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-s18320" xml:space="preserve">
              <pb o="263" file="0269" n="269" rhead="OPTICAE LIBER VII."/>
            fractè & rectè:</s>
            <s xml:id="echoid-s18321" xml:space="preserve"> & huius rei uiſæ imago erit centrum uiſus [per 13 n.</s>
            <s xml:id="echoid-s18322" xml:space="preserve">] Item ſi fixerimus lineam
              <lb/>
            a g b, & reuoluerimus figuram a e b in circuitu a b, & pars ſuperficiei corporis diaphani, quod
              <lb/>
            eſt ex parte rei uiſæ, fuerit ſphærica:</s>
            <s xml:id="echoid-s18323" xml:space="preserve"> tuncpunctum e ſignabit circumferentiam in ſuperficie cir-
              <lb/>
            culari conuexa, quæ eſt ex parte uiſus, ex qua circumferentia refringetur b ad a:</s>
            <s xml:id="echoid-s18324" xml:space="preserve"> ſed imago in to-
              <lb/>
            ta circumferentia refractionis erit una, ſcilicet centrum uiſus.</s>
            <s xml:id="echoid-s18325" xml:space="preserve"> Imago ergo rei uiſæ etiam erit u-
              <lb/>
            na.</s>
            <s xml:id="echoid-s18326" xml:space="preserve"> Sed ex hac poſitione accidit, ut uiſus comprehendat formam rei uiſæ apud locum refra-
              <lb/>
            ctionis ea de cauſſa, quam diximus in reflexione ex ſpeculis, [61 n 5] cum fuerit reflexio à
              <lb/>
            circumferentia in aliqua ſphæra, & fuerit imago centrum uiſus.</s>
            <s xml:id="echoid-s18327" xml:space="preserve"> Ergo huius rei uiſæ forma à
              <lb/>
            uiſu circularis comprehenditur apud circulum refractionis:</s>
            <s xml:id="echoid-s18328" xml:space="preserve"> & punctum eius ſuperius circa d ui-
              <lb/>
            detur in rectitudine perpendicularis, tranſeuntis per uiſum & rem uiſam ſimul.</s>
            <s xml:id="echoid-s18329" xml:space="preserve"> Et hoc eſt quod
              <lb/>
            uoluimus.</s>
            <s xml:id="echoid-s18330" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div597" type="section" level="0" n="0">
          <figure number="231">
            <variables xml:id="echoid-variables218" xml:space="preserve">e a g e z b</variables>
          </figure>
          <head xml:id="echoid-head513" xml:space="preserve" style="it">30. Si communis ſectio ſuperficierum, refractionis & refractiui caui, denſioris fuerit peri-
            <lb/>
          pheria: uiſibile in perpendiculari à uiſu ſuper refractiuum ducta, re
            <lb/>
          ctè: & unum uidebitur. 26 p 10.</head>
          <p>
            <s xml:id="echoid-s18331" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s18332" xml:space="preserve"> ſit a uiſus:</s>
            <s xml:id="echoid-s18333" xml:space="preserve"> & ſit b in aliquo uiſo, & ultra corpus diaphanum
              <lb/>
            groſsius illo, in quo eſt uiſus:</s>
            <s xml:id="echoid-s18334" xml:space="preserve"> & ſit ſuperficies corporis, quod eſt ex
              <lb/>
            parte uiſus, circularis concaua:</s>
            <s xml:id="echoid-s18335" xml:space="preserve"> cuius concauitas ſit ex parte uiſus.</s>
            <s xml:id="echoid-s18336" xml:space="preserve">
              <lb/>
            Dico ergo, quòd b unam ſolam habebit imaginem, & unam tãtùm for-
              <lb/>
            mam apud a.</s>
            <s xml:id="echoid-s18337" xml:space="preserve"> Et ſit centrum concauitatis g:</s>
            <s xml:id="echoid-s18338" xml:space="preserve"> & continuemus a g:</s>
            <s xml:id="echoid-s18339" xml:space="preserve"> & ex-
              <lb/>
            trahamus ipſam rectè uſque ad z.</s>
