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-s17870" xml:space="preserve">
              <pb o="257" file="0263" n="263" rhead="OPTICAE LIBER VII."/>
            a ex p, neque ex alio puncto:</s>
            <s xml:id="echoid-s17871" xml:space="preserve"> a ergo non comprehendit b, niſi in rectitudine lineæ a g b:</s>
            <s xml:id="echoid-s17872" xml:space="preserve"> non ergo cõ
              <lb/>
            prehendit ipſum, niſi puncto uno tantùm.</s>
            <s xml:id="echoid-s17873" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div583" type="section" level="0" n="0">
          <head xml:id="echoid-head505" xml:space="preserve" style="it">22. Si communis ſectio ſuperficierum, refractionis & refractiui denſioris fuerit linea rect a:
            <lb/>
          uiſibile extra perpendicularem à uiſu ſuper refractiuum ductam, ab uno puncto refringetur, &
            <lb/>
          unam habebit imaginem. 20 p 10.</head>
          <p>
            <s xml:id="echoid-s17874" xml:space="preserve">SIuerò b fuerit extra a g c:</s>
            <s xml:id="echoid-s17875" xml:space="preserve"> extrahamus ſuperficiem, in qua eſt a g c linea, & punctum b:</s>
            <s xml:id="echoid-s17876" xml:space="preserve"> ergo [per
              <lb/>
            18 p 11] erit perpendicularis ſuper ſuperficiem corporis diaphani:</s>
            <s xml:id="echoid-s17877" xml:space="preserve"> & fiat in ſuperficie huius cor
              <lb/>
            poris linea g d ſectio communis:</s>
            <s xml:id="echoid-s17878" xml:space="preserve"> ergo [per 3 p 11] g d eſt recta:</s>
            <s xml:id="echoid-s17879" xml:space="preserve"> non ergo refringetur forma b ad
              <lb/>
            a, niſi in ſuperficie, in qua eſt g d [per 5.</s>
            <s xml:id="echoid-s17880" xml:space="preserve">9 n:</s>
            <s xml:id="echoid-s17881" xml:space="preserve">] non enim tranſit per duo puncta a, b ſuperficies perpẽ-
              <lb/>
            dicularis ſuper ſuperficiem corporis diaphani, niſi ſuperficies tranſiens per perpendicularem a c:</s>
            <s xml:id="echoid-s17882" xml:space="preserve"> &
              <lb/>
            per punctum b & per pendicularem a c non tranſit ſuperficies æqualis, niſi una ſola tantùm.</s>
            <s xml:id="echoid-s17883" xml:space="preserve"> Forma
              <lb/>
            ergo b non refringitur ad a, niſi ex linea g d.</s>
            <s xml:id="echoid-s17884" xml:space="preserve"> Refringatur ergo forma b ad a à puncto e:</s>
            <s xml:id="echoid-s17885" xml:space="preserve"> & continue-
              <lb/>
            mus duas lineas b e, e a:</s>
            <s xml:id="echoid-s17886" xml:space="preserve"> & [per 11 p 1] extrahamus ex e perpendicularem ſuper lineam g e d:</s>
            <s xml:id="echoid-s17887" xml:space="preserve"> ſit ergo
              <lb/>
            h e z:</s>
            <s xml:id="echoid-s17888" xml:space="preserve"> erit ergo h e z perpendicularis ſuper duas ſuperficies duorum corporum diaphanorum:</s>
            <s xml:id="echoid-s17889" xml:space="preserve"> [per
              <lb/>
            9 n & conuerſionem 4 d 11] & extrahamus b e rectè ad p:</s>
            <s xml:id="echoid-s17890" xml:space="preserve"> erit ergo e p inter duas lineas e h, e a:</s>
            <s xml:id="echoid-s17891" xml:space="preserve"> nam
              <lb/>
            corpus diaphanum, quod eſt ex parte a, eſt ſubtilius illo, quod eſt ex parte b, [ex theſi.</s>
            <s xml:id="echoid-s17892" xml:space="preserve">] Forma ergo
              <lb/>
            b, quæ extenditur per lineam b e, cum peruenerit ad e, refringetur ad partem contrariam parti per-
              <lb/>
            pendicularis z e h [per 14 n] ideo
              <lb/>
              <figure xlink:label="fig-0263-01" xlink:href="fig-0263-01a" number="221">
