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-s17947" xml:space="preserve">
              <pb o="258" file="0264" n="264" rhead="ALHAZEN"/>
            gulus e b k minor angulo o b k [per 9 axio.</s>
            <s xml:id="echoid-s17948" xml:space="preserve">] erit ergo angulus p e h minor angulo l o f:</s>
            <s xml:id="echoid-s17949" xml:space="preserve"> erit ergo angu
              <lb/>
            lus p e a, qui eſt angulus refractionis, minor angulo l o a, qui eſt angulus refractionis:</s>
            <s xml:id="echoid-s17950" xml:space="preserve"> angulus ergo
              <lb/>
            a e h eſt maior angulo a o f:</s>
            <s xml:id="echoid-s17951" xml:space="preserve"> quod eſt impoſsibile, [ut ꝓximè oſtenſum eſt.</s>
            <s xml:id="echoid-s17952" xml:space="preserve">] Ergo impoſsibile eſt, ut
              <lb/>
            punctum n ſit imago puncti b:</s>
            <s xml:id="echoid-s17953" xml:space="preserve"> neque aliud punctum eſt præter m.</s>
            <s xml:id="echoid-s17954" xml:space="preserve"> Ergo punctum b, reſpectu uiſus
              <lb/>
            a, nullam habet imaginem, præterquam punctum m:</s>
            <s xml:id="echoid-s17955" xml:space="preserve"> & hoc declarare uoluimus.</s>
            <s xml:id="echoid-s17956" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div585" type="section" level="0" n="0">
          <head xml:id="echoid-head506" xml:space="preserve" style="it">23. Si cõmunis ſectio ſuperficierũ refractionis & refractiui rarioris fuerit linea recta: uiſibi-
            <lb/>
          le extra perpendicularem, à uiſu ſuper refractiuum ductã: ab uno puncto refringetur: & unam
            <lb/>
          habebit imaginem. 21 p 10.</head>
          <p>
            <s xml:id="echoid-s17957" xml:space="preserve">ET iterũ:</s>
            <s xml:id="echoid-s17958" xml:space="preserve"> ſit corpus groſsius ex parte uiſus, & ſubtilius ex parte rei uiſę:</s>
            <s xml:id="echoid-s17959" xml:space="preserve"> & ſit differẽtia cõmunis
              <lb/>
            inter hãc ſuperficiẽ & ſuperficiẽ corporis diaphani linea g d:</s>
            <s xml:id="echoid-s17960" xml:space="preserve"> & [ք 12 p 1] extrahamus ex b li-
              <lb/>
            neã perpẽdicularẽ ſuper lineã g d:</s>
            <s xml:id="echoid-s17961" xml:space="preserve"> & ſit b k:</s>
            <s xml:id="echoid-s17962" xml:space="preserve"> erit ergo b k քpendicularis ſuք ſuperficiẽ corporis
              <lb/>
            diaphani:</s>
            <s xml:id="echoid-s17963" xml:space="preserve"> [per 9 n & cõuerſionẽ 4 d 11] & refringatur forma b ad a ex e:</s>
            <s xml:id="echoid-s17964" xml:space="preserve"> & cõtinuemus lineas b e, e a:</s>
            <s xml:id="echoid-s17965" xml:space="preserve">
              <lb/>
            & extrahamus perpendicularẽ h e:</s>
            <s xml:id="echoid-s17966" xml:space="preserve"> & extrahamus b e rectè ad p:</s>
            <s xml:id="echoid-s17967" xml:space="preserve"> erit ergo a e linea media inter duas
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            lineas e p, e h.</s>
            <s xml:id="echoid-s17968" xml:space="preserve"> Nam prima linea, per
              <lb/>
              <figure xlink:label="fig-0264-01" xlink:href="fig-0264-01a" number="223">
                <variables xml:id="echoid-variables210" xml:space="preserve">a f h p l g o e k d b m c q z n</variables>
              </figure>
            quã extẽditur forma ad locũ refra-
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            ctionis, eſt linea b e p:</s>
            <s xml:id="echoid-s17969" xml:space="preserve"> refractio.</s>
            <s xml:id="echoid-s17970" xml:space="preserve"> n.</s>
            <s xml:id="echoid-s17971" xml:space="preserve">
              <lb/>
            eſt ad partẽ perpẽdicularis e h:</s>
