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-div914" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s24562" xml:space="preserve">
              <pb o="70" file="0372" n="372" rhead="VITELLONIS OPTICAE"/>
            quia per 1 p 6 triangulus a b g eſt maior triãgulo a h t, quoniam baſis b g eſt maior baſi h t:</s>
            <s xml:id="echoid-s24563" xml:space="preserve"> plus itaq;</s>
            <s xml:id="echoid-s24564" xml:space="preserve">
              <lb/>
            luminis diffuſum eſt in trigono a b g, quàm in trigono a h t:</s>
            <s xml:id="echoid-s24565" xml:space="preserve"> in quolibet enim iſtorum triangulorum
              <lb/>
            puncto eſt lumen ęqualiter diffuſum.</s>
            <s xml:id="echoid-s24566" xml:space="preserve"> Lumen ergo in-
              <lb/>
              <figure xlink:label="fig-0372-01" xlink:href="fig-0372-01a" number="414">
                <variables xml:id="echoid-variables397" xml:space="preserve">a b h t g d u z e</variables>
              </figure>
            cidens corpori exiſtenti in linea u z, illud corpus debi
              <lb/>
            lius illuminat quã corpus b g:</s>
            <s xml:id="echoid-s24567" xml:space="preserve"> quia paucius ſibi lumen
              <lb/>
            incidit:</s>
            <s xml:id="echoid-s24568" xml:space="preserve"> proportio enim uirtutis luminis incidentis li-
              <lb/>
            neę h t ad impreſsionẽ ſuã in corpus u z, eſt minor ꝓ-
              <lb/>
            portione uirtutis incidentis lineę b g ad impreſsionẽ
              <lb/>
            ſuam in corpus u z per 8 p 5:</s>
            <s xml:id="echoid-s24569" xml:space="preserve"> quoniam, ut patet ex prę
              <lb/>
            miſsis, lumen incidens lineę b g, eſt plus lumine inci-
              <lb/>
            dente lineę h t.</s>
            <s xml:id="echoid-s24570" xml:space="preserve"> Proportio uerò uirtutis incidẽtis lineę
              <lb/>
            h t ad impreſsionẽ ſuam in corpus u z, eſt ſicut propor
              <lb/>
            tio uirtutis incidentis lineæ b g ad impreſsionẽ ſuam
              <lb/>
            in corpus b g per 6 huius:</s>
            <s xml:id="echoid-s24571" xml:space="preserve"> ergo per 16 p 5 erit permuta
              <lb/>
            tim proportio uirtutis perueniẽtis ad lineã h t, ad uir-
              <lb/>
            tutẽ peruenientẽ ad lineã b g, ſicut impreſsionis factę
              <lb/>
            in corpus u z ad impreſsionẽ factã in corpus b g:</s>
            <s xml:id="echoid-s24572" xml:space="preserve"> ſed ք
              <lb/>
            p̃miſſa lumẽ քueniens ad lineã h t eſt debilius lumine
              <lb/>
            քueniẽte ad lineã b g.</s>
            <s xml:id="echoid-s24573" xml:space="preserve"> Ergo impreſsio քueniẽs à linea
              <lb/>
            h t in corpus u z, eſt debilior impreſsiõe քueniẽte à uirtute luminis incidẽtis lineę b g in corpus b g.</s>
            <s xml:id="echoid-s24574" xml:space="preserve">
              <lb/>
            Corp
              <emph style="sub">9</emph>
            itaq;</s>
            <s xml:id="echoid-s24575" xml:space="preserve"> ꝓpinꝗus corpori luminoſo forti
              <emph style="sub">9</emph>
            illuminatur ꝗ̃ remotius ab eodẽ.</s>
            <s xml:id="echoid-s24576" xml:space="preserve"> Et hoc eſt ꝓpoſitũ.</s>
            <s xml:id="echoid-s24577" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div916" type="section" level="0" n="0">
