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-s29366" xml:space="preserve">
              <pb o="155" file="0457" n="457" rhead="LIBER QVARTVS."/>
            ducatur linea d lad centrum uiſus à centro baſis pyramidis:</s>
            <s xml:id="echoid-s29367" xml:space="preserve"> & ducanturlineæ d b & d a contingen
              <lb/>
            tes circulũ, qui eſt baſis coni, in pũctis b & a:</s>
            <s xml:id="echoid-s29368" xml:space="preserve"> & ducãtur à uertice pyra
              <lb/>
              <figure xlink:label="fig-0457-01" xlink:href="fig-0457-01a" number="505">
                <variables xml:id="echoid-variables485" xml:space="preserve">g l a z i b e d</variables>
              </figure>
            midis lineæ lõgitudinis coni, quæ ſint g a & g b:</s>
            <s xml:id="echoid-s29369" xml:space="preserve"> ergo p̀er ea, quæ pri-
              <lb/>
            us in pręcedẽtibus dicta ſunt, ſuperficies g a b uidetur ſub oculo d:</s>
            <s xml:id="echoid-s29370" xml:space="preserve"> &
              <lb/>
            eſt minorhemiconio.</s>
            <s xml:id="echoid-s29371" xml:space="preserve"> Appropinquet aũt oculus, & fiat in pũcto e:</s>
            <s xml:id="echoid-s29372" xml:space="preserve"> du
              <lb/>
            canturq́;</s>
            <s xml:id="echoid-s29373" xml:space="preserve"> lineæ e z, e i cõtingentes circulũ, qui eſt baſis coni:</s>
            <s xml:id="echoid-s29374" xml:space="preserve"> & à uerti
              <lb/>
            ce coni cõtinuẽtur lineæ g z & g i.</s>
            <s xml:id="echoid-s29375" xml:space="preserve"> Videbitur itaq;</s>
            <s xml:id="echoid-s29376" xml:space="preserve"> ab uno oculo exi-
              <lb/>
            ſtente in puncto e portio ſuperficiei conicæ, quæ eſt g z i minor por-
              <lb/>
            tione g a b.</s>
            <s xml:id="echoid-s29377" xml:space="preserve"> Videtur autẽ apparere maior portiõe g a b propter maio-
              <lb/>
            ritatẽ anguli z e i ſupra angulum a d b.</s>
            <s xml:id="echoid-s29378" xml:space="preserve"> Ethoc eſt propoſitum.</s>
            <s xml:id="echoid-s29379" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1180" type="section" level="0" n="0">
          <head xml:id="echoid-head935" xml:space="preserve" style="it">87. Lineis à centro uiſus ad baſim coni cõtingenter ductis, & à
            <lb/>
          punctis contactuum ductis lineis logitudinis coni: ſi in cõmuni ſe-
            <lb/>
          ctione ſuperficierum per eaſdem line as & per cẽtrum oculi produ-
            <lb/>
          ctarum uiſus cono appropin quet: eadẽ portio ſuperficiei conicæ ui-
            <lb/>
          debitur, quæ prius, & eiuſdem quantitatis apparebit. Eucli-des 33th. opt.</head>
          <p>
            <s xml:id="echoid-s29380" xml:space="preserve">Eſto conus, cuius baſis ſit circulus b z g:</s>
            <s xml:id="echoid-s29381" xml:space="preserve"> & uertex eius punctũ a:</s>
            <s xml:id="echoid-s29382" xml:space="preserve">
              <lb/>
            axis quoq;</s>
            <s xml:id="echoid-s29383" xml:space="preserve"> ſit a h:</s>
            <s xml:id="echoid-s29384" xml:space="preserve"> centrumq́;</s>
            <s xml:id="echoid-s29385" xml:space="preserve"> oculi ſit d:</s>
            <s xml:id="echoid-s29386" xml:space="preserve"> & ducantur per 17 p 3 lineæ à
