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-s12300" xml:space="preserve">
              <pb o="183" file="0189" n="189" rhead="OPTICAE LIBER V."/>
            perpendicularem:</s>
            <s xml:id="echoid-s12301" xml:space="preserve"> quædam illarum ſuperficierum efficiet lineam cõmunem, lineam rectam:</s>
            <s xml:id="echoid-s12302" xml:space="preserve"> & non
              <lb/>
            fiet reflexio, niſi ſuper illam perpendicularem:</s>
            <s xml:id="echoid-s12303" xml:space="preserve"> [per 11 n 4] & locus imaginis erit centrum uiſus:</s>
            <s xml:id="echoid-s12304" xml:space="preserve"> &
              <lb/>
            non uidebitur punctum, niſi quod fuerit in ſuperficie uiſus [per 13 n.</s>
            <s xml:id="echoid-s12305" xml:space="preserve">] Quædam autẽillarũ ſuper-
              <lb/>
            ficierum efficiet lineam communem, circulum:</s>
            <s xml:id="echoid-s12306" xml:space="preserve"> & tunc puncta, inter quæ & uiſum fuerit centrum
              <lb/>
            circuli:</s>
            <s xml:id="echoid-s12307" xml:space="preserve"> poterunt reflecti ad uiſum, ſingula à duobus punctis circuli:</s>
            <s xml:id="echoid-s12308" xml:space="preserve"> cum à ſingulis ducantur lineæ
              <lb/>
            facientes angulũ cum ſuperficie contingente, quem
              <lb/>
              <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a" number="145">
                <variables xml:id="echoid-variables135" xml:space="preserve">a s c p c f d
                  <gap/>
                d e b</variables>
              </figure>
            per æqualia diuidit perpendicularis ducta ad cen-
              <lb/>
            trum.</s>
            <s xml:id="echoid-s12309" xml:space="preserve"> [Nam cum a b ſit diameter circuli, & f g axis
              <lb/>
            cylindri:</s>
            <s xml:id="echoid-s12310" xml:space="preserve"> erit per 3 d 11 e f perpẽdicularis f g:</s>
            <s xml:id="echoid-s12311" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s12312" xml:space="preserve"> an-
              <lb/>
            guli ad f erunt recti:</s>
            <s xml:id="echoid-s12313" xml:space="preserve"> at ex theſic e æquatur ipſi e d:</s>
            <s xml:id="echoid-s12314" xml:space="preserve"> &
              <lb/>
            communis eſt e f:</s>
            <s xml:id="echoid-s12315" xml:space="preserve"> ergo per 4 p 1 triangula d f e, c f e
              <lb/>
            ſunt æquiangula.</s>
            <s xml:id="echoid-s12316" xml:space="preserve"> Quare perpẽdicularis fe bifariam
              <lb/>
            ſecat angulum c e d:</s>
            <s xml:id="echoid-s12317" xml:space="preserve"> eodemq́;</s>
            <s xml:id="echoid-s12318" xml:space="preserve"> modo oſtẽdetur per-
              <lb/>
            pendicularem g f bifariam ſecare angulũ d g c.</s>
            <s xml:id="echoid-s12319" xml:space="preserve">] Et
              <lb/>
            hæc quidem dico de punctis, quę ſunt in illa perpen
              <lb/>
            diculari:</s>
            <s xml:id="echoid-s12320" xml:space="preserve"> & loca imaginũ erunt in centro circuli:</s>
            <s xml:id="echoid-s12321" xml:space="preserve"> alia
              <lb/>
            puncta illius perpendicularis nõ reflectentur ad ui-
              <lb/>
            ſum, præter punctum, quod eſt in ſuperficie uiſus:</s>
            <s xml:id="echoid-s12322" xml:space="preserve"> &
              <lb/>
            illud per illam perpendicularem [per 11 n 4.</s>
            <s xml:id="echoid-s12323" xml:space="preserve">] Cum
              <lb/>
            autem fuerit linea cõmunis, ſectio columnaris:</s>
            <s xml:id="echoid-s12324" xml:space="preserve"> non
              <lb/>
            poterunt puncta perpendicularis reflecti ab aliqui-
