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-s18382" xml:space="preserve">
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            perpendiculari exeunte à loco refractionis:</s>
            <s xml:id="echoid-s18383" xml:space="preserve"> & ſimiliter angulus n m g:</s>
            <s xml:id="echoid-s18384" xml:space="preserve"> & erit angulus c h a angulus
              <lb/>
            refractionis:</s>
            <s xml:id="echoid-s18385" xml:space="preserve"> & ſimiliter angulus n m a.</s>
            <s xml:id="echoid-s18386" xml:space="preserve"> Angulus autem n m g aut erit æqualis angulo c h g, aut ma-
              <lb/>
            ior, aut minor.</s>
            <s xml:id="echoid-s18387" xml:space="preserve"> Si æqualis:</s>
            <s xml:id="echoid-s18388" xml:space="preserve"> erit [per 12 n] n m a æqualis
              <lb/>
              <figure xlink:label="fig-0270-01" xlink:href="fig-0270-01a" number="232">
                <variables xml:id="echoid-variables219" xml:space="preserve">k o g e c n a d z f h m l p b</variables>
              </figure>
            angulo a h c:</s>
            <s xml:id="echoid-s18389" xml:space="preserve"> ergo [per 13 p 1.</s>
            <s xml:id="echoid-s18390" xml:space="preserve"> 3 ax.</s>
            <s xml:id="echoid-s18391" xml:space="preserve">] angulus b h a erit æ-
              <lb/>
            qualis angulo b m a:</s>
            <s xml:id="echoid-s18392" xml:space="preserve"> quod eſt impoſsibile.</s>
            <s xml:id="echoid-s18393" xml:space="preserve"> [Ducta enim
              <lb/>
            recta b a:</s>
            <s xml:id="echoid-s18394" xml:space="preserve"> erit angulus b m a maior angulo b h a per 21
              <lb/>
            p 1.</s>
            <s xml:id="echoid-s18395" xml:space="preserve">] Si maior:</s>
            <s xml:id="echoid-s18396" xml:space="preserve"> tunc [per 12 n] angulus n m a erit maior
              <lb/>
            angulo a h c:</s>
            <s xml:id="echoid-s18397" xml:space="preserve"> & ſic [per 13 p 1.</s>
            <s xml:id="echoid-s18398" xml:space="preserve"> 3 ax.</s>
            <s xml:id="echoid-s18399" xml:space="preserve">] angulus b m a erit mi-
              <lb/>
            nor angulo b h a:</s>
            <s xml:id="echoid-s18400" xml:space="preserve"> quod eſt impoſsibile [& contra 21 p 1.</s>
            <s xml:id="echoid-s18401" xml:space="preserve">]
              <lb/>
            Si minor:</s>
            <s xml:id="echoid-s18402" xml:space="preserve"> tunc [per 12 n] angulus n m a erit minor angu
              <lb/>
            lo a h c:</s>
            <s xml:id="echoid-s18403" xml:space="preserve"> & ſic totus angulus a m g erit minor toto angulo
              <lb/>
            a h g:</s>
            <s xml:id="echoid-s18404" xml:space="preserve"> & erit [per 12 n] diminutio anguli n m a, ab angu-
              <lb/>
            lo a h c minor, quàm diminutio anguli a m g, ab angulo
              <lb/>
            a h g:</s>
            <s xml:id="echoid-s18405" xml:space="preserve"> Sed diminutio anguli a m g ab angulo a h g, eſt æ-
              <lb/>
            qualis diminutioni anguli h g m ab angulo h a m:</s>
            <s xml:id="echoid-s18406" xml:space="preserve"> duo
              <lb/>
            enim anguli, qui ſunt in ſectione linearum a h, m g ſunt
              <lb/>
            æquales [per 15 p 1:</s>
            <s xml:id="echoid-s18407" xml:space="preserve"> & per 32 p 1 reliquus ſimul uterque
              <lb/>
            trianguli h g fæquatur reliquo ſimul utrique trianguli
              <lb/>
            m a f.</s>
            <s xml:id="echoid-s18408" xml:space="preserve"> Itaque quantò minor eſt angulus a m g angulo a h