          <head xml:id="echoid-head738" xml:space="preserve" style="it">23. Puncto remotiori à corpore luminoſo incidunt radij à plurib. pun
            <lb/>
          ctis corporis luminoſi, quàm puncto propinquiori.</head>
          <figure number="415">
            <variables xml:id="echoid-variables398" xml:space="preserve">g h c e f a b d</variables>
          </figure>
          <p>
            <s xml:id="echoid-s24578" xml:space="preserve">Sit corporis luminoſi circulus a b c, cuius centrum d:</s>
            <s xml:id="echoid-s24579" xml:space="preserve"> & ducatur perpen
              <lb/>
            dicularis d g, in qua ſignentur duo puncta g remotior, & h propinquior.</s>
            <s xml:id="echoid-s24580" xml:space="preserve"> Di
              <lb/>
            co, quòd puncto remotiori, qui eſt g, incidunt radij à plurib.</s>
            <s xml:id="echoid-s24581" xml:space="preserve"> punctis corpo
              <lb/>
            ris luminoſi, ꝗ̃ ipſi puncto h.</s>
            <s xml:id="echoid-s24582" xml:space="preserve"> Ducãtur enim radij longiſsimi à corpore lumi
              <lb/>
            noſo ad punctum g.</s>
            <s xml:id="echoid-s24583" xml:space="preserve"> Et ſimiliter ducantur radij lõgiſsimi à corpore lumino
              <lb/>
            ſo ad punctũ h:</s>
            <s xml:id="echoid-s24584" xml:space="preserve"> erunt itaq;</s>
            <s xml:id="echoid-s24585" xml:space="preserve"> per 16 huius illi radij cõtingentes ſphęrã.</s>
            <s xml:id="echoid-s24586" xml:space="preserve"> Contin
              <lb/>
            gant itaq;</s>
            <s xml:id="echoid-s24587" xml:space="preserve"> radij incidentes puncto g in punctis a & b, & radij incidentes pũ
              <lb/>
            cto h, contingant ſphæram in punctis e & f:</s>
            <s xml:id="echoid-s24588" xml:space="preserve"> palamq́;</s>
            <s xml:id="echoid-s24589" xml:space="preserve"> per 60 t 1 huius, quo-
              <lb/>
            niam puncta contingentiæ e & f cadent intra puncta a & b.</s>
            <s xml:id="echoid-s24590" xml:space="preserve"> Quia itaq;</s>
            <s xml:id="echoid-s24591" xml:space="preserve"> pun-
              <lb/>
            ctum h ſolum irradiatur à punctis arcus e c f, & non ab alijs:</s>
            <s xml:id="echoid-s24592" xml:space="preserve"> punctũ uerò g
              <lb/>
            irradiatur à punctis arcus a c b, qui eſt maior arcu e c f, patet propoſitũ:</s>
            <s xml:id="echoid-s24593" xml:space="preserve"> quo
              <lb/>
            niam punctũ g illuminabitur à ſuperficie corporis luminoſi, quã per ęqua-
              <lb/>
            lia diuidit arcus a c b:</s>
            <s xml:id="echoid-s24594" xml:space="preserve"> & punctum h illuminabitur à ſuperficie corporis lu-
              <lb/>
            minoſi, quã per ęqualia diuidit arcus e c f:</s>
            <s xml:id="echoid-s24595" xml:space="preserve"> tamen propter radiorum fortitu-
              <lb/>
            dinem, quæ conſequitur ipſorum breuitatem, fortius illuminabitur punctũ
              <lb/>
            h à paucioribus radijs, quã punctum g à plurib.</s>
            <s xml:id="echoid-s24596" xml:space="preserve"> multiplicitas enim luminis
              <lb/>
            in puncto remotiori eſt ex concurſu radiorum multorum obliquè inciden-
              <lb/>
            tium & debilium, ſed in puncto propinquiori fortificatur lux ex breuitate radij, ſecundum quam à
              <lb/>
            corpore luminoſo immittitur plus uirtutis.</s>
            <s xml:id="echoid-s24597" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div917" type="section" level="0" n="0">
