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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          <p>
            <s xml:id="echoid-s7631" xml:space="preserve">
              <pb o="130" file="0136" n="136" rhead="ALHAZEN"/>
            uiſus acquirit longitudinem per ſyllogiſmum ex magnitudine corporis, & angulo aliquo, ſub quo
              <lb/>
            comprehenditur magnitudo.</s>
            <s xml:id="echoid-s7632" xml:space="preserve"> Et acquiſitio rei uiſæ notæ manifeſta eſt in hunc modum.</s>
            <s xml:id="echoid-s7633" xml:space="preserve"> Res etiam
              <lb/>
            ignotæ comprehenduntur in hunc modum:</s>
            <s xml:id="echoid-s7634" xml:space="preserve"> conferuntur enim rebus cognitis & magnitudinibus
              <lb/>
            uel longitudinibus notis.</s>
            <s xml:id="echoid-s7635" xml:space="preserve"> Cum uiſus comprehendit rem aliquam per reflexionem:</s>
            <s xml:id="echoid-s7636" xml:space="preserve"> non compre-
              <lb/>
            hendit longitudinem imaginis, niſi per æſtimationem:</s>
            <s xml:id="echoid-s7637" xml:space="preserve"> dein de adhibita diligentia, acquirit longitu-
              <lb/>
            dinem, & uerificat per ſyllogiſmum ex magnitudine rei uiſæ & angulo pyramidis, ſuper quam for-
              <lb/>
            ma reflectitur ad uiſum.</s>
            <s xml:id="echoid-s7638" xml:space="preserve"> Cum ergo res uiſa ex rebus notis fuerit, uiſus acquirit eius longitudinem
              <lb/>
            per iam notam longitudinem angulum æqualem huic tenentem, & huic longitudini ſimilem.</s>
            <s xml:id="echoid-s7639" xml:space="preserve"> Simi-
              <lb/>
            liter res uiſa cum fuerit ignota, confertur magnitudo eius alij magnitudini rerum uiſarum nota-
              <lb/>
            rum, & acquiritur longitudo eius imaginis per ſyllogiſmum menſuræ anguli, quem tenet imago in
              <lb/>
            centro uiſus, in hora reflexionis.</s>
            <s xml:id="echoid-s7640" xml:space="preserve"> Et à loco, in quo eſt forma rei uiſæ comprehenſa per reflexionem,
              <lb/>
            forma directè ueniens ad angulum circa oculum, accedit ſuper pyramidem ipſam, per quam for-
              <lb/>
            ma reflectitur ad uiſum:</s>
            <s xml:id="echoid-s7641" xml:space="preserve"> & eadem pyramis occupabit totam formam, quæ fuerit in loco imaginis.</s>
            <s xml:id="echoid-s7642" xml:space="preserve">
              <lb/>
            Viſus ergo cum acquirit rem uiſam per reflexionem:</s>
            <s xml:id="echoid-s7643" xml:space="preserve"> acquirit eam in loco imaginis:</s>
            <s xml:id="echoid-s7644" xml:space="preserve"> quoniam for-
              <lb/>
            ma comprehenſa eſt in loco imaginis per reflexionem.</s>
            <s xml:id="echoid-s7645" xml:space="preserve"> Quare ſimilis eſt formæ directè comprehen
              <lb/>
            ſæ, occupatæ ab illa pyramide.</s>
            <s xml:id="echoid-s7646" xml:space="preserve"> Et hæc eſt cauſa, quare comprehendatur in loco imaginis.</s>
            <s xml:id="echoid-s7647" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div288" type="section" level="0" n="0">
          <head xml:id="echoid-head312" xml:space="preserve" style="it">9. Imago in ſpeculo plano uidetur in perpendiculari incidentiæ. 36 p 5.</head>
          <p>
            <s xml:id="echoid-s7648" xml:space="preserve">QVare autem comprehendatur imago in perpendiculari, dicemus.</s>
            <s xml:id="echoid-s7649" xml:space="preserve"> Scimus [per16 n 4] quòd
              <lb/>