              <lb/>
            g:</s>
            <s xml:id="echoid-s18409" xml:space="preserve"> tãtò minor erit angulus h g m angulo h a m per 32 p 1.</s>
            <s xml:id="echoid-s18410" xml:space="preserve">]
              <lb/>
            Ergo diminutio anguli n m a ab angulo a h c minor eſt,
              <lb/>
            quàm diminutio anguli h g m ab angulo h a m.</s>
            <s xml:id="echoid-s18411" xml:space="preserve"> Et extra-
              <lb/>
            hamus duas a h, m a ad duo puncta e, o:</s>
            <s xml:id="echoid-s18412" xml:space="preserve"> erit ergo [per 24
              <lb/>
            n] angulus h a m ille, quem reſpiciunt in circumferen-
              <lb/>
            tia duo arcus h m, e o:</s>
            <s xml:id="echoid-s18413" xml:space="preserve"> & angulũ h g m reſpicit in circũ-
              <lb/>
            ferentia arcus h m duplicatus [angulus enim h g m du-
              <lb/>
            plus eſt anguli in peripheria conſtituti, & in eandẽ peri-
              <lb/>
            pheriã h m inſiſtentis per 20 p 3.</s>
            <s xml:id="echoid-s18414" xml:space="preserve"> Si igitur angulus, æqua-
              <lb/>
            lis angulo h g m in peripheria conſtituatur:</s>
            <s xml:id="echoid-s18415" xml:space="preserve"> inſiſtet in pe
              <lb/>
            ripheriam duplã peripheriæ h m per 33 p 6.</s>
            <s xml:id="echoid-s18416" xml:space="preserve">] Et cum angulus h g m ſit minor angulo h a m:</s>
            <s xml:id="echoid-s18417" xml:space="preserve"> [angu-
              <lb/>
            lus enim a h g maior eſt concluſus angulo a m g:</s>
            <s xml:id="echoid-s18418" xml:space="preserve"> & ad uerticem f ęquantur per 15 p 1:</s>
            <s xml:id="echoid-s18419" xml:space="preserve"> reliquus igitur
              <lb/>
            h g m minor eſt reliquo h a m per 32 p 1] erit arcus h m duplicatus minor duobus arcubus h m, e o
              <lb/>
            [per 33 p 6:</s>
            <s xml:id="echoid-s18420" xml:space="preserve">] & erit dimin utio arcus h m duplicati à duobus arcubus h m, e o, ſicut diminutio ar-
              <lb/>
            cus h m ab arcu e o [quia h m communis eſt.</s>
            <s xml:id="echoid-s18421" xml:space="preserve">] Ergo diminutio anguli n m a ab angulo a h c erit mi
              <lb/>
            nor angulo, quem reſpicit apud circumferentiam dimi-
              <lb/>
              <figure xlink:label="fig-0270-02" xlink:href="fig-0270-02a" number="233">
                <variables xml:id="echoid-variables220" xml:space="preserve">e o k a c n g d z h m l p b</variables>
              </figure>
            nutio arcus h m ab arcu e o.</s>
            <s xml:id="echoid-s18422" xml:space="preserve"> Sed angulus, quẽ reſpicit a-
              <lb/>
            pud circumferẽtiam diminutio arcus h m ab arcu e o, eſt
              <lb/>
            minor angulo h a m.</s>
            <s xml:id="echoid-s18423" xml:space="preserve"> Eſt ergo diminutio anguli n m a ab
              <lb/>
            angulo a h c minor angulo h a m.</s>
            <s xml:id="echoid-s18424" xml:space="preserve"> Exceſſus ergo anguli
              <lb/>
            b m a ſupra angulũ b h a eſt minor, quàm angulus h a m.</s>
            <s xml:id="echoid-s18425" xml:space="preserve">
              <lb/>
            [Nam per 13 p 1 exuperantia anguli b m a ſupra angulum
              <lb/>
            b h a eſt exuperantia anguli a h c ſupra angulum n m a,
              <lb/>
            quæ minor eſt concluſa angulo h a m.</s>
            <s xml:id="echoid-s18426" xml:space="preserve">] Sed exceſſus an-
