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

Table of figures

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[261] a b c d g c d g f
Page: 307
[262] a b c d
Page: 308
[263] a b e c d
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[264] a b c d e f
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[265] a b c d
Page: 308
[266] a b c d
Page: 309
[267] a b e c d
Page: 309
[268] a b e c d
Page: 309
[269] a b c e d
Page: 309
[270] a b g d e z
Page: 310
[271] e a b c d f
Page: 310
[272] a d e c b
Page: 310
[273] a c f d b e
Page: 311
[274] g d a h b c f k
Page: 311
[275] g d e a z b f c
Page: 311
[Figure 276]
Page: 311
[277] a b c d e f
Page: 312
[278] e a b k l f g h m c d
Page: 312
[Figure 279]
Page: 312
[280] a b c e f g h d i
Page: 313
[281] a c b d
Page: 313
[282] c d a b
Page: 313
[283] b c l a e f d h k m g
Page: 314
[284] k a e i l g b c ſ h d
Page: 314
[285] d e b f h g l a k c
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[286] b a g c e d f
Page: 314
[287] b a h c ſ d g e
Page: 315
[288] b a d c f
Page: 315
[289] a b d c
Page: 315
[290] g e
Page: 315
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            <s xml:id="echoid-s18185" xml:space="preserve">
              <pb o="261" file="0267" n="267" rhead="OPTICAE LIBER VII."/>
            erit æqualis angulo n m a, qui eſt angulus refractionis [per 12 n:</s>
            <s xml:id="echoid-s18186" xml:space="preserve">] angulus ergo a m b erit æqua-
              <lb/>
            lis angulo a e b [per 13 p 1.</s>
            <s xml:id="echoid-s18187" xml:space="preserve"> 3 ax.</s>
            <s xml:id="echoid-s18188" xml:space="preserve">] quod eſt impoſsibile.</s>
            <s xml:id="echoid-s18189" xml:space="preserve"> [Ducta enim recta linea a b:</s>
            <s xml:id="echoid-s18190" xml:space="preserve"> erit angulus
              <lb/>
            a m b maior angulo a e b per 21 p 1.</s>
            <s xml:id="echoid-s18191" xml:space="preserve">] Si minor:</s>
            <s xml:id="echoid-s18192" xml:space="preserve"> erit [per 12 n] angulus h e a minor angulo n m a:</s>
            <s xml:id="echoid-s18193" xml:space="preserve">
              <lb/>
            angulus ergo a m b erit minor angulo a e b [per 13 p 1]
              <lb/>
              <figure xlink:label="fig-0267-01" xlink:href="fig-0267-01a" number="229">
                <variables xml:id="echoid-variables216" xml:space="preserve">a n r l c x m h e p z g b b f d o k</variables>
              </figure>
            quod eſt impoſsibile [& contra 21 p 1.</s>
            <s xml:id="echoid-s18194" xml:space="preserve">] Si maior:</s>
            <s xml:id="echoid-s18195" xml:space="preserve"> extra-
              <lb/>
            hamus lineam e b in partem b ad f:</s>
            <s xml:id="echoid-s18196" xml:space="preserve"> & extrahamus m b
              <lb/>
            uſque ad o:</s>
            <s xml:id="echoid-s18197" xml:space="preserve"> angulus ergo e m b erit æqualis angulo, qui
              <lb/>
            eſt apud circumferentiam, quem reſpiciunt duo arcus
              <lb/>
            e m, f o [per 24 n.</s>
            <s xml:id="echoid-s18198" xml:space="preserve">] Et cum [ex hypotheſi] angulus
              <lb/>
            h e p ſit maior angulo n m l:</s>
            <s xml:id="echoid-s18199" xml:space="preserve"> erit [per 15 p 1] angulus z
              <lb/>
            e b maior angulo n m l:</s>
            <s xml:id="echoid-s18200" xml:space="preserve"> & cum angulus z e b ſit maior
              <lb/>
            angulo n m l:</s>
            <s xml:id="echoid-s18201" xml:space="preserve"> angulus m z p erit maior angulo m b e.</s>
            <s xml:id="echoid-s18202" xml:space="preserve">
              <lb/>
            [Nam quia in triangulis e b g, m z g, angulus b e g ma-
              <lb/>
            ior eſt angulo z m g per theſin & 15 p 1:</s>
            <s xml:id="echoid-s18203" xml:space="preserve"> & anguli ad g æ-
              <lb/>
            quantur per eandem:</s>
            <s xml:id="echoid-s18204" xml:space="preserve"> erit reliquus m z p maior reliquo
              <lb/>
            m b e per 32 p 1:</s>
            <s xml:id="echoid-s18205" xml:space="preserve">] & exceſſus anguli m z e ſupra angu-
              <lb/>
            lum m b e, erit æqualis exceſſui anguli z e b ſupra an-
              <lb/>
            gulum z m b:</s>