                <variables xml:id="echoid-variables208" xml:space="preserve">a p h f l g e o k a n m e z q b</variables>
              </figure>
            erit linea e p inter duas lineas e h
              <lb/>
            e a:</s>
            <s xml:id="echoid-s17893" xml:space="preserve"> & [per 12 p 1] extrahamus ex
              <lb/>
            b perpendicularem ſuper lineam
              <lb/>
            g d:</s>
            <s xml:id="echoid-s17894" xml:space="preserve"> ſcilicet b k:</s>
            <s xml:id="echoid-s17895" xml:space="preserve"> erit ergo b k per-
              <lb/>
            pendicularis ſuper ſuperficiẽ dia
              <lb/>
            phani corporis, quod eſt ex par-
              <lb/>
            re b:</s>
            <s xml:id="echoid-s17896" xml:space="preserve"> [per 9 n & conuerſionem 4
              <lb/>
            d 11:</s>
            <s xml:id="echoid-s17897" xml:space="preserve">] & extrahamus a e rectè, ut
              <lb/>
            ſecet angulũ b e k:</s>
            <s xml:id="echoid-s17898" xml:space="preserve"> & ſecet lineã
              <lb/>
            b k in m:</s>
            <s xml:id="echoid-s17899" xml:space="preserve"> m ergo erit imago pun-
              <lb/>
            cti b [per 18 n]:</s>
            <s xml:id="echoid-s17900" xml:space="preserve"> & angulus p e a e-
              <lb/>
            rit angulus refractionis.</s>
            <s xml:id="echoid-s17901" xml:space="preserve"> Dico er
              <lb/>
            go, quòd b nõ habebit aliã imagi
              <lb/>
            nem, pręter m.</s>
            <s xml:id="echoid-s17902" xml:space="preserve"> Quoniã enim de-
              <lb/>
            mõſtratum eſt [19 n] quòd b nõ
              <lb/>
            comprehẽditur à uiſu, niſi ſuper
              <lb/>
            perpendicularem b k:</s>
            <s xml:id="echoid-s17903" xml:space="preserve"> Si ergo b
              <lb/>
            aliam habuerit imaginem:</s>
            <s xml:id="echoid-s17904" xml:space="preserve"> erit in linea b k, & inter duo pũcta b, k:</s>
            <s xml:id="echoid-s17905" xml:space="preserve"> corpus enim, quod eſt ex parte b,
              <lb/>
            eſt groſsius illo, quod eſt ex parte a.</s>
            <s xml:id="echoid-s17906" xml:space="preserve"> Sit ergo illa alia imago, ſi poſsibile eſt, punctum n:</s>
            <s xml:id="echoid-s17907" xml:space="preserve"> erit ergo aut
              <lb/>
            inter duo pũcta m, k:</s>
            <s xml:id="echoid-s17908" xml:space="preserve"> aut inter duo puncta m, b:</s>
            <s xml:id="echoid-s17909" xml:space="preserve"> ſit inter m, k:</s>
            <s xml:id="echoid-s17910" xml:space="preserve"> & cõtinuemus a n:</s>
            <s xml:id="echoid-s17911" xml:space="preserve"> ſecabit ergo lineam
              <lb/>
            g d in puncto o:</s>
            <s xml:id="echoid-s17912" xml:space="preserve"> & continuemus b o:</s>
            <s xml:id="echoid-s17913" xml:space="preserve"> & trãſeat uſq;</s>
            <s xml:id="echoid-s17914" xml:space="preserve"> ad l:</s>
            <s xml:id="echoid-s17915" xml:space="preserve"> erit ergo o pũctũ refractionis:</s>
            <s xml:id="echoid-s17916" xml:space="preserve"> quia linea b o l
              <lb/>
            eſt illa, per quã extenditur forma, quę eſt apud b:</s>
            <s xml:id="echoid-s17917" xml:space="preserve"> & erit angulus l o a angulus refractiõis:</s>
            <s xml:id="echoid-s17918" xml:space="preserve"> & [ք 11 p 1]
              <lb/>
            extrahamus ex o perpẽdicularem ſuք lineã g d:</s>
            <s xml:id="echoid-s17919" xml:space="preserve"> & ſit f o q:</s>
            <s xml:id="echoid-s17920" xml:space="preserve"> erit ergo linea f o q perpendicularis ſuper
              <lb/>
            ſuperficiẽ corporis diaphani [ք 9 n & conuerſionẽ 4 d 11] & erit angulus l o f ſicù