            <s xml:id="echoid-s18340" xml:space="preserve"> Erit ergo a z perpendicularis ſuper ſu
              <lb/>
            perficiem concauam:</s>
            <s xml:id="echoid-s18341" xml:space="preserve"> [ut oſtenſum eſt 25 n 4:</s>
            <s xml:id="echoid-s18342" xml:space="preserve">] & b aut erit in a z, aut
              <lb/>
            extra.</s>
            <s xml:id="echoid-s18343" xml:space="preserve"> Sit ergo primò in linea a z.</s>
            <s xml:id="echoid-s18344" xml:space="preserve"> A ergo comprehendet b in rectitudi-
              <lb/>
            ne a b, cum a b ſit perpendicularis ſuper ſuperficiem concauam, & nun
              <lb/>
            quam refractè [per 13 n.</s>
            <s xml:id="echoid-s18345" xml:space="preserve">] Quòd ſi eſt poſsibile, refringatur forma b ad
              <lb/>
            a ex e, & continuemus b e, g e, & extrahamus b e uſque ad t:</s>
            <s xml:id="echoid-s18346" xml:space="preserve"> angulus er-
              <lb/>
            go t e g eſt ille, quem continet linea, per quam extenditur forma, & per-
              <lb/>
            pendicularis exiens à loco refractionis.</s>
            <s xml:id="echoid-s18347" xml:space="preserve"> Et quia corpus, quod eſt ex par
              <lb/>
            te a, ſubtilius eſt illo, quod eſt ex parte b:</s>
            <s xml:id="echoid-s18348" xml:space="preserve"> erit [per 14 n] refractio ad par
              <lb/>
            tem contrariam illi, in qua eſt e g.</s>
            <s xml:id="echoid-s18349" xml:space="preserve"> Linea ergo e t, quan do refringitur, re-
              <lb/>
            mouetur à linea e g:</s>
            <s xml:id="echoid-s18350" xml:space="preserve"> & non concurret cum linea b a aliquo modo.</s>
            <s xml:id="echoid-s18351" xml:space="preserve"> For-
              <lb/>
            ma ergo b non refringetur ad a:</s>
            <s xml:id="echoid-s18352" xml:space="preserve"> non ergo comprehẽdetur refractè, ſed
              <lb/>
            rectè:</s>
            <s xml:id="echoid-s18353" xml:space="preserve"> ergo non habebit apud uiſum, niſi unam formam tantùm.</s>
            <s xml:id="echoid-s18354" xml:space="preserve"> Et hoc
              <lb/>
            eſt quod uoluimus.</s>
            <s xml:id="echoid-s18355" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div598" type="section" level="0" n="0">
          <head xml:id="echoid-head514" xml:space="preserve" style="it">31. Si communis ſectio ſuperficierum, refractionis & refractiui
            <lb/>
          caui, denſioris fuerit peripheria: uiſibile extra perpendicularem à ui
            <lb/>
          ſu ſuper refractiuum ductam, ab uno puncto refringetur, unam́
            <lb/>
          habebit imaginem, uariè pro uaria uiſ{us} uel uiſibilis poſitione ſi-
            <lb/>
          tam. 27 p 10.</head>
          <p>
            <s xml:id="echoid-s18356" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s18357" xml:space="preserve"> iteremus figurã, & ſit b extra lineam a z, & extrahamus ſuperficiem, in qua eſt a z b:</s>
            <s xml:id="echoid-s18358" xml:space="preserve"> Hæc
              <lb/>
            ergo ſuperficies erit perpendicularis ſuper ſuperficiem concauam [per 9 n] & non refringetur
              <lb/>
            forma b ad a, niſi in hac ſuperficie.</s>
            <s xml:id="echoid-s18359" xml:space="preserve"> Non enim erigitur perpendicularis ſuper ſuperficiem con-
              <lb/>
            cauam alia ſuperficies æqualis, quæ tranſit per a, niſi illa, quæ tranſit per a z:</s>
            <s xml:id="echoid-s18360" xml:space="preserve"> ſed per a z & per b non
              <lb/>
