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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            <s xml:id="echoid-s18975" xml:space="preserve">
              <pb o="273" file="0279" n="279" rhead="OPTICAE LIBER VII."/>
            ciem b c d e:</s>
            <s xml:id="echoid-s18976" xml:space="preserve"> & cõtinuemus a z:</s>
            <s xml:id="echoid-s18977" xml:space="preserve"> & ſit a z poſita perpẽdiculariter ſuper b z c.</s>
            <s xml:id="echoid-s18978" xml:space="preserve"> Poſitio ergo b reſpectu a
              <lb/>
            eſt ſimilis poſitioni c, reſpectu a:</s>
            <s xml:id="echoid-s18979" xml:space="preserve"> & diſtantia b ex a eſt æqualis diſtantiæ c ex a, [ut 39 n oſtẽſum eſt.</s>
            <s xml:id="echoid-s18980" xml:space="preserve">]
              <lb/>
            Et refringatur b ad a ex p:</s>
            <s xml:id="echoid-s18981" xml:space="preserve"> & c ad a ex k.</s>
            <s xml:id="echoid-s18982" xml:space="preserve"> Poſitio ergo p, reſpectu a, eſt ſimilis poſitioni k, reſpectu a:</s>
            <s xml:id="echoid-s18983" xml:space="preserve"> &
              <lb/>
            diſtantia p ex a, ſicut diſtantia k ex a:</s>
            <s xml:id="echoid-s18984" xml:space="preserve"> & continuemus lineas b p, p a, c k, k a.</s>
            <s xml:id="echoid-s18985" xml:space="preserve"> Eſt ergo [per 9 n] ſu-
              <lb/>
            perficies, in qua ſunt duę lineæ, a p, b p perpendicularis ſuper ſuperficiem corporis diaphani:</s>
            <s xml:id="echoid-s18986" xml:space="preserve"> quia
              <lb/>
            eſt ſuperficies refractionis:</s>
            <s xml:id="echoid-s18987" xml:space="preserve"> perpendicularis ergo b d erit
              <lb/>
              <figure xlink:label="fig-0279-01" xlink:href="fig-0279-01a" number="237">
                <variables xml:id="echoid-variables224" xml:space="preserve">a p k d m e l o g h b z c</variables>
              </figure>
            in hac ſuperficie:</s>
            <s xml:id="echoid-s18988" xml:space="preserve"> & perpendicularis, quæ exit ex p, erit
              <lb/>
            in illa ſuperficie:</s>
            <s xml:id="echoid-s18989" xml:space="preserve"> linea ergo a p ſecabit b d [per lemma
              <lb/>
            Procli ad 29 p 1:</s>
            <s xml:id="echoid-s18990" xml:space="preserve">] extrahatur ergo a p, & ſecet b d in l:</s>
            <s xml:id="echoid-s18991" xml:space="preserve"> &
              <lb/>
            extrahatur a k, & ſecet c e in o:</s>
            <s xml:id="echoid-s18992" xml:space="preserve"> erit ergo a l, ſicut a o:</s>
            <s xml:id="echoid-s18993" xml:space="preserve"> [ꝓ-
              <lb/>
            pter ſimilem poſitionem punctorum l & o ad punctum
              <lb/>
            a:</s>
            <s xml:id="echoid-s18994" xml:space="preserve">] & erit b l, ſicut c o:</s>
            <s xml:id="echoid-s18995" xml:space="preserve"> & continuemus l o, quæ eſt dia-
              <lb/>
            meter imaginis b c:</s>
            <s xml:id="echoid-s18996" xml:space="preserve"> & [per 33 p 1] erit l o æqualis b c:</s>
            <s xml:id="echoid-s18997" xml:space="preserve"> &
              <lb/>
            continuemus a b, a c.</s>
            <s xml:id="echoid-s18998" xml:space="preserve"> Vtraque ergo ſuperficies a l b, a o c
              <lb/>
            eſt perpendicularis ſuper ſuperficiem corporis diaphani
              <lb/>
            [per 9 n:</s>
            <s xml:id="echoid-s18999" xml:space="preserve">] & tres ſuperficies perpendiculares ſuper ſu
              <lb/>
            perficiem corporis diaphani, quæ tranſeunt per puncta