              <lb/>
            bus alijs punctis ſectionis:</s>
            <s xml:id="echoid-s12325" xml:space="preserve"> cum forma accedens ſu-
              <lb/>
            per perpendicularem, reflectatur ſuper perpendicularem:</s>
            <s xml:id="echoid-s12326" xml:space="preserve"> & in ſectione una ſit perpendicularis [ut
              <lb/>
            proximo numero oſtenſum eſt.</s>
            <s xml:id="echoid-s12327" xml:space="preserve">] Quare per hanc ſolam perpendicularem fiet reflexio:</s>
            <s xml:id="echoid-s12328" xml:space="preserve"> & ſolũ pun-
              <lb/>
            ctu m ſuperficiei uiſus uidebitur:</s>
            <s xml:id="echoid-s12329" xml:space="preserve"> & locus imaginis erit centrum uiſus.</s>
            <s xml:id="echoid-s12330" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div436" type="section" level="0" n="0">
          <head xml:id="echoid-head395" xml:space="preserve" style="it">92. Siuiſus fuerit in centro circuli ſpeculi cylindracei caui: reflectetur ab eiuſdẽ circuli peri-
            <lb/>
          pheria, ſimili peripheriæ circuli per centrũ uiſus ducti: & imago uidebitur in cẽtro uiſus. 12 p 9.</head>
          <p>
            <s xml:id="echoid-s12331" xml:space="preserve">SI uerò fuerit uiſus in cẽtro circuli:</s>
            <s xml:id="echoid-s12332" xml:space="preserve"> reflectetur portio uiſus, quam ſecant perpendiculares, du-
              <lb/>
            ctæ à centro uiſus ad circulum, [per cẽtrum uiſus ductum] à portione ſimili circulo, [ſpeculi]
              <lb/>
            quam ſecant ſimiliter eædem perpendiculares.</s>
            <s xml:id="echoid-s12333" xml:space="preserve"> Quia cum quælibet linea ducta à centro uiſus
              <lb/>
            ad circulum, ſit perpendicularis:</s>
            <s xml:id="echoid-s12334" xml:space="preserve"> [ſuper ſuperficies uiſus & ſpeculi per 25 n 4:</s>
            <s xml:id="echoid-s12335" xml:space="preserve"> quia tranſit per cen-
              <lb/>
            tra uiſus & ſpeculi] fiet reflexio ſuper perpendicularem:</s>
            <s xml:id="echoid-s12336" xml:space="preserve"> [per 11 n 4] & locus imaginis erit cẽtrum
              <lb/>
            uiſus:</s>
            <s xml:id="echoid-s12337" xml:space="preserve"> quod eſt centrum circuli.</s>
            <s xml:id="echoid-s12338" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div437" type="section" level="0" n="0">
          <head xml:id="echoid-head396" xml:space="preserve" style="it">93. Si communis ſectio ſuperficierum, reflexionis & ſpeculi cylindracei cauifuerit ellipſis: à
            <lb/>
          pluribus punct is idem uiſibile ad eundem uiſum reflecti
            <lb/>
          poteſt. 9 p 9.</head>
          <figure number="146">
            <variables xml:id="echoid-variables136" xml:space="preserve">e b
              <gap/>
            g q l m d o a z n
              <gap/>
            h k</variables>
          </figure>
          <p>
            <s xml:id="echoid-s12339" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s12340" xml:space="preserve"> ſuper punctum a fiat angulus acutus quo
              <gap/>
              <lb/>
            quo modo:</s>
            <s xml:id="echoid-s12341" xml:space="preserve"> qui ſit f a g.</s>
            <s xml:id="echoid-s12342" xml:space="preserve"> Palàm, quòd cõcurret f a cũ
              <lb/>
            g z:</s>
            <s xml:id="echoid-s12343" xml:space="preserve"> [quia g z cadens intra ellipſin ex theſi 90 n ef-
              <lb/>
            ficit angulum z g d acutum:</s>
            <s xml:id="echoid-s12344" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s12345" xml:space="preserve"> cũ anguli z g d, f a g duo-
              <lb/>
            bus rectis ſint minores:</s>
            <s xml:id="echoid-s12346" xml:space="preserve"> rectæ a f, g z concurrent ad partes
              <lb/>
            z, per 11 a x] ſit concurſus in puncto z:</s>
            <s xml:id="echoid-s12347" xml:space="preserve"> & [per 23 p 1] fiat an-
              <lb/>
            gulus c a g æqualis angulo f a g:</s>
            <s xml:id="echoid-s12348" xml:space="preserve"> concurret equidẽ a c cum
              <lb/>
            g q:</s>
            <s xml:id="echoid-s12349" xml:space="preserve"> [per 11 ax.</s>
            <s xml:id="echoid-s12350" xml:space="preserve"> Nam quia angulus q g d æquatus eſt angulo
              <lb/>
            z g a acuto, ut patuit 90 n:</s>
            <s xml:id="echoid-s12351" xml:space="preserve"> & modo angulus c a g æquatur
              <lb/>
            z a g:</s>
            <s xml:id="echoid-s12352" xml:space="preserve"> anguli q g d, c a g ſunt minores duobus rectis] ſit cõ-
              <lb/>
            curſus in puncto c.</s>
            <s xml:id="echoid-s12353" xml:space="preserve"> Palàm [per 12 n 4] quòd c reflectetur
              <lb/>
            ad z à puncto g:</s>
            <s xml:id="echoid-s12354" xml:space="preserve"> & ita reflectetur à puncto a ad z, & non ab
              <lb/>
            alio puncto ſectionis.</s>
            <s xml:id="echoid-s12355" xml:space="preserve"> Quia non poterit reflecti, niſi à ter-
              <lb/>
            mino perpendicularis:</s>
            <s xml:id="echoid-s12356" xml:space="preserve"> & una eſt in ſectione illa perpendi-
              <lb/>
            cularis [ut oſtenſum eſt 90 n] ſcilicet g a.</s>
            <s xml:id="echoid-s12357" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div438" type="section" level="0" n="0">
          <head xml:id="echoid-head397" xml:space="preserve" style="it">94. Si duo puncta ſumantur in axeſpeculi cylindra-
            <lb/>
          ceicaui: poſſunt à tota circuli peripheria inter ſe mutuò
            <lb/>
          reflecti: & imago uidebitur in peripheria circuliextra
            <lb/>
          ſpeculi ſuperficiem deſcripti. 13 p 9.</head>
          <p>
            <s xml:id="echoid-s12358" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s12359" xml:space="preserve"> ſumptis duobus punctis in axe columnæ:</s>
            <s xml:id="echoid-s12360" xml:space="preserve">
              <lb/>
            poterit unum reflecti ad aliud ab uno circulo colu-
              <lb/>
            mnæ toto:</s>
            <s xml:id="echoid-s12361" xml:space="preserve"> & locus imaginis erit circulus quidam
              <lb/>
            extra columnam.</s>
            <s xml:id="echoid-s12362" xml:space="preserve"> Verbi gratia:</s>
            <s xml:id="echoid-s12363" xml:space="preserve"> ſit e z axis:</s>
            <s xml:id="echoid-s12364" xml:space="preserve"> t, h puncta ſum-
              <lb/>
            pta in axe:</s>
            <s xml:id="echoid-s12365" xml:space="preserve"> a g, b d baſes.</s>
            <s xml:id="echoid-s12366" xml:space="preserve"> Diuidatur t h per æqualia in puncto q [per 10 p 1] & fiat circulus, cuius q
              <lb/>
            centrum:</s>
            <s xml:id="echoid-s12367" xml:space="preserve"> eius diameter l m:</s>
            <s xml:id="echoid-s12368" xml:space="preserve"> qui erit æquidiſtans baſibus:</s>
            <s xml:id="echoid-s12369" xml:space="preserve"> [per 5 th.</s>
            <s xml:id="echoid-s12370" xml:space="preserve"> Sereni de ſectione cylindri] la-
              <lb/>
            tera columnæ b l a, d m g.</s>
            <s xml:id="echoid-s12371" xml:space="preserve"> Fiat etiam circulus k p, cuius h centrum, p k diameter:</s>
            <s xml:id="echoid-s12372" xml:space="preserve"> & ducantur lineæ
              <lb/>
            </s>
          </p>
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