            <s xml:id="echoid-s17972" xml:space="preserve"> [ք
              <lb/>
            14 n] nã corpus, quod eſt ex parte
              <lb/>
            a, eſt groſsius illo, qđ eſt ex parte
              <lb/>
            b [ex theſi.</s>
            <s xml:id="echoid-s17973" xml:space="preserve">] Linea ergo a e eſt me-
              <lb/>
            dia inter duas lineas e p, e h:</s>
            <s xml:id="echoid-s17974" xml:space="preserve"> & ex-
              <lb/>
            trahamus a e, directè ad partem e,
              <lb/>
            quouſq;</s>
            <s xml:id="echoid-s17975" xml:space="preserve"> occurrat lineę b k:</s>
            <s xml:id="echoid-s17976" xml:space="preserve"> ſecat.</s>
            <s xml:id="echoid-s17977" xml:space="preserve"> n.</s>
            <s xml:id="echoid-s17978" xml:space="preserve">
              <lb/>
            h e z.</s>
            <s xml:id="echoid-s17979" xml:space="preserve"> [Itaq;</s>
            <s xml:id="echoid-s17980" xml:space="preserve"> ſecabit k b ipſi h e z per
              <lb/>
            6 p 11 parallelã, per lẽma Procli ad
              <lb/>
            29 p 1] occurrat ergo illi in puncto
              <lb/>
            m:</s>
            <s xml:id="echoid-s17981" xml:space="preserve"> m ergo erit imago pũcti b:</s>
            <s xml:id="echoid-s17982" xml:space="preserve"> [per
              <lb/>
            18 n] nã corpus, qđ eſt ex parte b,
              <lb/>
            eſt ſubtilius illo, quod eſt ex parte
              <lb/>
            a.</s>
            <s xml:id="echoid-s17983" xml:space="preserve"> Dico igitur, qđ b nõ habet ima-
              <lb/>
            ginẽ, niſi m.</s>
            <s xml:id="echoid-s17984" xml:space="preserve"> Habeat enim n:</s>
            <s xml:id="echoid-s17985" xml:space="preserve"> ſi poſ-
              <lb/>
            ſibile eſt:</s>
            <s xml:id="echoid-s17986" xml:space="preserve"> n ergo erit in perpendiculari b k, [per 19 n] & infra punctũ b:</s>
            <s xml:id="echoid-s17987" xml:space="preserve"> quia corpus, quod eſt in par-
              <lb/>
            te b, eſt ſubtilius illo, quod eſt ex parte a.</s>
            <s xml:id="echoid-s17988" xml:space="preserve"> Eſt ergo aut inter duo puncta m, b:</s>
            <s xml:id="echoid-s17989" xml:space="preserve"> aut infra m:</s>
            <s xml:id="echoid-s17990" xml:space="preserve"> & cõtinue-
              <lb/>
            mus a n:</s>
            <s xml:id="echoid-s17991" xml:space="preserve"> ſecabit ergo lineã d g in o:</s>
            <s xml:id="echoid-s17992" xml:space="preserve"> o ergo eſt punctũ refractionis.</s>
            <s xml:id="echoid-s17993" xml:space="preserve"> Et cõtinuemus b o:</s>
            <s xml:id="echoid-s17994" xml:space="preserve"> & trãſeat uſq;</s>
            <s xml:id="echoid-s17995" xml:space="preserve">
              <lb/>
            a d l:</s>
            <s xml:id="echoid-s17996" xml:space="preserve"> & [ք 11 p 1] extrahamus ex o perpẽdicularẽ f o q.</s>
            <s xml:id="echoid-s17997" xml:space="preserve"> Linea ergo b o eſt linea, ք quã extẽditur forma
              <lb/>
            ad locũ refractionis:</s>
            <s xml:id="echoid-s17998" xml:space="preserve"> ergo linea o a erit inter duas lineas o l, o f:</s>
            <s xml:id="echoid-s17999" xml:space="preserve"> refractio enim eſt ad partẽ perpẽdicu
              <lb/>
            laris [ք theſin & 14 n.</s>
            <s xml:id="echoid-s18000" xml:space="preserve">] Si ergo fuerit n inter duo pũcta m, b:</s>
            <s xml:id="echoid-s18001" xml:space="preserve"> tũc punctũ o erit inter duo puncta e, k:</s>
            <s xml:id="echoid-s18002" xml:space="preserve"> er
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            go erit angulus o b k minor angulo e b k:</s>