            <s xml:id="echoid-s18206" xml:space="preserve"> nam duo anguli apud gſunt æquales [per
              <lb/>
            15 p 1.</s>
            <s xml:id="echoid-s18207" xml:space="preserve"> Itaq;</s>
            <s xml:id="echoid-s18208" xml:space="preserve"> cum per 32 p 1 anguli trianguli z m g æquen-
              <lb/>
            tur angulis trianguli b e g:</s>
            <s xml:id="echoid-s18209" xml:space="preserve"> erunt exuperantiæ angulo-
              <lb/>
            rum m z e, z e b ſupra angulos m b e, z m b æquales.</s>
            <s xml:id="echoid-s18210" xml:space="preserve">]
              <lb/>
            Arcus uero, qui reſpicit angulum m z e, cũ fuerit apud
              <lb/>
            circumferentiam, erit duplus ad arcum m e.</s>
            <s xml:id="echoid-s18211" xml:space="preserve"> [Quia enim
              <lb/>
            angulus m z e duplus eſt anguli in peripheria, in ean-
              <lb/>
            dem peripheriam m e inſiſtentis per 20 p 3:</s>
            <s xml:id="echoid-s18212" xml:space="preserve"> ergo angulus
              <lb/>
            m z e in peripheria conſtitutus, inſiſtet in duplam peri-
              <lb/>
            pheriam m e per 33 p 6.</s>
            <s xml:id="echoid-s18213" xml:space="preserve">] Si ergo angulus m z e fuerit maior angulo m b e:</s>
            <s xml:id="echoid-s18214" xml:space="preserve"> tunc arcus m e dupli-
              <lb/>
            catus erit maior duobus arcubus m e, f o:</s>
            <s xml:id="echoid-s18215" xml:space="preserve"> & erit exceſſus arcus m e duplicati ſupra duos arcus
              <lb/>
            m e, f o, æqualis exceſſui arcus m e ſupra arcum f o [ſubducta enim communi peripheria m e, ſu
              <lb/>
            pereſt eadem exuperantia.</s>
            <s xml:id="echoid-s18216" xml:space="preserve">] Exceſſus ergo anguli m z e ſupra angulum m b e eſt iſte, quem re-
              <lb/>
            ſpicit apud circumferentiam exceſſus arcus m e ſupra arcum f o:</s>
            <s xml:id="echoid-s18217" xml:space="preserve"> ſed exceſſus arcus m e ſupra ar-
              <lb/>
            cum f o eſt minor duobus arcubus m e, f o [per 9 ax.</s>
            <s xml:id="echoid-s18218" xml:space="preserve">] Ergo exceſſus anguli m z e ſupra angu-
              <lb/>
            lum m b e, eſt minor angulo m b e [per 33 p 6.</s>
            <s xml:id="echoid-s18219" xml:space="preserve">] Exceſſus igitur anguli z e b ſupra angulum z m
              <lb/>
            b eſt minor angulo m b e:</s>
            <s xml:id="echoid-s18220" xml:space="preserve"> ergo [per 15 p 1] exceſſus anguli h e p ſupra angulum n m l eſt minor
              <lb/>
            angulo m b e.</s>
            <s xml:id="echoid-s18221" xml:space="preserve"> Ergo [per 12 n] exceſſus anguli h e a, qui eſt angulus refractionis, ſupra angulum
              <lb/>
            n m a, qui eſt angulus refractionis, eſt multò minor angulo m b e.</s>
            <s xml:id="echoid-s18222" xml:space="preserve"> Sed exceſſus anguli h e a ſu-
              <lb/>
            pra angulum n m a, eſt exceſſus anguli a m b ſupra angulum a e b [per 13 p 1.</s>
            <s xml:id="echoid-s18223" xml:space="preserve">] Ergo exceſſus an-
              <lb/>
            guli a m b ſupra angulum a e b eſt minor angulo m b e.</s>
            <s xml:id="echoid-s18224" xml:space="preserve"> Sed exceſſus anguli a m b ſupra angu-
              <lb/>
            lum a e b, ſunt duo anguli m a e, m b e.</s>
            <s xml:id="echoid-s18225" xml:space="preserve"> [Nam connexa recta a b & continuata e m ultra m in x:</s>
            <s xml:id="echoid-s18226" xml:space="preserve">
              <lb/>
            æquabitur per 32 p 1 angulus a m x duobus interioribus ad a & e:</s>
            <s xml:id="echoid-s18227" xml:space="preserve"> itemq́ue b m x duobus interiori-
              <lb/>
            bus ad b & e.</s>
            <s xml:id="echoid-s18228" xml:space="preserve"> Totus igitur a m b exuperat totum a e b duobus angulis m a e, m b e.</s>
            <s xml:id="echoid-s18229" xml:space="preserve">] Ergo duo an-
              <lb/>
            guli m a e, m b e ſunt minores angulo m b e:</s>
            <s xml:id="echoid-s18230" xml:space="preserve"> quod eſt impoſsibile [& cõtra 9 ax.</s>
            <s xml:id="echoid-s18231" xml:space="preserve">] Forma ergo b non
              <lb/>
            refringetur ad a ex alio puncto, præterquam ex e.</s>
            <s xml:id="echoid-s18232" xml:space="preserve"> Et hoc eſt quod uoluimus.</s>
            <s xml:id="echoid-s18233" xml:space="preserve"> Cum ergo b non re-
              <lb/>
            fringatur ad a, niſi ex uno puncto:</s>
            <s xml:id="echoid-s18234" xml:space="preserve"> nec habebit, niſi unam imaginem.</s>
            <s xml:id="echoid-s18235" xml:space="preserve"> Sed locus imaginis diuerſatur
              <lb/>
            ſecundum diuerſitatem loci, in quo eſt b.</s>
            <s xml:id="echoid-s18236" xml:space="preserve"> Continuemus enim b z:</s>
            <s xml:id="echoid-s18237" xml:space="preserve"> linea ergo b z aut concurret cum
              <lb/>
            linea e a:</s>
            <s xml:id="echoid-s18238" xml:space="preserve"> aut erit ei æquidiſtans:</s>
            <s xml:id="echoid-s18239" xml:space="preserve"> & concurſus aut erit in parte e b, ut in k:</s>
            <s xml:id="echoid-s18240" xml:space="preserve"> aut in parte a, ut in r.</s>
            <s xml:id="echoid-s18241" xml:space="preserve"> Et
              <lb/>
            cum b z fuerit æquidiſtans lineæ e a:</s>
            <s xml:id="echoid-s18242" xml:space="preserve"> erit ut linea b z ſit media inter duas lineas k b z, b z r.</s>
            <s xml:id="echoid-s18243" xml:space="preserve"> Si uerò
              <lb/>
            concurſus harum duarum linearum fuerit in k:</s>
            <s xml:id="echoid-s18244" xml:space="preserve"> erit imago ante uiſum, & erit forma manifeſta &
              <lb/>
            comprehenſa à uiſu in k [per 18 n.</s>
            <s xml:id="echoid-s18245" xml:space="preserve">] Si uerò concurſus fuerit in r:</s>
            <s xml:id="echoid-s18246" xml:space="preserve"> erit imago punctum r:</s>
            <s xml:id="echoid-s18247" xml:space="preserve"> & tunc for
              <lb/>
            ma comprehendetur à uiſu in eius oppoſitione:</s>
            <s xml:id="echoid-s18248" xml:space="preserve"> ſed non tam manifeſtè, quia comprehenditur à ui-
              <lb/>
            ſu extra ſuum locum.</s>
            <s xml:id="echoid-s18249" xml:space="preserve"> Hoc autem declaratum eſt in loco, in quo locuti ſumus de reflexiõe [61 n 5.</s>
            <s xml:id="echoid-s18250" xml:space="preserve">]
              <lb/>
            Si linea b z fuerit æquidiſtans lineæ e a:</s>
            <s xml:id="echoid-s18251" xml:space="preserve"> tunc imago erit indeterminata, & forma comprehendetur
              <lb/>
            in loco refractionis.</s>
            <s xml:id="echoid-s18252" xml:space="preserve"> Huius autem cauſſa ſimilis eſt illi, quam diximus in loco reflexionis [61 n 5]
              <lb/>
            cum fuerit reflexio per lineam æquidiſtantem perpendiculari.</s>
            <s xml:id="echoid-s18253" xml:space="preserve"> Ex prædictis ergo patet, quòd res,
              <lb/>
            quæ comprehenditur à uiſu ultra corpus diaphanum groſsius corpore, quod eſt ex parte uiſus:</s>
            <s xml:id="echoid-s18254" xml:space="preserve"> nõ
              <lb/>
            habet, niſi unam imaginem, neq;</s>
            <s xml:id="echoid-s18255" xml:space="preserve"> comprehenditur, niſi unum tantùm.</s>
            <s xml:id="echoid-s18256" xml:space="preserve"> Hæc uerò refractio eſt à con-
              <lb/>
            cauitate corporis diaphani ex parte uιſus contingentis conuexum corporis diaphani, quod eſt ex
              <lb/>
            parte rei uiſæ.</s>
            <s xml:id="echoid-s18257" xml:space="preserve"> Et hoc eſt quod uoluimus.</s>
            <s xml:id="echoid-s18258" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div594" type="section" level="0" n="0">
          <head xml:id="echoid-head511" xml:space="preserve" style="it">28. Si communis ſectio ſuperficierum refractionis & refractiui conuexi rarioris fuerit peri
            <lb/>
          pherιa: uiſibile extra perpendicularem à uiſu ſuper refractiuum ductam: ab uno puncto refrin
            <lb/>
          getur, unam́ habebit imaginem, uariè pro uaria uiſ{us} ueluiſibilis poſitione ſit am. 24 p 10.</head>
          <p>
            <s xml:id="echoid-s18259" xml:space="preserve">ET ſi corpus diaphanum fuerit groſsius ex parte uiſus, & ſubtilius ex parte rei uiſæ:</s>
            <s xml:id="echoid-s18260" xml:space="preserve"> tunc
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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