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

List of thumbnails

< >
121
121 (115) 		122
122 (116)
123
123 (117) 		124
124 (118)
125
125 (119) 		126
126 (120)
127
127 (121) 		128
128 (122)
129
129 (123) 		130
130 (124)
< >
page |< < (119) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div251" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s7012" xml:space="preserve">
              <pb o="119" file="0125" n="125" rhead="OPTICAE LIBER IIII."/>
            cadem ſuperficie, reſpectu eiuſdem uiſus:</s>
            <s xml:id="echoid-s7013" xml:space="preserve"> quoniam reſpectu duorum uiſuum poteſt reflexio fieri à
              <lb/>
            duobus pũctis ſuperficiei ſpeculi, ut circuli diametri terminis, quæ eſt perpendicularis ſuper ipſam
              <lb/>
            ſectionem:</s>
            <s xml:id="echoid-s7014" xml:space="preserve"> reſpectu uerò unius uiſus non accidit:</s>
            <s xml:id="echoid-s7015" xml:space="preserve"> quoniam illa duo puncta nõ ſimul ab eodem uiſu
              <lb/>
            poſſunt comprehendi:</s>
            <s xml:id="echoid-s7016" xml:space="preserve"> ſemper enim neceſſe eſt partem columnæ medietate minorem uideri.</s>
            <s xml:id="echoid-s7017" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div252" type="section" level="0" n="0">
          <head xml:id="echoid-head281" xml:space="preserve" style="it">34. Si rect a line à reflexionis puncto, ſit perpendicularis ſpeculo cylindraceo conuexo: in-
            <lb/>
          t{us} continuata, tranſibit per centrum circuli baſib{us} par alleli: & contrà. 21 p 7.</head>
          <p>
            <s xml:id="echoid-s7018" xml:space="preserve">PAlàm ex prædictis, perpendicularẽ ſuper punctum reflexionis intellectam extrà & intrà pro-
              <lb/>
            duci, diametrum circuli efficere.</s>
            <s xml:id="echoid-s7019" xml:space="preserve"> Quia ſi non:</s>
            <s xml:id="echoid-s7020" xml:space="preserve"> cum conſtet diametrum circuli ſuper punctum
              <lb/>
            illud tranſeuntem, perpendicularem eſſe ſuper ſuperficiem contingentem columnam in illo
              <lb/>
            puncto [ut oſtenſum eſt 32 n] & perpendicularem extrà ſimiliter:</s>
            <s xml:id="echoid-s7021" xml:space="preserve"> erit [per 14 p 1] cõtinuitas inter
              <lb/>
            has perpendiculares, & unam efficient lineam.</s>
            <s xml:id="echoid-s7022" xml:space="preserve"> Quia ſi non eſt, quòd diameter extrà producta, per-
              <lb/>
            pendicularis ſit ſuper illã ſuperficiem:</s>
            <s xml:id="echoid-s7023" xml:space="preserve"> accidet ex eodẽ ſuperficiei puncto duas erigi perpendicula-
              <lb/>
            res [cõtra 13 p 11] In omni ergo ſuperficie reflexionis patet quatuor punctorũ cõcurſus:</s>
            <s xml:id="echoid-s7024" xml:space="preserve"> cẽtri uiſus:</s>
            <s xml:id="echoid-s7025" xml:space="preserve">
              <lb/>
            pũcti axis, in qđ cadit քpẽdicularis:</s>
            <s xml:id="echoid-s7026" xml:space="preserve"> pũcti reflexiõis in ſpeculo:</s>
            <s xml:id="echoid-s7027" xml:space="preserve"> pũcti, à quo forma corporis ꝓcedit.</s>
            <s xml:id="echoid-s7028" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div253" type="section" level="0" n="0">
          <head xml:id="echoid-head282" xml:space="preserve" style="it">35. Si à uiſu extra ſpeculi conici conuexirecti ſuperficiem, uel ipſi continuam ſito, recta li-