              <lb/>
            guli b m a ſupra angulum b h a ſunt duo anguli h a m, h b
              <lb/>
            m, [ut oſtenſum eſt 27 n.</s>
            <s xml:id="echoid-s18427" xml:space="preserve">] Ergo iſtí duo anguli ſimul
              <lb/>
            ſunt minores angulo h a m:</s>
            <s xml:id="echoid-s18428" xml:space="preserve"> quod eſt impoſsibile.</s>
            <s xml:id="echoid-s18429" xml:space="preserve"> Et
              <lb/>
            ſi a fuerit in linea g k:</s>
            <s xml:id="echoid-s18430" xml:space="preserve"> tunc linea h c erit inter duas lineas
              <lb/>
            h g, h a:</s>
            <s xml:id="echoid-s18431" xml:space="preserve"> & ſimiliter linea m n erit inter duas lineas m g,
              <lb/>
            m a:</s>
            <s xml:id="echoid-s18432" xml:space="preserve"> Erit ergo angulus b h a ex parte k:</s>
            <s xml:id="echoid-s18433" xml:space="preserve"> & ſimiliter angu-
              <lb/>
            lus b m a erit ex parte k:</s>
            <s xml:id="echoid-s18434" xml:space="preserve"> & erit b infra lineam g m p, ſci-
              <lb/>
            licet ex parte d, à linea g m p:</s>
            <s xml:id="echoid-s18435" xml:space="preserve"> & uterque angulus c h g.</s>
            <s xml:id="echoid-s18436" xml:space="preserve"> n
              <lb/>
            m g eſt ille, quem continet linea, per quam extẽditur for-
              <lb/>
            ma, & perpendicularis exiens à loco refractionis:</s>
            <s xml:id="echoid-s18437" xml:space="preserve"> & uter-
              <lb/>
            que angulus c h a, n m a erit angulus refractionis.</s>
            <s xml:id="echoid-s18438" xml:space="preserve"> Si ergo
              <lb/>
            c h g fuerit æqualis n m g:</s>
            <s xml:id="echoid-s18439" xml:space="preserve"> tunc [per 12 n] angulus c h a e-
              <lb/>
            rit æqualis angulo n m a:</s>
            <s xml:id="echoid-s18440" xml:space="preserve"> & ſic [per 13 p 1] angulus b h a
              <lb/>
            erit æqualis angulo b m a:</s>
            <s xml:id="echoid-s18441" xml:space="preserve"> quod eſt impoſsibile [& con-
              <lb/>
            tra 21 p 1, connexa recta b a.</s>
            <s xml:id="echoid-s18442" xml:space="preserve">] Et ſi fuerit maior:</s>
            <s xml:id="echoid-s18443" xml:space="preserve"> tunc [per
              <lb/>
            12 n] angulus c h a erit maior angulo n m a:</s>
            <s xml:id="echoid-s18444" xml:space="preserve"> & ſic [per 13
              <lb/>
            p 1] angulus b h a erit minor angulo b m a:</s>
            <s xml:id="echoid-s18445" xml:space="preserve"> quod eſt im-
              <lb/>
            poſsibile.</s>
            <s xml:id="echoid-s18446" xml:space="preserve"> Et ſi fuerit minor:</s>
            <s xml:id="echoid-s18447" xml:space="preserve"> tunc [per 12 n] angulus c h a
              <lb/>
            erit minor angulo n m a:</s>
            <s xml:id="echoid-s18448" xml:space="preserve"> & ſic totus angulus g h a erit minor toto angulo g m a:</s>
            <s xml:id="echoid-s18449" xml:space="preserve"> Ergo [ut ſuprà o-
              <lb/>
            ſtenſum eſt] erit angulus h g m minor angulo h a m.</s>
            <s xml:id="echoid-s18450" xml:space="preserve"> Et erit diminutio anguli h g m ab angulo h a m
              <lb/>
            minor, quàm angulus g m a, ut prius declarauimus.</s>
            <s xml:id="echoid-s18451" xml:space="preserve"> Et diminutio anguli c h a ab angulo n m a eſt
              <lb/>
            </s>
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