ uiſum, niſi ab uno pun-
              <lb/>
            cto tantùm.</s>
            <s xml:id="echoid-s7849" xml:space="preserve"> Sit enim a centrum uiſus:</s>
            <s xml:id="echoid-s7850" xml:space="preserve"> b pun
              <lb/>
              <figure xlink:label="fig-0139-01" xlink:href="fig-0139-01a" number="42">
                <variables xml:id="echoid-variables32" xml:space="preserve">a b h e d z</variables>
              </figure>
            ctum uiſum:</s>
            <s xml:id="echoid-s7851" xml:space="preserve"> z h ſpeculum.</s>
            <s xml:id="echoid-s7852" xml:space="preserve"> Si ergo dicatur,
              <lb/>
            quod à duobus punctis ſpeculi reflectatur forma b
              <lb/>
            ad uiſum a:</s>
            <s xml:id="echoid-s7853" xml:space="preserve"> ſit unum punctũ d, aliud e:</s>
            <s xml:id="echoid-s7854" xml:space="preserve"> & ducatur
              <lb/>
            linea à puncto uiſo ad uiſum, ſcilicet b a:</s>
            <s xml:id="echoid-s7855" xml:space="preserve"> quæ quidẽ
              <lb/>
            linea aut erit perpendicularis ſupra ſpeculũ:</s>
            <s xml:id="echoid-s7856" xml:space="preserve"> aut nõ.</s>
            <s xml:id="echoid-s7857" xml:space="preserve">
              <lb/>
            [Siquidẽ cum ſpeculi ſuperficie concurrit.</s>
            <s xml:id="echoid-s7858" xml:space="preserve"> Nã cum
              <lb/>
            ſit in plano lineæ h z per 23 n 4:</s>
            <s xml:id="echoid-s7859" xml:space="preserve"> h neceſſariò uel ad
              <lb/>
            ipſam parallela eſt, uel concurrit.</s>
            <s xml:id="echoid-s7860" xml:space="preserve">] Si non fuerit per
              <lb/>
            pendicularis, ſcimus, quòd illa linea eſt in ſuperficie
              <lb/>
            reflexionis orthogonali ſuper ſuperficiem ſpeculi
              <lb/>
            [quia cõnectit duo pũcta a & b, quæ per 23 n 4 ſunt
              <lb/>
            in reflexionis ſuperficie, perpẽdiculari ad ſpeculi ſu-
              <lb/>
            perficiẽ, per 13 n 4:</s>
            <s xml:id="echoid-s7861" xml:space="preserve">] & in una ſola tali.</s>
            <s xml:id="echoid-s7862" xml:space="preserve"> Quoniam ſi in
              <lb/>
            duabus:</s>
            <s xml:id="echoid-s7863" xml:space="preserve"> erit communis duabus ſuperficiebus ortho
              <lb/>
            gonalibus:</s>
            <s xml:id="echoid-s7864" xml:space="preserve"> & ſumpto in ea puncto, & ducta ab illo
              <lb/>
            linea in alteram ſuperficierum, ſuper lineam, com-
              <lb/>
            munem huic ſuperficiei & ſuperficiei ſpeculi, erit
              <lb/>
            [per 19 p 11] hæc linea orthogonalis ſuper ſpeculum.</s>
            <s xml:id="echoid-s7865" xml:space="preserve"> Similiter ab eodem puncto ducatur linea in
              <lb/>
            alia ſuperficie ſuper lineam, communem huic ſuperficiei & ſuperficiei ſpeculi:</s>
            <s xml:id="echoid-s7866" xml:space="preserve"> erit hęc linea ortho-
              <lb/>
            gonalis ſuper ſpeculum.</s>
            <s xml:id="echoid-s7867" xml:space="preserve"> Quare ab eodem puncto erit ducere duas perpendiculares ad ſuperficiem
              <lb/>
            ſpeculi [& ſic connexis per rectam lineam perpendicularium duarũ terminis:</s>
            <s xml:id="echoid-s7868" xml:space="preserve"> erunt ipſæ ad con-
              <lb/>
            nectentem perpendiculares, per 3 d 11:</s>
            <s xml:id="echoid-s7869" xml:space="preserve"> itaque in triangulo rectilineo erunt duo anguli recti, co n-
              <lb/>
            tra 32 p 1.</s>
            <s xml:id="echoid-s7870" xml:space="preserve">] Cum ergo b a ſit in una ſola ſuperficie orthogonali:</s>
            <s xml:id="echoid-s7871" xml:space="preserve"> & tria puncta a, b, e ſint in eadem ſu-
              <lb/>
            perficie orthogonali [per 23 n 4] erunt a e, e b in illa ſuperficie orthogonali:</s>
            <s xml:id="echoid-s7872" xml:space="preserve"> ſimiliter [per 2 p 11]
              <lb/>
            e d, d b, d a.</s>
            <s xml:id="echoid-s7873" xml:space="preserve"> Quare e a, e b ſunt in eadem ſuperficie cum d a, d b:</s>