            <lb/>
          nea cum uertice axis acutum angulũ faciat: duo plana educta per rect{as} à uiſu, ſpeculum tan-
            <lb/>
          gentes & conica latera, per tact{us} puncta tranſeuntia, tangent ſpeculum, & cõſpicuam ſuper-
            <lb/>
          ficiem dimidiat a minorem, à qua ad uiſum reflexio fiat, terminabunt. 1. 2 p 7.</head>
          <p>
            <s xml:id="echoid-s7029" xml:space="preserve">IN ſpeculis pyramidalibus ſuper baſes ſuas orthogonalibus politis exterius eſt oppoſitio uiſus:</s>
            <s xml:id="echoid-s7030" xml:space="preserve">
              <lb/>
            ut non ſit uiſus in ſuperficie ſpeculi, aut in continua ei:</s>
            <s xml:id="echoid-s7031" xml:space="preserve"> & ſecũdum uiſus ſitum, reſpectu ſpeculi
              <lb/>
            pyramidalis erit quantitas comprehẽſæ in eo partis.</s>
            <s xml:id="echoid-s7032" xml:space="preserve"> Igitur ſi radius ab oculi centro ad terminũ
              <lb/>
            axis pyramidis, id eſt ad acumen intellectus, faciat cum axe angulũ
              <lb/>
              <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a" number="28">
                <variables xml:id="echoid-variables18" xml:space="preserve">a b f g c d n</variables>
              </figure>
            acutum ex parte pyramidis:</s>
            <s xml:id="echoid-s7033" xml:space="preserve"> intelligemus à centro uiſus ſuperficiem
              <lb/>
            ſecantem pyramidem ſuper circulũ æquidiſtantem baſi pyramidis:</s>
            <s xml:id="echoid-s7034" xml:space="preserve">
              <lb/>
            & intelligemus duas lineas à centro quidẽ uiſus, tangẽtes illum cir-
              <lb/>
            culum in punctis oppoſitis, à quibus protrahemus lineas ſecundum
              <lb/>
            longitudinẽ pyramidis.</s>
            <s xml:id="echoid-s7035" xml:space="preserve"> Superficies ergo ex una harum linearũ lon-
              <lb/>
            gitudinis & altera contingentium circulum, continget pyramidem.</s>
            <s xml:id="echoid-s7036" xml:space="preserve">
              <lb/>
            Si enim ſecuerit:</s>
            <s xml:id="echoid-s7037" xml:space="preserve"> continget aliud punctum, quàm punctum contin-
              <lb/>
            gentiæ circuli:</s>
            <s xml:id="echoid-s7038" xml:space="preserve"> ſuper illud punctum producatur linea longitudinis,
              <lb/>
            & illud punctum & acumen pyramidis ſimul ſunt in hac ſuperficie.</s>
            <s xml:id="echoid-s7039" xml:space="preserve">
              <lb/>
            Quare illa linea erit in hac ſuperficie, & tranſibit per aliquod punctũ
              <lb/>
            circuli:</s>
            <s xml:id="echoid-s7040" xml:space="preserve"> illud igitur punctum in hac ſuperficie eſt, & in circulo:</s>
            <s xml:id="echoid-s7041" xml:space="preserve"> quare
              <lb/>
            eſt in linea cõmuni circulo & ſuperficiei:</s>
            <s xml:id="echoid-s7042" xml:space="preserve"> ſed illa contingit circulum:</s>
            <s xml:id="echoid-s7043" xml:space="preserve">
              <lb/>
            quare cõtingens tranſit per duo puncta circuli, quẽ contingit, quod
              <lb/>
            eſt impoſsibile [& contra 2 d 3.</s>
            <s xml:id="echoid-s7044" xml:space="preserve">] Reſtat igitur, ut illa ſuperficies tan-
              <lb/>
            gat pyramidem.</s>