              <lb/>
            b, z, c, [nempe a l b:</s>
            <s xml:id="echoid-s19000" xml:space="preserve"> a m z:</s>
            <s xml:id="echoid-s19001" xml:space="preserve"> a o c] ſecant ſe in perpendicu-
              <lb/>
            lari exeunte ex a ſuper ſuperficiẽ corporis diaphani [per
              <lb/>
            19 p 11:</s>
            <s xml:id="echoid-s19002" xml:space="preserve">] & erit angulus b p l angulus refractionis:</s>
            <s xml:id="echoid-s19003" xml:space="preserve"> & linea
              <lb/>
            b l d perpendicularis eſt ſuper ſuperficiem corporis:</s>
            <s xml:id="echoid-s19004" xml:space="preserve"> ergo
              <lb/>
            [per 13 p 11] linea a l eſt obliqua ſuper ipſam.</s>
            <s xml:id="echoid-s19005" xml:space="preserve"> Linea ergo
              <lb/>
            a p continet cum perpendiculari exeunte ex p ſuper ſu-
              <lb/>
            perficiem corporis angulum acutum ex parte l:</s>
            <s xml:id="echoid-s19006" xml:space="preserve"> & extra-
              <lb/>
            hamus perpendicularem:</s>
            <s xml:id="echoid-s19007" xml:space="preserve"> & ſit p g:</s>
            <s xml:id="echoid-s19008" xml:space="preserve"> ergo [per 6 p 11] erit ę-
              <lb/>
            quidiſtans l d:</s>
            <s xml:id="echoid-s19009" xml:space="preserve"> angulus ergo p l d eſt acutus [per 29 p 1:</s>
            <s xml:id="echoid-s19010" xml:space="preserve">]
              <lb/>
            ergo [per 13 p 1] angulus a l b eſt obtuſus.</s>
            <s xml:id="echoid-s19011" xml:space="preserve"> Linea ergo a l
              <lb/>
            eſt minor, quàm linea a b [per 19 p 1.</s>
            <s xml:id="echoid-s19012" xml:space="preserve">] Et ſimiliter declara
              <lb/>
            tur, quòd a o erit minor a c:</s>
            <s xml:id="echoid-s19013" xml:space="preserve"> ſed lineæ a l, a o ſunt æquales,
              <lb/>
            & a b, a c ſunt æquales, & linea l o eſt ęqualis lineæ c b:</s>
            <s xml:id="echoid-s19014" xml:space="preserve"> er
              <lb/>
            go angulus o a l eſt maior angulo c a b:</s>
            <s xml:id="echoid-s19015" xml:space="preserve"> [ut patuit 39 n] &
              <lb/>
            poſitio l o eſt conſimilis poſitioni b c:</s>
            <s xml:id="echoid-s19016" xml:space="preserve"> quia linea, quę exit
              <lb/>
            exa ad medium l o, eſt perpendicularis ſuper lineam l o, quia [per 29 p 1] l o eſt æquidiſtans b c, &
              <lb/>
            b c eſt perpendicularis ſuper ſuperficiem, in qua ſunt a z, d b:</s>
            <s xml:id="echoid-s19017" xml:space="preserve">ergo [per 8 p 11] l o eſt perpendicularis
              <lb/>
            ſuper eandem ſuperficiem.</s>
            <s xml:id="echoid-s19018" xml:space="preserve"> Linea ergo l o eſt perpendicularis ſuper ſuperficiem, quæ continuat a
              <lb/>
            cum medio l o.</s>
            <s xml:id="echoid-s19019" xml:space="preserve"> Poſitio ergo l o reſpectu a eſt, ſicut poſitio b c reſpectu a:</s>
            <s xml:id="echoid-s19020" xml:space="preserve"> Sed l o comprehenditur re-
              <lb/>
            motior, propter debilitatem formæ:</s>
            <s xml:id="echoid-s19021" xml:space="preserve"> ergo l o uidebitur maior quàm b c:</s>
            <s xml:id="echoid-s19022" xml:space="preserve"> ſed l o eſt imago b c.</s>
            <s xml:id="echoid-s19023" xml:space="preserve"> Ergo
              <lb/>
            b c uidebitur maior, quàm ſit.</s>
            <s xml:id="echoid-s19024" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div613" type="section" level="0" n="0">
