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
111 105
112 106
113 107
114 108
115 109
116 110
117 111
118 112
119 113
120 114
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
< >
page |< < (132) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div291" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s7780" xml:space="preserve">
              <pb o="132" file="0138" n="138" rhead="ALHAZEN"/>
            angulus b d e æqualis eſt angulo a d c [per 10 n 4, & per 15 p 1 angulus b d e æqualis angulo g d c:</s>
            <s xml:id="echoid-s7781" xml:space="preserve"> er-
              <lb/>
            go per 1 ax:</s>
            <s xml:id="echoid-s7782" xml:space="preserve"> angulus a d c æquatur angulo g d c] & angulus a c d æ-
              <lb/>
              <figure xlink:label="fig-0138-01" xlink:href="fig-0138-01a" number="40">
                <variables xml:id="echoid-variables30" xml:space="preserve">a f b c d e g</variables>
              </figure>
            qualis angulo g c d [per 10 ax:</s>
            <s xml:id="echoid-s7783" xml:space="preserve">] & latus c d commune.</s>
            <s xml:id="echoid-s7784" xml:space="preserve"> Quare [per 26
              <lb/>
            p 1] triangulum æquale triangulo.</s>
            <s xml:id="echoid-s7785" xml:space="preserve"> Quare g c æqualis a c.</s>
            <s xml:id="echoid-s7786" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div293" type="section" level="0" n="0">
          <head xml:id="echoid-head315" xml:space="preserve" style="it">12. Viſu & uiſibili datis, in ſpeculo plano punctum reflexionis
            <lb/>
          inuenire. 46 p 5.</head>
          <p>
            <s xml:id="echoid-s7787" xml:space="preserve">ET ſi uoluerimus per perpendicularem inuenire locum reflexio
              <lb/>
            nis:</s>
            <s xml:id="echoid-s7788" xml:space="preserve"> ſecetur ex perpendiculari ultra ſpeculum pars, æqualis par
              <lb/>
            ti eius uſq;</s>
            <s xml:id="echoid-s7789" xml:space="preserve"> ad ſpeculum:</s>
            <s xml:id="echoid-s7790" xml:space="preserve"> & eſt, ut ſit g c æqualis a c:</s>
            <s xml:id="echoid-s7791" xml:space="preserve"> & ducatur li
              <lb/>
            nea à centro uiſus ad punctum g, quæ ſit b d g.</s>
            <s xml:id="echoid-s7792" xml:space="preserve"> Dico, quòd d, eſt pun-
              <lb/>
            ctum reflexionis.</s>
            <s xml:id="echoid-s7793" xml:space="preserve"> Quoniam enim [per fabricationem & 2 ax:</s>
            <s xml:id="echoid-s7794" xml:space="preserve">] a c &
              <lb/>
            c d ſunt æqualia c g & c d, & angulus angulo [a c d ipſi g c d per theſin
              <lb/>
            & 10 ax.</s>
            <s xml:id="echoid-s7795" xml:space="preserve">] Ergo [per 4 p 1] triangulum triangulo.</s>
            <s xml:id="echoid-s7796" xml:space="preserve"> Igitur angulus g d c
              <lb/>
            eſt æqualis angulo a d c:</s>
            <s xml:id="echoid-s7797" xml:space="preserve"> Sed g d c eſt æqualis angulo b d e [per 15 p 1]
              <lb/>
            reſtat ergo [per 1 ax] ut angulus b d e ſit æqualis angulo a d c.</s>
            <s xml:id="echoid-s7798" xml:space="preserve"> Et ita
              <lb/>
            [per 10 n 4] d eſt punctum reflexionis:</s>
            <s xml:id="echoid-s7799" xml:space="preserve"> & ita patet propoſitum.</s>
            <s xml:id="echoid-s7800" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div294" type="section" level="0" n="0">
          <head xml:id="echoid-head316" xml:space="preserve" style="it">13. Si recta linea ab uno uiſu ſit perpendicularis ſpeculo plano,
            <lb/>
          unum ipſi{us} punctũ; in quo uiſ{us} ſuperficiem ſecat, ab uno ſpeculi