            <s xml:id="echoid-s7045" xml:space="preserve"> Et generaliter omnis ſuperficies, in qua cõcurrunt
              <lb/>
            linea, tangẽs aliquod punctum pyramidis, & longitudinis linea, per
              <lb/>
            punctum illud tranſiens, tangit pyramidem ſuper lineam longitudi-
              <lb/>
            nis.</s>
            <s xml:id="echoid-s7046" xml:space="preserve"> Habemus ergo duas ſuperficies ab oculi centro procedẽtes, py-
              <lb/>
            ramidem contingentes, inter quas eſt portio pyramidis apparentis
              <lb/>
            uiſui in hoc ſitu:</s>
            <s xml:id="echoid-s7047" xml:space="preserve"> & eſt minor medietate pyramidis:</s>
            <s xml:id="echoid-s7048" xml:space="preserve"> quoniam lineæ tangentes circulum, includun
              <gap/>
              <lb/>
            eius partem medietate minorem.</s>
            <s xml:id="echoid-s7049" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div255" type="section" level="0" n="0">
          <figure number="29">
            <variables xml:id="echoid-variables19" xml:space="preserve">b a f l g e k h n d c</variables>
          </figure>
          <head xml:id="echoid-head283" xml:space="preserve" style="it">36. Si à uiſu recta linea, ſit perpendicularis uertici axis ſpecu-
            <lb/>
          li conici cõuexi recti: duo plana educta per rect{as} ſpeculum in ter- minis diametricirculi, ad baſim paralleli tangentes, & later a co- nica per tact{us} puncta tranſeuntia: tangent ſpeculum: & dimi- diatam ſuperficiem conſpicuam, à qua ad uiſum reflexio fiat, ter- minabunt. 89 p 4.</head>
          <p>
            <s xml:id="echoid-s7050" xml:space="preserve">SI uerò linea à centro uiſus ad acumen pyramidis ducta, teneat
              <lb/>
            angulum rectum cum axe, & intelligatur circulus ſecans pyra-
              <lb/>
            midem æquidiſtanter baſi:</s>
            <s xml:id="echoid-s7051" xml:space="preserve"> linea communis huic circulo, & ſu-
              <lb/>
            perficiei, in qua ſunt axis pyramidis, & centrũ uiſus:</s>
            <s xml:id="echoid-s7052" xml:space="preserve"> erit orthogona-
              <lb/>
            lis ſuper axem pyramidis:</s>
            <s xml:id="echoid-s7053" xml:space="preserve"> quoniã axis eſt orthogonalis ſuper ſuper-
              <lb/>
            ficiem circuli [per cõuerſam 14 p 11:</s>
            <s xml:id="echoid-s7054" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s7055" xml:space="preserve"> per 3 d 11 axis coni eſt ad per
              <lb/>
            pendiculum omnibus lineis, à quibus in plano circuli tangitur.</s>
            <s xml:id="echoid-s7056" xml:space="preserve">] Et
              <lb/>
            ſuper lineam communem protrahatur per cẽtrum circuli diameter
              <lb/>
            orthogonalis ſuper hãc lineam:</s>
            <s xml:id="echoid-s7057" xml:space="preserve"> & à terminis huius diametri ortho-
              <lb/>
            gonalis protrahãtur duæ cõtingentes circulum:</s>
            <s xml:id="echoid-s7058" xml:space="preserve"> & etiam duæ lineæ
              <lb/>
            uſq;</s>
            <s xml:id="echoid-s7059" xml:space="preserve"> ad acumen pyramidis.</s>
            <s xml:id="echoid-s7060" xml:space="preserve"> Duæ ſuperficies, in quibus erũt hæ duæ
              <lb/>
            lineæ cũ contingẽtibus, cõtingẽt pyramidẽ ſecũdũ modũ prædictũ.</s>
            <s xml:id="echoid-s7061" xml:space="preserve">
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum