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-s15299" xml:space="preserve">
              <pb o="217" file="0223" n="223" rhead="OPTICAE LIBER VI."/>
            per 13 p 1, minorẽ recto b e t, & terminabitur in linea b d inter pũcta b & t.</s>
            <s xml:id="echoid-s15300" xml:space="preserve"> Quare b t erit maior b n] er
              <lb/>
            go linea r b eſt maior b n.</s>
            <s xml:id="echoid-s15301" xml:space="preserve"> [ſuperiore enim numero t b æqualis cõcluſa eſt ipſi b h, & r b maior eſt b h
              <lb/>
            ք 9 ax:</s>
            <s xml:id="echoid-s15302" xml:space="preserve"> ergo r b maior eſt t b.</s>
            <s xml:id="echoid-s15303" xml:space="preserve"> Quare eadẽ multò maior eſt b n] & [per 3 p 6] proportio r b ad b n eſt, ſi-
              <lb/>
            cut proportio r e ad e n.</s>
            <s xml:id="echoid-s15304" xml:space="preserve"> [angulus enim n b r bifariã ſecatur ք
              <lb/>
              <figure xlink:label="fig-0223-01" xlink:href="fig-0223-01a" number="192">
                <variables xml:id="echoid-variables181" xml:space="preserve">d g t k n z u e b a o ſ
                  <unsure/>
                h m r</variables>
              </figure>
            lineã b e, ut patuit ꝓximo numero.</s>
            <s xml:id="echoid-s15305" xml:space="preserve">] Quare linea r e eſt maior
              <lb/>
            quàm linea e n.</s>
            <s xml:id="echoid-s15306" xml:space="preserve"> Et extrahamus a l rectè in m:</s>
            <s xml:id="echoid-s15307" xml:space="preserve"> & ſit a m æqua-
              <lb/>
            lis b r:</s>
            <s xml:id="echoid-s15308" xml:space="preserve"> & continuemus m e, & tranſeat uſq;</s>
            <s xml:id="echoid-s15309" xml:space="preserve"> ad u.</s>
            <s xml:id="echoid-s15310" xml:space="preserve"> Erit ergo m e
              <lb/>
            maior quàm e u [Quia enim latera e a, m a æquantur duobus
              <lb/>
            lateribus e b, r b per 15 d 1, & proximam fabricationem, &
              <lb/>
            angulus e a m æqualis concluſus eſt ſuperiore numero angu
              <lb/>
            lo e b r:</s>
            <s xml:id="echoid-s15311" xml:space="preserve"> erit per 4 p 1 baſis m e æqualis baſi r e, & angulus m
              <lb/>
            e a ęqualis angulo r e b, per concluſionem obtuſo:</s>
            <s xml:id="echoid-s15312" xml:space="preserve"> ergo m e a
              <lb/>
            eſt obtuſus, & a e u acutus per 13 p 1.</s>
            <s xml:id="echoid-s15313" xml:space="preserve"> Quare cũ angulus a e u
              <lb/>
            ſit minor angulo m e a, & u a e ęqualis e a m per cõcluſionẽ:</s>
            <s xml:id="echoid-s15314" xml:space="preserve">
              <lb/>
            reliquus a u e maior erit reliquo a m e per 32 p 1:</s>
            <s xml:id="echoid-s15315" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s15316" xml:space="preserve"> per 19
              <lb/>
            p 1 in triangulo a u m latus m a maius latere a u:</s>
            <s xml:id="echoid-s15317" xml:space="preserve"> ſed ut m a ad
              <lb/>
            a u, ſic m e ad e u per 3 p 6:</s>
            <s xml:id="echoid-s15318" xml:space="preserve"> quia angulus m a u bifariam ſectus
              <lb/>
            eſt per rectam a e, ut patuit proximo numero.</s>
            <s xml:id="echoid-s15319" xml:space="preserve"> Quare m e ma
              <lb/>
            ior eſt e u.</s>
            <s xml:id="echoid-s15320" xml:space="preserve">] Et continuemus m r, n u:</s>
            <s xml:id="echoid-s15321" xml:space="preserve"> erit ergo m r maior quã
              <lb/>
            n u [Nam quia anguli e a u, e b n æquales concluſi ſunt, & an-
              <lb/>
            gulus a e u æquatur angulo b e n per 13 p 1:</s>
            <s xml:id="echoid-s15322" xml:space="preserve"> quia anguli m e a,
              <lb/>
            r e b æquales demõſtrati ſunt, & a e ipſi e b:</s>
            <s xml:id="echoid-s15323" xml:space="preserve"> ęquabitur e u ipſi
              <lb/>
            e n per 26 p 1:</s>
            <s xml:id="echoid-s15324" xml:space="preserve"> & m e æquatur ipſi r e per concluſionem, & an-
              <lb/>
            gulus u e n angulo m e r per 13 p 1:</s>