            <lb/>
          puncto, in quod cadit, ad eundem uiſum reflectetur. 32 p 5.</head>
          <p>
            <s xml:id="echoid-s7801" xml:space="preserve">SIt a centrum uiſus:</s>
            <s xml:id="echoid-s7802" xml:space="preserve"> & a g perpendicularis ſuper ſpeculũ planũ:</s>
            <s xml:id="echoid-s7803" xml:space="preserve"> & d ſecet hanc perpendicularẽ in
              <lb/>
            ſuperficie oculi.</s>
            <s xml:id="echoid-s7804" xml:space="preserve"> Dico, quòd in hac perpendiculari non eſt punctũ, quod reflectatur ab hoc ſpe-
              <lb/>
            culo ad uiſum, præter d.</s>
            <s xml:id="echoid-s7805" xml:space="preserve"> Sin autem:</s>
            <s xml:id="echoid-s7806" xml:space="preserve"> ſumatur ultra uiſum punctum in hac perpendiculari:</s>
            <s xml:id="echoid-s7807" xml:space="preserve"> & ſit
              <lb/>
            h:</s>
            <s xml:id="echoid-s7808" xml:space="preserve"> Non iam perueniet forma eius ad ſpeculũ ſuper
              <lb/>
              <figure xlink:label="fig-0138-02" xlink:href="fig-0138-02a" number="41">
                <variables xml:id="echoid-variables31" xml:space="preserve">h t a d ſ s g k b e</variables>
              </figure>
            perpendicularẽ a h, propter ſolidi corporis inter-
              <lb/>
            poſitionem:</s>
            <s xml:id="echoid-s7809" xml:space="preserve"> & ita nõ reflectetur forma eius ſuper
              <lb/>
            perpendicularẽ.</s>
            <s xml:id="echoid-s7810" xml:space="preserve"> Et ſi dicatur, quòd ab alio puncto
              <lb/>
            ſpeculi poſsit reflecti:</s>
            <s xml:id="echoid-s7811" xml:space="preserve"> ſit illud b.</s>
            <s xml:id="echoid-s7812" xml:space="preserve"> Mouebitur quidẽ
              <lb/>
            forma eius ad punctũ b per lineã h b:</s>
            <s xml:id="echoid-s7813" xml:space="preserve"> & reflectetur
              <lb/>
            per lineam b a.</s>
            <s xml:id="echoid-s7814" xml:space="preserve"> Diuidatur angulus h b a [per 9 p 1]
              <lb/>
            per ęqualia, per lineã t b.</s>
            <s xml:id="echoid-s7815" xml:space="preserve"> Igitur erit perpẽdicularis
              <lb/>
            ſuper ſuperficiẽ ſpeculi.</s>
            <s xml:id="echoid-s7816" xml:space="preserve"> [Quia enim angulus h b c
              <lb/>
            æquatur angulo a b g ք theſin & 10 n 4, & h b t ipſi
              <lb/>
            a b t per fabricationẽ:</s>
            <s xml:id="echoid-s7817" xml:space="preserve"> totus t b c æquabitur toti t b
              <lb/>
            g.</s>
            <s xml:id="echoid-s7818" xml:space="preserve"> quare per 10 d 1 t b eſt perpendicularis ipſi g c cõ
              <lb/>
            muni ſectioni ſuperficierũ reflexionis & ſpeculi.</s>
            <s xml:id="echoid-s7819" xml:space="preserve">
              <lb/>
            Itaq;</s>
            <s xml:id="echoid-s7820" xml:space="preserve"> cũ reflexiõis ſuperficies, in qua eſt t b, ſit per
              <lb/>
            pendicularis ſuperficiei ſpeculi per 13 n 4:</s>
            <s xml:id="echoid-s7821" xml:space="preserve"> erit t b
              <lb/>
            քpẽdicularis ſuperficiei ſpeculi per cõuerſam 4 d
              <lb/>
            11] ſed [per hypotheſin] t g eſt perpẽdicularis ſuper
              <lb/>
            eandẽ.</s>
            <s xml:id="echoid-s7822" xml:space="preserve"> Quare ab eodẽ puncto eſt ducere duas per
              <lb/>
            pendiculares ad ſuperficiem ſpeculi, quod eſt im-
              <lb/>
            poſsibile:</s>
            <s xml:id="echoid-s7823" xml:space="preserve"> [ſic enim tres interiores anguli triangu-
              <lb/>