            punctum uiſui perceptibile, non eſt intellectuale, ſed ſenſuale, & forma eius ſenſualis.</s>
            <s xml:id="echoid-s7650" xml:space="preserve"> Dico
              <lb/>
            igitur in ſpeculis planis, quòd cum imago non appareat in ſuperficie ſpeculi, ſed ultra:</s>
            <s xml:id="echoid-s7651" xml:space="preserve"> com-
              <lb/>
            petentius eſt, & rationabilius, ut appareat ſupra perpendicularem, quàm extra eam.</s>
            <s xml:id="echoid-s7652" xml:space="preserve"> Cum enim in
              <lb/>
            loco perpendicularis aſsignata fuerit diſtantia eius à puncto refle-
              <lb/>
              <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a" number="39">
                <variables xml:id="echoid-variables29" xml:space="preserve">a f b c d e</variables>
              </figure>
            xionis ſpeculi, quæ ſcilicet eſt pars lineæ reflexionis, à loco imaginis
              <lb/>
            ad punctum reflexionis ductæ:</s>
            <s xml:id="echoid-s7653" xml:space="preserve"> erit æqualis diſtantiæ puncti uiſi à
              <lb/>
            puncto reflexionis.</s>
            <s xml:id="echoid-s7654" xml:space="preserve"> Quia enim ſuperficies ſpeculi eſt orthogonalis
              <lb/>
            ſuper perpendicularem, [per theſin] & linea à puncto reflexionis
              <lb/>
            ad perpendicularem ducta eſt latus duobus triangulis commune, &
              <lb/>
            angulus lineæ acceſſus eſt æqualis angulo reflexionis [per 10 n 4, &
              <lb/>
            angulus f c d æquatur angulo e c b per 15 p 1:</s>
            <s xml:id="echoid-s7655" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s7656" xml:space="preserve"> angulo a c b]
              <lb/>
            quare duo anguli unius trianguli ſuntæquales duobus angulis al-
              <lb/>
            terius trianguli [anguli enim ad b recti ſunt per theſin & 3 d 11] & u-
              <lb/>
            num latus commune eſt:</s>
            <s xml:id="echoid-s7657" xml:space="preserve"> quare [per 26 p 1] reliqua latera æqualia
              <lb/>
            ſunt reliquis lateribus.</s>
            <s xml:id="echoid-s7658" xml:space="preserve"> Si ergo imago in perpendiculari apparuerit:</s>
            <s xml:id="echoid-s7659" xml:space="preserve">
              <lb/>
            æqualiter à ſpeculo diſtabit cum corpore, à quo procedit:</s>
            <s xml:id="echoid-s7660" xml:space="preserve"> & erit ima
              <lb/>
            gini idem ſitus, reſpectu puncti reflexionis, qui eſt in puncto uiſo,
              <lb/>
            reſpectu puncti eiuſdẽ:</s>
            <s xml:id="echoid-s7661" xml:space="preserve"> & idem eſt ſitus, reſpectu uiſus.</s>
            <s xml:id="echoid-s7662" xml:space="preserve"> Vnde in hoc
              <lb/>
            ſitu apparebit ueritas & puncti uiſi, & imaginis.</s>
            <s xml:id="echoid-s7663" xml:space="preserve"> Si uerò imago fuerit
              <lb/>
            extra perpendicularem, cum fuerit neceſſe eam in linea reflexionis
              <lb/>
            eſſe, [per 2 n 4] aut erit ultra perpendicularem, aut citra, reſpectu
              <lb/>
            uiſus.</s>
            <s xml:id="echoid-s7664" xml:space="preserve"> Si fuerit ultra:</s>
            <s xml:id="echoid-s7665" xml:space="preserve"> erit quidem remotior à puncto reflexionis, & à
              <lb/>
            uiſu, quàm punctum uiſum, unde tenebit minorem angulum in ocu
              <lb/>
            lo, quàm punctum uiſum, & minorem occupabit uiſus partem:</s>
            <s xml:id="echoid-s7666" xml:space="preserve"> unde cum ſit æqualis, uidebitur mi-