          <head xml:id="echoid-head739" xml:space="preserve" style="it">24. Omne corp{us} luminoſum min{us} ſpatium, à quo non egreditur, forti{us} illuminat quàm
            <lb/>
          ſpatium mai{us} illo.</head>
          <p>
            <s xml:id="echoid-s24598" xml:space="preserve">Quod hic proponitur, ſatis patet per exemplũ:</s>
            <s xml:id="echoid-s24599" xml:space="preserve"> u-
              <lb/>
              <figure xlink:label="fig-0372-03" xlink:href="fig-0372-03a" number="416">
                <variables xml:id="echoid-variables399" xml:space="preserve">a e h f b d g</variables>
              </figure>
            na enim candela paruam cameram fortius illuminat
              <lb/>
            quã domum uel cameram maiorem:</s>
            <s xml:id="echoid-s24600" xml:space="preserve"> poteſt tamen i-
              <lb/>
            dem figuraliter demonſtrari.</s>
            <s xml:id="echoid-s24601" xml:space="preserve"> Eſto enim, ut ſit pũctus
              <lb/>
            aliquis corporis luminoſi a:</s>
            <s xml:id="echoid-s24602" xml:space="preserve"> à quo per ſpatiũ magnũ,
              <lb/>
            in quo ſit linea b g, diffundantur radij a g, a b, a d:</s>
            <s xml:id="echoid-s24603" xml:space="preserve"> & ſit
              <lb/>
            radius a d perpendicularis ſuper lineam b g:</s>
            <s xml:id="echoid-s24604" xml:space="preserve"> illumi-
              <lb/>
            natur itaq;</s>
            <s xml:id="echoid-s24605" xml:space="preserve"> ſpatium totum b g ſecundum has lineas
              <lb/>
            à puncto a ſibi incidentes.</s>
            <s xml:id="echoid-s24606" xml:space="preserve"> Abſcindatur itaq;</s>
            <s xml:id="echoid-s24607" xml:space="preserve"> à linea
              <lb/>
            a b linea a e, ut placuerit, & â linea a g abſcindetur li-
              <lb/>
            nea a f æqualis lineæ a e:</s>
            <s xml:id="echoid-s24608" xml:space="preserve"> productaq́;</s>
            <s xml:id="echoid-s24609" xml:space="preserve"> linea e f ſecet li-
              <lb/>
            neam perpẽdicularẽ, quę eſt a d, in puncto h.</s>
            <s xml:id="echoid-s24610" xml:space="preserve"> Si ergo
              <lb/>
            in linea e h f terminetur ſpatium, ne lumen ultrà per-
              <lb/>
            tranſeat, erit illud ſpatium minus ſpatio terminato ք
              <lb/>
            lineam b d g per 2 p 6.</s>
            <s xml:id="echoid-s24611" xml:space="preserve"> Omnes autem radij peruenien
              <lb/>
            tes ad lineam b g, perueniunt ad lineam e f:</s>
            <s xml:id="echoid-s24612" xml:space="preserve"> plus ergo
              <lb/>
            aggregantur radij in ſpatio e f quã in ſpatio b g:</s>
            <s xml:id="echoid-s24613" xml:space="preserve"> fortiores ergo fiunt, cum ſint uirtutis plus unitæ:</s>
            <s xml:id="echoid-s24614" xml:space="preserve"> ma
              <lb/>
            gis ergo agunt quã in ſpatio b g, in quo ſunt diffuſiores.</s>
            <s xml:id="echoid-s24615" xml:space="preserve"> Plus ergo illuminatur ſpatium minus, cùm
              <lb/>
            ad eius terminos uirtus luminis terminatur, quàm ſpatium maius illo.</s>
            <s xml:id="echoid-s24616" xml:space="preserve"> Et hoc eſt propoſitum.</s>
            <s xml:id="echoid-s24617" xml:space="preserve"/>
          </p>
        </div>
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    </echo>
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