            <s xml:id="echoid-s15325" xml:space="preserve"> erit per 7 p 5 m e ad r e, ſi-
              <lb/>
            cut u e ad n e.</s>
            <s xml:id="echoid-s15326" xml:space="preserve"> Quare cum triangula m e r, u e n ſint per 6 p 6
              <lb/>
            æquiangula:</s>
            <s xml:id="echoid-s15327" xml:space="preserve"> erit per 4 p 6, ut m e ad e u, ſic m r ad u n.</s>
            <s xml:id="echoid-s15328" xml:space="preserve"> Itaque
              <lb/>
            cum m e maior ſit per concluſionem ipſa e u, erit m r maior
              <lb/>
            u n.</s>
            <s xml:id="echoid-s15329" xml:space="preserve">] Si ergo m r fuerit in aliquo uiſibili, & uiſus fuerit in d:</s>
            <s xml:id="echoid-s15330" xml:space="preserve">
              <lb/>
            erit n u diameter imaginis m r:</s>
            <s xml:id="echoid-s15331" xml:space="preserve"> & n u eſt minor quàm m r.</s>
            <s xml:id="echoid-s15332" xml:space="preserve"> Et
              <lb/>
            ſi uiſus fuerit in o, & u n fuerit in aliquo uiſibili:</s>
            <s xml:id="echoid-s15333" xml:space="preserve"> erit m r ima-
              <lb/>
            go n u:</s>
            <s xml:id="echoid-s15334" xml:space="preserve"> & eſt maior quàm n u.</s>
            <s xml:id="echoid-s15335" xml:space="preserve"> Sed cũ m r fuerit uiſibile, & n u fuerit imago, & d uiſus:</s>
            <s xml:id="echoid-s15336" xml:space="preserve"> erit imago cõ-
              <lb/>
            uerſa.</s>
            <s xml:id="echoid-s15337" xml:space="preserve"> Et ſi res uiſa fuerit n u, & uiſus o:</s>
            <s xml:id="echoid-s15338" xml:space="preserve"> imago m r erit recta.</s>
            <s xml:id="echoid-s15339" xml:space="preserve"> Nam imago ſi fuerit ultra uiſum, uide-
              <lb/>
            bitur ante.</s>
            <s xml:id="echoid-s15340" xml:space="preserve"> Et omne punctum imaginis uidebitur in linea, in qua eſt de lineis radialibus.</s>
            <s xml:id="echoid-s15341" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div520" type="section" level="0" n="0">
          <head xml:id="echoid-head459" xml:space="preserve" style="it">43. In ſpeculo ſphærico cauo imago inter uiſum & ſpeculum aliquando maior eſt uiſibili, &
            <lb/>
          euerſa: pone uiſum aliquando minor eſt, & erecta. 50 p 8.</head>
          <p>
            <s xml:id="echoid-s15342" xml:space="preserve">IT ẽ:</s>
            <s xml:id="echoid-s15343" xml:space="preserve"> ſignemus in linea o h punctum q:</s>
            <s xml:id="echoid-s15344" xml:space="preserve"> & cõtinuemus q e:</s>
            <s xml:id="echoid-s15345" xml:space="preserve"> & trãſeat ad p:</s>
            <s xml:id="echoid-s15346" xml:space="preserve"> & ſit o f æqualis o q:</s>
            <s xml:id="echoid-s15347" xml:space="preserve"> [per
              <lb/>
            3 p 1] & continuemus e f, & tranſeat ad i.</s>
            <s xml:id="echoid-s15348" xml:space="preserve"> Erunt ergo duę li-
              <lb/>
              <figure xlink:label="fig-0223-02" xlink:href="fig-0223-02a" number="193">
                <variables xml:id="echoid-variables182" xml:space="preserve">d g p i t k b e a o l f q h</variables>
              </figure>
            neæ p e, e i maiores duabus lineis e f, e q:</s>
            <s xml:id="echoid-s15349" xml:space="preserve"> [Quia enim angu
              <lb/>
            lus a e l rectus eſt, ut patuit 4 n:</s>
            <s xml:id="echoid-s15350" xml:space="preserve"> erit a e f acutus.</s>
            <s xml:id="echoid-s15351" xml:space="preserve"> Itaq;</s>
            <s xml:id="echoid-s15352" xml:space="preserve"> f e con-
              <lb/>
            tinuata ultra e, fac
              <unsure/>
            iet cũ a e angulũ obtuſum per 13 p 1, & cadet
              <lb/>
            ultra e k.</s>
            <s xml:id="echoid-s15353" xml:space="preserve"> Erit igitur a i maior a k:</s>
            <s xml:id="echoid-s15354" xml:space="preserve"> ſed a k æqualis concluſa eſt ci
              <lb/>
            tato numero ipſi a l:</s>
            <s xml:id="echoid-s15355" xml:space="preserve"> ergo a i maior eſt a l, ideoq́;</s>
            <s xml:id="echoid-s15356" xml:space="preserve"> multò maior
              <lb/>
            ipſa a f.</s>