            tranſit, niſi una ſola tantùm.</s>
            <s xml:id="echoid-s18361" xml:space="preserve"> Forma ergo b non refringetur ad a, niſi in ſuperficie tranſeunte per li-
              <lb/>
            neam a z, & per b.</s>
            <s xml:id="echoid-s18362" xml:space="preserve"> Et ſit differentia communis inter hanc ſuperficiem & ſuperficiem concauam ar-
              <lb/>
            cus h d e, & refringatur forma b ad a ex h.</s>
            <s xml:id="echoid-s18363" xml:space="preserve"> Dico ergo, quòd non refringetur ex alio puncto.</s>
            <s xml:id="echoid-s18364" xml:space="preserve"> Quòd ſi
              <lb/>
            poſsibile fuerit, refringatur ex m, & continuemus lineas a h, b h, g h, a m, b m, g m, & extrahamus h b
              <lb/>
            rectè uſque ad c, & b m rectè uſque ad n, & g h rectè uſq;</s>
            <s xml:id="echoid-s18365" xml:space="preserve"> ad l, & g m rectè uſque ad p, & perficiamus
              <lb/>
            circumferentiam h e d, & ſecet lineam a g in k.</s>
            <s xml:id="echoid-s18366" xml:space="preserve"> A ergo aut erit in linea k d:</s>
            <s xml:id="echoid-s18367" xml:space="preserve"> aut extrà in parte k, [quia
              <lb/>
            ea pars obiecta eſt cauæ refractiui ſuperficiei, à qua refractio fit ad uiſum a.</s>
            <s xml:id="echoid-s18368" xml:space="preserve">] ſi ergo a fuerit in k d,
              <lb/>
            aut erit in g, aut in altera duarum linearumg d, g k.</s>
            <s xml:id="echoid-s18369" xml:space="preserve"> Si ergo fuerit a in g:</s>
            <s xml:id="echoid-s18370" xml:space="preserve"> tunc forma b non refrin-
              <lb/>
            getur a d a [per præcedentem numerum:</s>
            <s xml:id="echoid-s18371" xml:space="preserve">] lineæ enim, quæ continuant corpus circulare cum g,
              <lb/>
            ſunt perpendiculares ſuper ſuperficiem corporis, [per 25 n 4,] quod eſt ex parte a:</s>
            <s xml:id="echoid-s18372" xml:space="preserve"> Refractio au-
              <lb/>
            tem non fit per ipſam perpendicularem, ſed extra ipſam.</s>
            <s xml:id="echoid-s18373" xml:space="preserve"> Forma ergo b non refringetur ad a, ſi a
              <lb/>
            fuerit in g.</s>
            <s xml:id="echoid-s18374" xml:space="preserve"> Et ſi a fuerit in g d:</s>
            <s xml:id="echoid-s18375" xml:space="preserve"> tunc linea h c erit inter duas lineas h a, h g:</s>
            <s xml:id="echoid-s18376" xml:space="preserve"> & ideo linea n m erit
              <lb/>
            inter duas lineas m a, m g.</s>
            <s xml:id="echoid-s18377" xml:space="preserve"> Nam refractio eſt ad partem contrariam partι perpendicularis, [per
              <lb/>
            14 n] nam corpus diaphanum, quod eſt ex parte uiſus, eſt ſubtilius illo, quod eſt ex parte rei ui-
              <lb/>
            ſæ.</s>
            <s xml:id="echoid-s18378" xml:space="preserve"> Et ſi linea h c fuerit inter duas lineas h a, h g, & a fuerit in linea g d:</s>
            <s xml:id="echoid-s18379" xml:space="preserve"> tunc angulus b h a e-
              <lb/>
            rit ex parte d:</s>
            <s xml:id="echoid-s18380" xml:space="preserve"> & ſimiliter angulus b m a erit ex parte d:</s>
            <s xml:id="echoid-s18381" xml:space="preserve"> & erit b ultra lineam g h l, uidelicet ex par-
              <lb/>
            te k, à linea h g l.</s>
            <s xml:id="echoid-s18382" xml:space="preserve"> Et erit angulus c h g ille, quem continet linea, per quam extenditur forma cum
              <lb/>
            </s>
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