            <s xml:id="echoid-s18003" xml:space="preserve"> [ք 9 ax.</s>
            <s xml:id="echoid-s18004" xml:space="preserve">] ergo angulus l o f eſt minor angulo p e h, [ut de-
              <lb/>
            monſtratũ eſt ſuperiore numero] ergo [ք 12 n] angulus l o a qui eſt angulus refractionis) eſt minor
              <lb/>
            angulo p e a, qui eſt angulus refractionis:</s>
            <s xml:id="echoid-s18005" xml:space="preserve"> & angulus a o f, qui remanet poſt angulum refractionis, eſt
              <lb/>
            minor angulo a e h, qui remanet poſt angulũ refractionis [per 12 n] ſed [per 29 p 1] angulus a o f eſt
              <lb/>
            æqualis angulo a n k, & angulus a e h eſt æqualis angulo a m k:</s>
            <s xml:id="echoid-s18006" xml:space="preserve"> ergo angulus a n k eſt minor angulo
              <lb/>
            a m k:</s>
            <s xml:id="echoid-s18007" xml:space="preserve"> quod eſt impoſsibile [& cõtra 16 p 1.</s>
            <s xml:id="echoid-s18008" xml:space="preserve">] Si aũt n fuerit infra m:</s>
            <s xml:id="echoid-s18009" xml:space="preserve"> tũc erit e inter duo puncta o, k:</s>
            <s xml:id="echoid-s18010" xml:space="preserve"> &
              <lb/>
            erit angulus o b k maior angulo e b
              <lb/>
              <figure xlink:label="fig-0264-02" xlink:href="fig-0264-02a" number="224">
                <variables xml:id="echoid-variables211" xml:space="preserve">a
                  <gap/>
                f l p g e o k d b n m c z
                  <gap/>
                </variables>
              </figure>
            k:</s>
            <s xml:id="echoid-s18011" xml:space="preserve"> angulus ergo l o f erit maior an-
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            gulo p e h:</s>
            <s xml:id="echoid-s18012" xml:space="preserve"> [ut patuit proximo nu-
              <lb/>
            mero] ergo angulus l o a eſt maior
              <lb/>
            angulo p e a:</s>
            <s xml:id="echoid-s18013" xml:space="preserve"> & angulus a o f eſt ma
              <lb/>
            ior angulo a e h:</s>
            <s xml:id="echoid-s18014" xml:space="preserve"> [ք 12 n] ergo angu
              <lb/>
            lus a n k eſt maior angulo a m k:</s>
            <s xml:id="echoid-s18015" xml:space="preserve"> qđ
              <lb/>
            eſt impoſsibile:</s>
            <s xml:id="echoid-s18016" xml:space="preserve"> [& cõtra 16 p 1] n er
              <lb/>
            go non eſt imago b:</s>
            <s xml:id="echoid-s18017" xml:space="preserve"> nec aliud pun-
              <lb/>
            ctũ, præterquã m:</s>
            <s xml:id="echoid-s18018" xml:space="preserve"> b ergo non habet
              <lb/>
            imaginem, niſi m.</s>
            <s xml:id="echoid-s18019" xml:space="preserve"> Et hoc eſt, quod
              <lb/>
            uoluimus declarare.</s>
            <s xml:id="echoid-s18020" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div587" type="section" level="0" n="0">
          <head xml:id="echoid-head507" xml:space="preserve" style="it">24. Si duæ rectæ lineæ circulo
            <lb/>
          inſcriptæ interſecentur: angul{us}
            <lb/>
          ſectionis quilibet æquatur angulo
            <lb/>
          in peripheria, inſiſtẽti in periphe-
            <lb/>
          riam æqualẽ duab{us} peripherijs
            <lb/>
          eidem angulo, & ad uerticem oppoſito ſubtenſis 54 p 1.</head>
          <p>
            <s xml:id="echoid-s18021" xml:space="preserve">AD duas aũt lineas circulares conuexã & cõcauã pręmittemus hęc.</s>
            <s xml:id="echoid-s18022" xml:space="preserve"> Cũ duę chordę ſeſe ſecuerint
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            </s>
          </p>
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