            <s xml:id="echoid-s15357" xml:space="preserve"> Et quia angulus i a f bifariã ſectus eſt per rectã a e:</s>
            <s xml:id="echoid-s15358" xml:space="preserve"> erit
              <lb/>
            per 3 p 6 uti a ad a f, ſic i e ad e f:</s>
            <s xml:id="echoid-s15359" xml:space="preserve"> ſed cum i a maior ſit a f:</s>
            <s xml:id="echoid-s15360" xml:space="preserve"> erit i e
              <lb/>
            maior e f.</s>
            <s xml:id="echoid-s15361" xml:space="preserve"> Eodẽ argumento p e maior demonſtrabituripſa e q]
              <lb/>
            & erit linea p i maior quàm linea f q [cum enim duobus ſupe-
              <lb/>
            rioribus numeris æqualitas tum rectarum e h, e l, tum angulo-
              <lb/>
            rum e h q, e l f demonſtrata ſit:</s>
            <s xml:id="echoid-s15362" xml:space="preserve"> & l f æquetur h q:</s>
            <s xml:id="echoid-s15363" xml:space="preserve"> quia tota a l æ-
              <lb/>
            qualis eſt toti b h è concluſo duorũ numerorũ præcedẽtium,
              <lb/>
            & pars o f parti o h per theſin:</s>
            <s xml:id="echoid-s15364" xml:space="preserve"> æquabitur reliqua l f reliquę h q
              <lb/>
            per 19 p 5:</s>
            <s xml:id="echoid-s15365" xml:space="preserve"> & erit per 4 p 1 e f æqualis e q, & angulus l e fangulo
              <lb/>
            h e q.</s>
            <s xml:id="echoid-s15366" xml:space="preserve"> Et quia anguli recti a e l, b e h:</s>
            <s xml:id="echoid-s15367" xml:space="preserve"> itẽ a e o, b e o ęquantur:</s>
            <s xml:id="echoid-s15368" xml:space="preserve"> re-
              <lb/>
            liquus l e o æquabitur reliquo h e o, & l e f æqualis oſtenſus eſt
              <lb/>
            ipſi h e q:</s>
            <s xml:id="echoid-s15369" xml:space="preserve"> ergo f e o æquatur q e o, & ք 15 p 1, 1 ax.</s>
            <s xml:id="echoid-s15370" xml:space="preserve"> d e i ipſi d e p,
              <lb/>
            & d e a æquatus eſt d e b, 41 n:</s>
            <s xml:id="echoid-s15371" xml:space="preserve"> reliquus igitur i e a æquatur reli
              <lb/>
            quo p e b, & i a e æqualis concluſus eſt ipſi p b e, & a e æqualis
              <lb/>
            ipſi b e per 15 d 1.</s>
            <s xml:id="echoid-s15372" xml:space="preserve"> Quare per 26 p 1 i e æquaturipſi p e, & angu-
              <lb/>
            lus i e p angulo f e q per 15 p 1.</s>
            <s xml:id="echoid-s15373" xml:space="preserve"> Ergo ք 7 p 5.</s>
            <s xml:id="echoid-s15374" xml:space="preserve">6 p 6 triangula i e p,
              <lb/>
            f e q ſunt ęquiangula, & per 4 p 6, ut i e ad e f, ſic p i ad f q:</s>
            <s xml:id="echoid-s15375" xml:space="preserve"> ſed i e
              <lb/>
            maior eſt e f è cõcluſo:</s>
            <s xml:id="echoid-s15376" xml:space="preserve"> ergo p i maior eſt f q.</s>
            <s xml:id="echoid-s15377" xml:space="preserve">] Si ergo uiſus fue-
              <lb/>
            rit in o, & p i in aliquo uiſibili:</s>
            <s xml:id="echoid-s15378" xml:space="preserve"> erit f q imago p i:</s>
            <s xml:id="echoid-s15379" xml:space="preserve"> & f q eſt minor
              <lb/>
            quã p i:</s>
            <s xml:id="echoid-s15380" xml:space="preserve"> & f q uidebitur ſuper duas lineas a o, b o.</s>
            <s xml:id="echoid-s15381" xml:space="preserve"> Erit ergo for-
              <lb/>
            ma retro uiſum, & minor ꝗ̃ res uiſa:</s>
            <s xml:id="echoid-s15382" xml:space="preserve"> & erit recta.</s>
            <s xml:id="echoid-s15383" xml:space="preserve"> Et ſi uiſus fue
              <lb/>
            rit in d, & f q fuerit in aliquo uiſibili:</s>
            <s xml:id="echoid-s15384" xml:space="preserve"> erit p i imago f q:</s>
            <s xml:id="echoid-s15385" xml:space="preserve"> & eſt maior ꝗ̃ f q:</s>
            <s xml:id="echoid-s15386" xml:space="preserve"> & erit forma ante uiſum con
              <lb/>
            uerſa.</s>
            <s xml:id="echoid-s15387" xml:space="preserve"> Patet ergo, quòd in ſpeculis cõcauis cõprehẽditur forma rei uiſæ minor, & maior, & æqualis.</s>
            <s xml:id="echoid-s15388" xml:space="preserve"/>
          </p>
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