            <s xml:id="echoid-s7874" xml:space="preserve"> ſed angulus a e h eſt æqualis angu-
              <lb/>
            lo b e d, [per 10 n 4] & angulus a e h maior angulo a d e, [per 16 p 1] quia exterior.</s>
            <s xml:id="echoid-s7875" xml:space="preserve"> Quare b ed ma
              <lb/>
            ior a d e.</s>
            <s xml:id="echoid-s7876" xml:space="preserve"> Sed b d z æqualis a d e [per 10 n 4, & per 16 p 1 b d z maior b e d.</s>
            <s xml:id="echoid-s7877" xml:space="preserve">] Quare a d e maior b e d:</s>
            <s xml:id="echoid-s7878" xml:space="preserve">
              <lb/>
            & dictum eſt, quod minor.</s>
            <s xml:id="echoid-s7879" xml:space="preserve"> Reſtat ergo, ut à ſolo puncto fiat reflexio.</s>
            <s xml:id="echoid-s7880" xml:space="preserve"> Si uerò a b ſit perpendicularis
              <lb/>
            ſuper ſpeculum:</s>
            <s xml:id="echoid-s7881" xml:space="preserve"> iam dictum eſt, [13 n] quò d unicum eſt punctum in linea, à centro uiſus ad ſpecu
              <lb/>
            lum orthogonaliter ducta, cuius forma reflectitur à ſpeculo ad uiſum.</s>
            <s xml:id="echoid-s7882" xml:space="preserve"> Et iam probatum eſt, quòd
              <lb/>
            imago illius puncti ab uno ſolo reflectitur puncto.</s>
            <s xml:id="echoid-s7883" xml:space="preserve"> Quare patet propoſitum.</s>
            <s xml:id="echoid-s7884" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div298" type="section" level="0" n="0">
          <head xml:id="echoid-head318" xml:space="preserve" style="it">15. In ſpeculo plano, imagouni{us} puncti, una, & uno eodem́ in loco ab utroque uiſu uide-
            <lb/>
          tur. 51 p 5.</head>
          <p>
            <s xml:id="echoid-s7885" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s7886" xml:space="preserve"> inſpecto aliquo puncto ab utroque uiſu:</s>
            <s xml:id="echoid-s7887" xml:space="preserve"> una tantùm & eadem imago apparet u-
              <lb/>
            trique uiſui & in loco prædicto.</s>
            <s xml:id="echoid-s7888" xml:space="preserve"> Vnde planum eſt, quòd forma puncti non reflectitur ad u-
              <lb/>
            trumque uiſum ab eodem puncto ſpeculi.</s>
            <s xml:id="echoid-s7889" xml:space="preserve"> Quia enim linea reflexionis ad unum uiſum pro-
              <lb/>
            cedens, angulum tenet cum perpendiculari erecta ſuper ſuperficiem ſpeculi, æqualem angulo, quẽ
              <lb/>
            tenet linea acceſſus formæ a d ſpeculum cum eadem perpendiculari [per 10 n 4:</s>
            <s xml:id="echoid-s7890" xml:space="preserve">] non poterit in
              <lb/>
            eadem ſuperficie ſumi alia linea, quæ æqualem angulum huic efficiat cum perpendiculari [ſecus
              <lb/>
              <figure xlink:label="fig-0139-02" xlink:href="fig-0139-02a" number="43">
                <variables xml:id="echoid-variables33" xml:space="preserve">b a g q t d z e h</variables>
              </figure>
              <figure xlink:label="fig-0139-03" xlink:href="fig-0139-03a" number="44">
                <variables xml:id="echoid-variables34" xml:space="preserve">a g b e d z t q h</variables>
              </figure>
            pars æquaretur toti, contra 9 ax:</s>
            <s xml:id="echoid-s7891" xml:space="preserve">] Vnde ab hoc puncto non reflectetur linea aliqua ad alterũ ui-
              <lb/>
            ſum.</s>
            <s xml:id="echoid-s7892" xml:space="preserve"> Oportet ergo ut à diuerſis punctis ſpeculi fiat reflexio.</s>
            <s xml:id="echoid-s7893" xml:space="preserve"> Sint illa puncta t, z:</s>
            <s xml:id="echoid-s7894" xml:space="preserve"> & ſit ſpeculũ pla-
              <lb/>
            num q e:</s>
            <s xml:id="echoid-s7895" xml:space="preserve"> punctum uiſum a:</s>
            <s xml:id="echoid-s7896" xml:space="preserve"> duo uiſus b, g:</s>
            <s xml:id="echoid-s7897" xml:space="preserve"> perpendicularis a d.</s>
            <s xml:id="echoid-s7898" xml:space="preserve"> Palàm ergo [per 23 n 4] quòd b t,
              <lb/>
            </s>
          </p>
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