          <figure number="238">
            <variables xml:id="echoid-variables225" xml:space="preserve">a q p k d m e g l o b z f c</variables>
          </figure>
          <head xml:id="echoid-head527" xml:space="preserve" style="it">42. Si communis ſectio ſuperficierum, refractionis et
            <lb/>
          refractiui fuerit linea recta: & uiſ{us} ſit extr a planum perpendicularium à terminis uiſibilis obliqui ad com- munem ſectionem, ſuper refractiuum ductarum: ima- go maior uidebitur uiſibili. 34 p 10.</head>
          <p>
            <s xml:id="echoid-s19025" xml:space="preserve">ITem iteremus figuram:</s>
            <s xml:id="echoid-s19026" xml:space="preserve"> & ſit b c non æquidiſtans d e:</s>
            <s xml:id="echoid-s19027" xml:space="preserve">
              <lb/>
            & extrahamus c f æquidiſtantem lineæ d e:</s>
            <s xml:id="echoid-s19028" xml:space="preserve"> & conti-
              <lb/>
            nuemus a f:</s>
            <s xml:id="echoid-s19029" xml:space="preserve"> & ſit p punctum, ex quo refringatur f ad a:</s>
            <s xml:id="echoid-s19030" xml:space="preserve">
              <lb/>
            b autem refringatur ad a ex q:</s>
            <s xml:id="echoid-s19031" xml:space="preserve"> & continuemus a q:</s>
            <s xml:id="echoid-s19032" xml:space="preserve"> & ꝓ-
              <lb/>
            trahamus illam ad g.</s>
            <s xml:id="echoid-s19033" xml:space="preserve"> Sic ergo erit g altius quàm l:</s>
            <s xml:id="echoid-s19034" xml:space="preserve"> nam b
              <lb/>
            eſt ultra lineam a f:</s>
            <s xml:id="echoid-s19035" xml:space="preserve">unde linea a g eſt ultra lineam a l:</s>
            <s xml:id="echoid-s19036" xml:space="preserve"> ergo
              <lb/>
            g eſt altius, quàm l:</s>
            <s xml:id="echoid-s19037" xml:space="preserve"> & continuemus g o:</s>
            <s xml:id="echoid-s19038" xml:space="preserve"> erit ergo g o dia-
              <lb/>
            meter imaginis b g:</s>
            <s xml:id="echoid-s19039" xml:space="preserve"> & erit [per 19 p 1] g o maior l o [angu
              <lb/>
            lus enim g l o eſt rectus per fabricationem & 29 p 1:</s>
            <s xml:id="echoid-s19040" xml:space="preserve">] & a g
              <lb/>
            minor à l [per 19 p 1:</s>
            <s xml:id="echoid-s19041" xml:space="preserve"> quia angulus a g l eſt obtuſus, ut oſtẽ-
              <lb/>
            ſum eſt 40 n] & duæ lineæ a g, a o ſunt in duabus ſuperfi-
              <lb/>
            ciebus ſecantibus ſe, ſcilicet a g b, a o c:</s>
            <s xml:id="echoid-s19042" xml:space="preserve"> & differentia com
              <lb/>
            munis inter duas has ſuperficies tranſit per a:</s>
            <s xml:id="echoid-s19043" xml:space="preserve"> & duæ li-
              <lb/>
            neæ, quæ exeunt ex a perpendiculariter ſuper illam ſu-
              <lb/>
            perficiem corporis diaphani, ſunt extra hãc communem
              <lb/>
            differentiam in his duabus ſuperficiebus, & ſunt altiores
              <lb/>
            duabus lineis a g, a o:</s>
            <s xml:id="echoid-s19044" xml:space="preserve"> ergo angulus g a o eſt maior angulo
              <lb/>
            b a c:</s>
            <s xml:id="echoid-s19045" xml:space="preserve"> [ut oſtenſum eſt 39 n] & remotiones g o, b c ex a
              <lb/>
            non differũt multũ:</s>
            <s xml:id="echoid-s19046" xml:space="preserve"> quia linea g o aut erit æquidiſtãs b c,
              <lb/>
            </s>
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