              <lb/>
            centro uilus d contingentes circulũ b z g, quæ ſint d z & d g.</s>
            <s xml:id="echoid-s29387" xml:space="preserve"> Et quo-
              <lb/>
            niam hoc fit ex hypotheſi:</s>
            <s xml:id="echoid-s29388" xml:space="preserve"> tũc patet per 16 p 3 & 2 p 11, quoniã centrũ
              <lb/>
            uiſus eſt in ſuperficie baſis coni uiſi.</s>
            <s xml:id="echoid-s29389" xml:space="preserve"> Et ducátur à punctis contactuũ
              <lb/>
            z & g duæ lineæ longitudinis per coni uerticẽ punctũ a, quæ ſint z a
              <lb/>
            & g a:</s>
            <s xml:id="echoid-s29390" xml:space="preserve"> quod fiet per 101 th.</s>
            <s xml:id="echoid-s29391" xml:space="preserve"> 1 huius:</s>
            <s xml:id="echoid-s29392" xml:space="preserve"> & à centro uiſus puncto d ad uerti-
              <lb/>
            cem coni punctũ a ducatur linea d a:</s>
            <s xml:id="echoid-s29393" xml:space="preserve"> & ducátur duæ ſuperficies, una
              <lb/>
            per lineas d g & g a, alia uerò per lineas d z & z a.</s>
            <s xml:id="echoid-s29394" xml:space="preserve"> Et quoniá eę ſuper-
              <lb/>
            ficies cõcurrũtin centro uiſus d & in uertice conia:</s>
            <s xml:id="echoid-s29395" xml:space="preserve"> erit ipſarũ com-
              <lb/>
            munis ſectio linea a d per 1 p 11 & per 19 th.</s>
            <s xml:id="echoid-s29396" xml:space="preserve"> 1 huius.</s>
            <s xml:id="echoid-s29397" xml:space="preserve"> Dico, quòd ſi ocu.</s>
            <s xml:id="echoid-s29398" xml:space="preserve">
              <lb/>
            lus appropinquet cono ſecundum lineam d a:</s>
            <s xml:id="echoid-s29399" xml:space="preserve"> non uidebitur maior
              <lb/>
            conicæ ſuperficiei portio nũc quàm prius, oculo in puncto d exiſtente.</s>
            <s xml:id="echoid-s29400" xml:space="preserve"> Sit enim, ut approximando
              <lb/>
            ipſrcono perueniat in punctum e lineæ d a:</s>
            <s xml:id="echoid-s29401" xml:space="preserve"> & ducantur à puncto e lineę æquidiſtantes lineis d g &
              <lb/>
            d z a d ſuperficiẽ coni uiſam:</s>
            <s xml:id="echoid-s29402" xml:space="preserve"> hę eruntergo neceſſariò
              <lb/>
            cõtingẽtes aliquẽ circulũ coni ęquidiſtátẽ baſi b z g:</s>
            <s xml:id="echoid-s29403" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0457-02" xlink:href="fig-0457-02a" number="506">
                <variables xml:id="echoid-variables486" xml:space="preserve">a e c d z h b g</variables>
              </figure>
            ergo neceſſariò cadent in aliqua puncta linearum a z
              <lb/>
            & a g:</s>
            <s xml:id="echoid-s29404" xml:space="preserve"> ideo quòd illæ ſecant proportionaliter baſim
              <lb/>
            coni, & oẽs circulos ei æ quidiſtátes:</s>
            <s xml:id="echoid-s29405" xml:space="preserve"> quoniá ſecundũ
              <lb/>
            lineas illas terminatur uiſus, & ſecundũ illas ſuperfi
              <lb/>
            cies contingẽtes terminatur uiſio circulorũ.</s>
            <s xml:id="echoid-s29406" xml:space="preserve"> Si enim
              <lb/>
            dicatur, quòd illæ lineę contingentes aliquẽ dictorũ