            li eſſent maiores duobus rectis, cõtra 32 p 1.</s>
            <s xml:id="echoid-s7824" xml:space="preserve">] Eadẽ
              <lb/>
            erit probatio, quòd forma puncti d nõ poteſt refle
              <lb/>
            cti ab alio ſpeculi puncto, quam à puncto g.</s>
            <s xml:id="echoid-s7825" xml:space="preserve"> Quare
              <lb/>
            non reflectitur, niſi ſuper perpendicularẽ d g.</s>
            <s xml:id="echoid-s7826" xml:space="preserve"> Pun
              <lb/>
            ctum aũt in hac perpendiculari ſumptum inter g & d:</s>
            <s xml:id="echoid-s7827" xml:space="preserve"> ſi dicatur formã per reflexionẽ ad uiſum mit-
              <lb/>
            tere:</s>
            <s xml:id="echoid-s7828" xml:space="preserve"> improbo.</s>
            <s xml:id="echoid-s7829" xml:space="preserve"> Quoniã aut erit corpus ſolidum, aut rarũ.</s>
            <s xml:id="echoid-s7830" xml:space="preserve"> Si ſolidum, procedet ſecundum perpendi-
              <lb/>
            cularem forma eius ad ſpeculum, & regredietur ſecundũ eandem uſq;</s>
            <s xml:id="echoid-s7831" xml:space="preserve"> ad ipſum, [per 11 n 4] & pro-
              <lb/>
            pter ſoliditatẽ non poterit tranſire, & ad uiſum peruenire.</s>
            <s xml:id="echoid-s7832" xml:space="preserve"> Si aũt punctum illud fuerit rarum:</s>
            <s xml:id="echoid-s7833" xml:space="preserve"> forma
              <lb/>
            eius regrediẽs à ſpeculo ſuper perpendicularẽ miſcebitur ei, & adhærebit, nec reflectetur ad uiſum.</s>
            <s xml:id="echoid-s7834" xml:space="preserve">
              <lb/>
            Quòd autem forma cuiuſcunq;</s>
            <s xml:id="echoid-s7835" xml:space="preserve"> puncti in hac perpendiculari inter g & d ſumpti non poſsit ab alio
              <lb/>
            puncto ſpeculi ad uiſum reflecti, modo ſuprà dicto poteſt probari.</s>
            <s xml:id="echoid-s7836" xml:space="preserve"> Similiter forma puncti inter a &
              <lb/>
            d ſumpti non reflectitur ad uiſum per perpendicularem, nec per aliam.</s>
            <s xml:id="echoid-s7837" xml:space="preserve"> Quoniã puncta inter centrũ
              <lb/>
            uiſus & ſuperficiem eius interpoſita ſunt ualde rara.</s>
            <s xml:id="echoid-s7838" xml:space="preserve"> Vnde nec mittitur eorum forma, nec reflecti-
              <lb/>
            tur, ut ſentiatur.</s>
            <s xml:id="echoid-s7839" xml:space="preserve"> Et quoniám quodlibet punctum, præter d in ſuperficie uiſus ſumptum:</s>
            <s xml:id="echoid-s7840" xml:space="preserve"> opponitur
              <lb/>
            ſpeculo, non ad rectum angulum, uidebitur quodlibet ſuper perpendicularem ab eo ad ſpeculum
              <lb/>
            ductam, & imago eius ultra ſpeculum æquè diſtans à ſuperficie, ſicut ipſum punctum [per 11 n.</s>
            <s xml:id="echoid-s7841" xml:space="preserve">] Et
              <lb/>
            quoniam d uidetur continuum cum alijs ſuperficiei uiſus punctis, & imago eius cõtinua cum alijs
              <lb/>
            imaginibus:</s>
            <s xml:id="echoid-s7842" xml:space="preserve"> uidebitur imago d tantùm diſtans à ſuperficiei ſpeculi, quantùm diſtat d ab eadem.</s>
            <s xml:id="echoid-s7843" xml:space="preserve"> Pa-
              <lb/>
            làm ergo, quòd cuiuſcunq;</s>
            <s xml:id="echoid-s7844" xml:space="preserve"> puncti in ſpeculo uiſi imago uidebitur ſuper perpendicularem:</s>
            <s xml:id="echoid-s7845" xml:space="preserve"> & elon-
              <lb/>
            gatio imaginis, & uiſi corporis à ſuperficie ſpeculi eſt eadem.</s>
            <s xml:id="echoid-s7846" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum