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-div1746" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s45170" xml:space="preserve">
              <pb o="377" file="0679" n="679" rhead="LIBER NONVS."/>
            ſuperficiei ſpeculi circulus.</s>
            <s xml:id="echoid-s45171" xml:space="preserve"> Centrum itaq;</s>
            <s xml:id="echoid-s45172" xml:space="preserve"> uiſus, quod eſt punctum b, aut eſt in ſuperſicie illius cir-
              <lb/>
            culi, aut non.</s>
            <s xml:id="echoid-s45173" xml:space="preserve"> Si ſic:</s>
            <s xml:id="echoid-s45174" xml:space="preserve"> poteſt reflexionis punctum inuenlri in peripheria illius circuli, ſicut ſuprà in 27
              <lb/>
            th.</s>
            <s xml:id="echoid-s45175" xml:space="preserve"> 8.</s>
            <s xml:id="echoid-s45176" xml:space="preserve"> huius d dcuimus in ſpeculis ſphæricis cõcuais.</s>
            <s xml:id="echoid-s45177" xml:space="preserve"> Si uerò centrum uiſus b non ſuerit in ſuperficie
              <lb/>
            illius circuli:</s>
            <s xml:id="echoid-s45178" xml:space="preserve"> tũc cũ punctũ rei uiſæ, & centrũ uiſus ſemper ſint in ſuperficie reflexionis per;</s>
            <s xml:id="echoid-s45179" xml:space="preserve"> 3 huius.</s>
            <s xml:id="echoid-s45180" xml:space="preserve">
              <lb/>
            pater quòd cõmunis ſectio ſuperficiei reflexionis & ſpeculi in hoc ſitu eſt ſectio oxygonia.</s>
            <s xml:id="echoid-s45181" xml:space="preserve"> Duca-
              <lb/>
            tur ergo à puncto b cẽtro uiſus perpẽdicularis ſuper ſuperficiẽ illius circuli per 11 p 11:</s>
            <s xml:id="echoid-s45182" xml:space="preserve"> & replicetur
              <lb/>
            tota ꝓbatio proximæ præ cedẽcedẽtis:</s>
            <s xml:id="echoid-s45183" xml:space="preserve"> & palàm, quia inuenietur pũctus reflexionis.</s>
            <s xml:id="echoid-s45184" xml:space="preserve"> Quod eſt ꝓpoſitũ.</s>
            <s xml:id="echoid-s45185" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1747" type="section" level="0" n="0">
          <head xml:id="echoid-head1297" xml:space="preserve" style="it">17. Centro uiſus exiſtente in puncto, qui eſt communis ſectio axis & lineæ perpendicularis
            <lb/>
          ſuper ſuperficiem, contingentem ſpeculum pyramidale concauum: fiet reflexio formæ ipſius ocu-
            <lb/>
          li ab una totali peripheria circuli ſpeculi æquidiſtantis baſi: & ſolùm per line as perpẽdiculares:
            <lb/>
          locus́ imaginis erit in centro uiſus. Alhazen 98 n 5.</head>
          <p>
            <s xml:id="echoid-s45186" xml:space="preserve">Eſto ſpeculum pyramidale concauum, cuius axis ſit a h:</s>
            <s xml:id="echoid-s45187" xml:space="preserve"> & ducatur à puncto h linea perpendicu-
              <lb/>
            laris ſuper ſupeficiem, contingentem ſpeculum in puncto b:</s>
            <s xml:id="echoid-s45188" xml:space="preserve"> erit itaq;</s>
            <s xml:id="echoid-s45189" xml:space="preserve"> punctus h communis ſectio
              <lb/>
              <figure xlink:label="fig-0679-01" xlink:href="fig-0679-01a" number="813">
                <variables xml:id="echoid-variables790" xml:space="preserve">a b h</variables>
              </figure>
            axis a h & lineæ perpendicularis, quæ eſt h b.</s>
            <s xml:id="echoid-s45190" xml:space="preserve"> Dico quòd ſi centrum
              <lb/>
            uiſus poſitum fuerit in puncto h:</s>
            <s xml:id="echoid-s45191" xml:space="preserve"> fiet reflexio formæ oculi uidentis a
              <lb/>
            tota peripheria unius circuli ſpeculi æquidiftantis baſi, cuius polus erit
              <lb/>
            punctus h.</s>
            <s xml:id="echoid-s45192" xml:space="preserve"> Sit enlm punctus a uertex ſpeculi:</s>
            <s xml:id="echoid-s45193" xml:space="preserve"> & ducatur linea a b:</s>
            <s xml:id="echoid-s45194" xml:space="preserve"> ut ergo
              <lb/>
            pater per 95 th.</s>
            <s xml:id="echoid-s45195" xml:space="preserve"> 1 huius, erit linea a b pars lineæ lõgitudinis ſpeculi:</s>
            <s xml:id="echoid-s45196" xml:space="preserve"> eritq́;</s>
            <s xml:id="echoid-s45197" xml:space="preserve">
              <lb/>
            trigonum h b a orth ogonium:</s>
            <s xml:id="echoid-s45198" xml:space="preserve"> quoniam angulus a b h erit rectus propter
              <lb/>
            perpendicularitatem lineæ h b ſuper lineam a b.</s>
            <s xml:id="echoid-s45199" xml:space="preserve"> Imaginẽtur ergo à pun-
              <lb/>
            cto h plurimæ duci perpendiculares ſuper lineas longitudinis ſpeculi,
              <lb/>
            ſicut eſt linea h b perpendicularis ſuper lineam longitu dinis, quæ eſt a b:</s>
            <s xml:id="echoid-s45200" xml:space="preserve">
              <lb/>
            uel remanente fixo a h latere trignoi a b h, & circum ducto trigono, quo-
              <lb/>
            uſq;</s>
            <s xml:id="echoid-s45201" xml:space="preserve"> ad locum, unde exiuit, redeat:</s>
            <s xml:id="echoid-s45202" xml:space="preserve"> deſcribet punctũ b circulum in con-
              <lb/>
            cauitate ſpeculi, à cuius quolibet peripheriæ pũcto fiet reflexio ad uiſum
              <lb/>
            exiſtentem in puncto h ſecundum lineas perpendiculares, ſimiles lineæ
              <lb/>
            h b:</s>
            <s xml:id="echoid-s45203" xml:space="preserve"> hoc eſt ſecun dum lineas, quas motu ſuo determinabit linea h b.</s>
            <s xml:id="echoid-s45204" xml:space="preserve"> Fiet
              <lb/>
            autem reflexio ſolùm ſuperficiei ipſius uiſus per 21 th.</s>
            <s xml:id="echoid-s45205" xml:space="preserve"> 5 huius:</s>
            <s xml:id="echoid-s45206" xml:space="preserve"> & ſolùm
              <lb/>
            partis ſuperficiei uiſus, quam ſecant duę lineæ perpendiculares à centro
              <lb/>
            oculi exeuntes, & maiorem angulum, qui eſt ibi poſsibilis, continentes.</s>
            <s xml:id="echoid-s45207" xml:space="preserve">
              <lb/>
            Erit autem in omnibus his reflexionibus ſemper locus imaginis in cen-
              <lb/>
            tro uiſus:</s>
            <s xml:id="echoid-s45208" xml:space="preserve"> quoniam non ſit reflexio niſi ſecundum lineas perpẽdiculares.</s>
            <s xml:id="echoid-s45209" xml:space="preserve">
              <lb/>
            Patet itaq;</s>
            <s xml:id="echoid-s45210" xml:space="preserve"> propoſitum:</s>
            <s xml:id="echoid-s45211" xml:space="preserve"> ita tamen quòd inter centrum uiſus & ſpeculi
              <lb/>
            ſuperficiem non ſit aliquod corpus ſolidum, quod obſiſtat.</s>
            <s xml:id="echoid-s45212" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1749" type="section" level="0" n="0">
          <head xml:id="echoid-head1298" xml:space="preserve" style="it">18. Exiſtentibus centro uiſus puncto́ rei uiſæ in axe ſpeculi pyramidalis concaui: poßibile
            <lb/>
          eſt reflexionem fieri à toto uno circulo ſuperficiei reflexionis ſpeculi: locus́ imaginis erit quidũ
            <lb/>
          circulus extra ſpeculum. Alhazen 99 n 5.</head>
          <p>
            <s xml:id="echoid-s45213" xml:space="preserve">Eſto ſpeculum pyramidale concauum:</s>
            <s xml:id="echoid-s45214" xml:space="preserve"> cuius axis ſit linea a h:</s>
            <s xml:id="echoid-s45215" xml:space="preserve"> & uertex a:</s>
            <s xml:id="echoid-s45216" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s45217" xml:space="preserve"> centrum uiſus in
              <lb/>
              <figure xlink:label="fig-0679-02" xlink:href="fig-0679-02a" number="814">
                <variables xml:id="echoid-variables791" xml:space="preserve">a j t q s d b h</variables>
              </figure>
            puncto h:</s>
            <s xml:id="echoid-s45218" xml:space="preserve"> & ſit punctus rei uiſæ in puncto axis:</s>
            <s xml:id="echoid-s45219" xml:space="preserve"> qui ſit t:</s>
            <s xml:id="echoid-s45220" xml:space="preserve"> ima-
              <lb/>
            gineturq́ ſuperficies plana ſecans pyramidem ſpeculi ſecũ-
              <lb/>
            dum axis longitudinem, quæ ſit a b h g.</s>
            <s xml:id="echoid-s45221" xml:space="preserve"> Et quoniam linea a h
              <lb/>
            eſt axis ſpeculi:</s>
            <s xml:id="echoid-s45222" xml:space="preserve"> erunt lineæ a b & a g lineæ longitudinis ſpe-
              <lb/>
            culi per 90 th.</s>
            <s xml:id="echoid-s45223" xml:space="preserve"> 1 huius.</s>
            <s xml:id="echoid-s45224" xml:space="preserve"> Ducatur itaq;</s>
            <s xml:id="echoid-s45225" xml:space="preserve"> â puncto rei uiſæ (quod
              <lb/>
            eſt t) linea perpẽdicularis ſuper lineam a b:</s>
            <s xml:id="echoid-s45226" xml:space="preserve"> quę ſit t q:</s>
            <s xml:id="echoid-s45227" xml:space="preserve"> & pro-
              <lb/>
            ducatur ultra punctum q extra ſpeculum ad pũctum l, donec
              <lb/>
            linea q l ſit æ qualis lineæ t q:</s>
            <s xml:id="echoid-s45228" xml:space="preserve"> & à puncto h ducatut linea ad
              <lb/>
            punctum l, quæ ſit h l.</s>
            <s xml:id="echoid-s45229" xml:space="preserve"> Hęc itaq:</s>
            <s xml:id="echoid-s45230" xml:space="preserve"> neceſſariò ſecabit lineam a b:</s>
            <s xml:id="echoid-s45231" xml:space="preserve">
              <lb/>
            quoniam eſt cũ illa in eadẽ ſuperſicie:</s>
            <s xml:id="echoid-s45232" xml:space="preserve"> ſit ergo, ut ſecet ipſam
              <lb/>
            in puncto b:</s>
            <s xml:id="echoid-s45233" xml:space="preserve"> & à puncto b ducatur linea æ quidiſtans lineæ t
              <lb/>
            q per 31 p 1:</s>
            <s xml:id="echoid-s45234" xml:space="preserve"> quæ producta ad axem ſpeculi, ſit linea b d, ſecans
              <lb/>
            axem a h in puncto d:</s>
            <s xml:id="echoid-s45235" xml:space="preserve"> & copuletur linea t b.</s>
            <s xml:id="echoid-s45236" xml:space="preserve"> Palàm itaq;</s>
            <s xml:id="echoid-s45237" xml:space="preserve">, cum
              <lb/>
            linea t q ſit perpendicularis ſuper lineam a b, & æ qualis lineę
              <lb/>
            q l:</s>
            <s xml:id="echoid-s45238" xml:space="preserve"> erit per 4 p 1 triangulus t b q ęqualis triangulo q b l:</s>
            <s xml:id="echoid-s45239" xml:space="preserve"> & an-
              <lb/>
            gulus q l b æqualis angulo q t b:</s>
            <s xml:id="echoid-s45240" xml:space="preserve"> ſed angulus q t b æqualis eſt
              <lb/>
            angulo t b d per 29 p 1 quia ſunt coalterni:</s>
            <s xml:id="echoid-s45241" xml:space="preserve"> & angulus d b h
              <lb/>
            extrinſecus eſt æqualis angulo q l bintrinſeco.</s>
            <s xml:id="echoid-s45242" xml:space="preserve"> Eſt ergo angulus t b d ęqualis angulo d b h:</s>
            <s xml:id="echoid-s45243" xml:space="preserve"> ergo per
              <lb/>
            20 th.</s>
            <s xml:id="echoid-s45244" xml:space="preserve"> 5 huius forma punctit reflectitur à puncto ſpeculi, quod eſt b, ad centrum uiſus exiſtens in
              <lb/>
            puncto h.</s>
            <s xml:id="echoid-s45245" xml:space="preserve"> Et quoniam linea t q eſt perpẽdicularis ſuper ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s45246" xml:space="preserve"> pater per definitionem
              <lb/>
            quoniam ipſa eſt cathetus incidentiæ formę puncti t:</s>
            <s xml:id="echoid-s45247" xml:space="preserve"> concurrit autem cathetus t q cum linea refle-
              <lb/>
            xionis, quæ eſt h b, in puncto l:</s>
            <s xml:id="echoid-s45248" xml:space="preserve"> eſt ergo punctus l locus imaginis formæ puncti t per 37 th.</s>
            <s xml:id="echoid-s45249" xml:space="preserve"> 5 huius.</s>
            <s xml:id="echoid-s45250" xml:space="preserve">
              <lb/>
            Si itaq;</s>
            <s xml:id="echoid-s45251" xml:space="preserve"> fixo latere t h imaginetur trigonus t l h moueri, quouſq;</s>
            <s xml:id="echoid-s45252" xml:space="preserve"> redeat ad locum, unde incepit:</s>
            <s xml:id="echoid-s45253" xml:space="preserve"> tũc
              <lb/>
            </s>
          </p>
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