              <unsure/>
            t angulus, quẽ con
              <lb/>
            tinet perpendicularis, & linea, ք quã extenditur forma ad locũ refractionis [ք 15 p 1.</s>
            <s xml:id="echoid-s17921" xml:space="preserve">] Si igitur n fue
              <lb/>
            rit inter duo puncta m, k:</s>
            <s xml:id="echoid-s17922" xml:space="preserve"> tũc o erit inter duo pũcta e, k:</s>
            <s xml:id="echoid-s17923" xml:space="preserve"> angulus ergo e b k eſt maior angulo o b k [ք
              <lb/>
            9 ax.</s>
            <s xml:id="echoid-s17924" xml:space="preserve">] angulus ergo p e h eſt maior angulo l o f:</s>
            <s xml:id="echoid-s17925" xml:space="preserve"> [Quia.</s>
            <s xml:id="echoid-s17926" xml:space="preserve"> n.</s>
            <s xml:id="echoid-s17927" xml:space="preserve"> h e z, k b & f o q ſunt քpẽdiculares ipſi g d ք
              <lb/>
            fabricationẽ:</s>
            <s xml:id="echoid-s17928" xml:space="preserve"> erũt per 28 p 1 paral-
              <lb/>
              <figure xlink:label="fig-0263-02" xlink:href="fig-0263-02a" number="222">
                <variables xml:id="echoid-variables209" xml:space="preserve">a
                  <gap/>
                f h p g o e k d m n c q z b</variables>
              </figure>
            lelę:</s>
            <s xml:id="echoid-s17929" xml:space="preserve"> & ք 29 p 1 angulus p e h ęqua
              <lb/>
            bitur angulo e b k:</s>
            <s xml:id="echoid-s17930" xml:space="preserve"> eadẽq́;</s>
            <s xml:id="echoid-s17931" xml:space="preserve"> de cau-
              <lb/>
            ſa l o f ęquabitur o b k.</s>
            <s xml:id="echoid-s17932" xml:space="preserve"> Quare ſum
              <lb/>
            ptis ꝓ e b k, o b k:</s>
            <s xml:id="echoid-s17933" xml:space="preserve"> ęqualib.</s>
            <s xml:id="echoid-s17934" xml:space="preserve"> p e h, l o
              <lb/>
            f:</s>
            <s xml:id="echoid-s17935" xml:space="preserve"> erit angulus p e h maior angulo
              <lb/>
            l o f] & angulus p e a eſt angulus
              <lb/>
            refractionis ex angulo p e h:</s>
            <s xml:id="echoid-s17936" xml:space="preserve"> & an
              <lb/>
            gulus l o a eſt angulus refractiõis
              <lb/>
            ex angulo l o f:</s>
            <s xml:id="echoid-s17937" xml:space="preserve"> angulus ergo p e a
              <lb/>
            eſt maior angulo l o a, ut declara-
              <lb/>
            tũ eſt in tertio capite huius tracta
              <lb/>
            tus [12 n:</s>
            <s xml:id="echoid-s17938" xml:space="preserve">] angulus ergo a e h eſt
              <lb/>
            maior angulo a o f:</s>
            <s xml:id="echoid-s17939" xml:space="preserve"> qđ eſt impoſ-
              <lb/>
            ſibile.</s>
            <s xml:id="echoid-s17940" xml:space="preserve"> [Quia.</s>
            <s xml:id="echoid-s17941" xml:space="preserve"> n.</s>
            <s xml:id="echoid-s17942" xml:space="preserve"> anguli h e g, f o g
              <lb/>
            ęquantur ք 10 ax:</s>
            <s xml:id="echoid-s17943" xml:space="preserve"> & per 16 p 1 an-
              <lb/>
            gulus a e g maior eſt angulo a o g:</s>
            <s xml:id="echoid-s17944" xml:space="preserve">
              <lb/>
            reliquus igitur a e h minor eſt re-
              <lb/>
            liquo a o f.</s>
            <s xml:id="echoid-s17945" xml:space="preserve">] Si aũt n fuerit inter duo puncta m, b:</s>
            <s xml:id="echoid-s17946" xml:space="preserve"> tunc punctũ e erit inter duo puncta o, k:</s>
            <s xml:id="echoid-s17947" xml:space="preserve"> & erit an-
              <lb/>
            </s>
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