              <lb/>
            nor eo.</s>
            <s xml:id="echoid-s7667" xml:space="preserve"> Si autem fuerit citra perpendicularem, uidebitur maior, cum ſit propinquior.</s>
            <s xml:id="echoid-s7668" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div290" type="section" level="0" n="0">
          <head xml:id="echoid-head313" xml:space="preserve" style="it">10. Imago in ſpeculis conuexis, cauis: ſphærico, cylindraceo, conico uidetur in perpendiculari
            <lb/>
          incidentiæ. 36 p 5.</head>
          <p>
            <s xml:id="echoid-s7669" xml:space="preserve">IN ſpeculo ſphærico extrà polito uidetur imago ſuper perpendicularem.</s>
            <s xml:id="echoid-s7670" xml:space="preserve"> Aut enim uidetur ima-
              <lb/>
            go centri uiſus:</s>
            <s xml:id="echoid-s7671" xml:space="preserve"> aut alterius puncti.</s>
            <s xml:id="echoid-s7672" xml:space="preserve"> Si imago centri uiſus:</s>
            <s xml:id="echoid-s7673" xml:space="preserve"> dico, quòd dignior eſt perpendicula-
              <lb/>
            ris ab oculo ad centrum ſphæræ ducta, ut ſuper eam appareat imago centri uiſus, quàm alia.</s>
            <s xml:id="echoid-s7674" xml:space="preserve"> Si
              <lb/>
            enim forma directè procedat ſecundum hanc perpendicularem uſque ad centrum ſphæræ, eun-
              <lb/>
            dem ſemper ſeruabit ſitum, reſpectu uiſus:</s>
            <s xml:id="echoid-s7675" xml:space="preserve"> & ita cuicunque puncto ſphæræ opponatur forma:</s>
            <s xml:id="echoid-s7676" xml:space="preserve"> per-
              <lb/>
            pendicularis ad centrum mota, identitatem ſitus tenebit, reſpectu uiſus:</s>
            <s xml:id="echoid-s7677" xml:space="preserve"> & idem erit ſitus for-
              <lb/>
            mæ in una perpendiculari, quæ & in alia:</s>
            <s xml:id="echoid-s7678" xml:space="preserve"> quoniam centrum ſphæræ eundem habet ſitum, reſpe-
              <lb/>
            ctu cuiuslibet puncti ſphæræ, & omnes huiuſmodi perpendiculares eiuſdem ſunt ſitus.</s>
            <s xml:id="echoid-s7679" xml:space="preserve"> Si autem
              <lb/>
            extra perpendicularem imago moueatur, ad quodcunque punctum ſphæræ mutabitur ſitus e-
              <lb/>
            ius, reſpectu uiſus:</s>
            <s xml:id="echoid-s7680" xml:space="preserve"> quoniam alium habebit ſitum extra perpendicularem, quàm in perpendicu-
              <lb/>
            lari, & extra ſpeculum mouebitur perpendicularis, & non intra:</s>
            <s xml:id="echoid-s7681" xml:space="preserve"> & ſi extra ſpeculum appareat,
              <lb/>
            non ſeruabit ſitum.</s>
            <s xml:id="echoid-s7682" xml:space="preserve"> Et conuenientius fuit, ut ſeruaret ſitum imago, quàm ut mutaret, ut uiſus rem
              <lb/>
            uiſam certius comprehenderet.</s>
            <s xml:id="echoid-s7683" xml:space="preserve"> Ob hoc imago centri uiſus ſuper perpendicularem apparet.</s>
            <s xml:id="echoid-s7684" xml:space="preserve"> Et
              <lb/>
            huic imagini non poſſumus certum aſsignare in perpendiculari punctum:</s>
            <s xml:id="echoid-s7685" xml:space="preserve"> quoniam non inueni-
              <lb/>
            tur dignitas in uno perpendicularis puncto maior, quàm in alio, ut hæc imago determinatè appa-
              <lb/>
            reatin eo:</s>
            <s xml:id="echoid-s7686" xml:space="preserve"> ſed ſcimus, quòd in quocunque puncto huius perpendicularis appareat, ſemper appa-
              <lb/>
            </s>
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