              <lb/>
            circulorũ ductæ à puncto e, cadant extra lineas a z &
              <lb/>
            a g, cũ lineæ à pũcto e in lineas a z & a g ductæ termi-
              <lb/>
            nentuiſum, & ſimiliter illæ cõtingentes terminẽt ui-
              <lb/>
            ſum:</s>
            <s xml:id="echoid-s29407" xml:space="preserve"> ſequetur uel lineas radiales eſſe refractas in me-
              <lb/>
            dio unius diaphani:</s>
            <s xml:id="echoid-s29408" xml:space="preserve"> quod eſt cõtra ea, quæ demõſtra
              <lb/>
            ta ſuntper 44 & ſequẽtes ſecũdi huius:</s>
            <s xml:id="echoid-s29409" xml:space="preserve"> uel ſequetur
              <lb/>
            lineas radiales eſſe curuas:</s>
            <s xml:id="echoid-s29410" xml:space="preserve"> quod eſt cõtra 1 th.</s>
            <s xml:id="echoid-s29411" xml:space="preserve"> 2 hu-
              <lb/>
            ius:</s>
            <s xml:id="echoid-s29412" xml:space="preserve"> uel ſequetur duas rectas lineas ſuperficiẽ inclu-
              <lb/>
            dere:</s>
            <s xml:id="echoid-s29413" xml:space="preserve"> quod eſt impoſsibile.</s>
            <s xml:id="echoid-s29414" xml:space="preserve"> Cadent ergo dictę lineæ
              <lb/>
            pertingentes ad ſuperficiẽ conicã ductæ à puncto e
              <lb/>
            ιn lineas a z & a g:</s>
            <s xml:id="echoid-s29415" xml:space="preserve"> cadant ita q;</s>
            <s xml:id="echoid-s29416" xml:space="preserve"> in ipſarũ duo puncta,
              <lb/>
            quę ſinti & c, & ſint lineę e i & e c.</s>
            <s xml:id="echoid-s29417" xml:space="preserve"> Quia ergo angulus
              <lb/>
            c e ι eſt æ qualis angulo g d z per 10 p 11, ſicut & anguli
              <lb/>
            cõtenti ſub lineis c i & g z, quoniã oẽs illi anguli con-
              <lb/>
            tinentur ſub lineis æquidiſtantibus angulariter con-
              <lb/>
            runctis, patet per 20 huius uerum eſſe quod proponi
              <lb/>
            tur.</s>
            <s xml:id="echoid-s29418" xml:space="preserve"> Et quia ubicunq;</s>
            <s xml:id="echoid-s29419" xml:space="preserve"> uiſus in linea d a ponitur, ſemper anguli ad uiſum ſunt æ quales per 10 p 11, pa-
              <lb/>
            làm ergo eſt propoſitum.</s>
            <s xml:id="echoid-s29420" xml:space="preserve"> Et hocidem ſuo modo in ambobus poteſt uiſibus demonſtrari.</s>
            <s xml:id="echoid-s29421" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1182" type="section" level="0" n="0">
          <head xml:id="echoid-head936" xml:space="preserve" style="it">88. Eleuato uiſu, reſpectu ſuperficiei conicæ: maius erit, quod uidetur, uidebitur autem mi-
            <lb/>
          nus uideri: depreſſo uerò uiſu, minus erit quod uidebitur, ſed apparebit maius prius uiſo. Eu-
            <lb/>
          clides 34th. optico.</head>
          <p>
            <s xml:id="echoid-s29422" xml:space="preserve">Eſto conus, cuius baſis circulus b g:</s>
            <s xml:id="echoid-s29423" xml:space="preserve"> & uertex punctus a:</s>
            <s xml:id="echoid-s29424" xml:space="preserve"> & ducantur lineæ longitudinis, quæ
              <lb/>
            </s>
          </p>
        </div>
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