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-s12897" xml:space="preserve">
              <pb o="190" file="0196" n="196" rhead="ALHAZEN"/>
            henditur in ueritate, præter ordinationẽ partiũ, quæ talis apparet in ſpeculo, qualis eſt in imagine.</s>
            <s xml:id="echoid-s12898" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div459" type="section" level="0" n="0">
          <head xml:id="echoid-head418" xml:space="preserve" style="it">5. In ſpeculo ſphærico conuexo, imago uiſibilis, cuius uera magnitudo uiſione directa percipi
            <lb/>
          poteſt, minor eſt uiſibili. 39 p 6.</head>
          <p>
            <s xml:id="echoid-s12899" xml:space="preserve">QVòd autem res ſemper uideatur minor, quàm ſit:</s>
            <s xml:id="echoid-s12900" xml:space="preserve"> probatur.</s>
            <s xml:id="echoid-s12901" xml:space="preserve"> Sit a b linea uiſa:</s>
            <s xml:id="echoid-s12902" xml:space="preserve"> z x ſpeculum:</s>
            <s xml:id="echoid-s12903" xml:space="preserve"> d
              <lb/>
            centrum:</s>
            <s xml:id="echoid-s12904" xml:space="preserve"> e punctum uiſus.</s>
            <s xml:id="echoid-s12905" xml:space="preserve"> a reflectatur ad e à puncto h:</s>
            <s xml:id="echoid-s12906" xml:space="preserve"> b à puncto n.</s>
            <s xml:id="echoid-s12907" xml:space="preserve"> a b producta aut tranſi
              <lb/>
            bit per centrum ſpeculi, aut non.</s>
            <s xml:id="echoid-s12908" xml:space="preserve"> Tranſeat:</s>
            <s xml:id="echoid-s12909" xml:space="preserve"> & ducatur à puncto n linea contingens circulum
              <lb/>
            [per 17 p 3] quæ ſit n l:</s>
            <s xml:id="echoid-s12910" xml:space="preserve"> à puncto h contingens circulum, h m:</s>
            <s xml:id="echoid-s12911" xml:space="preserve"> & ducantur lineę acceſſus & reflexionis
              <lb/>
            b n, e n, a h, e h:</s>
            <s xml:id="echoid-s12912" xml:space="preserve"> & producãtur lineæ e h, e n, donec cadant in perpendicalarẽ, quæ eſt a d:</s>
            <s xml:id="echoid-s12913" xml:space="preserve"> & puncta ca
              <lb/>
            ſus ſint, t, q.</s>
            <s xml:id="echoid-s12914" xml:space="preserve"> Palàm [ք 3 n 5] quòd t eſt locus imaginis a:</s>
            <s xml:id="echoid-s12915" xml:space="preserve"> q eſt locus imaginis b.</s>
            <s xml:id="echoid-s12916" xml:space="preserve"> Dico, quòd a b maior
              <lb/>
            eſt q t.</s>
            <s xml:id="echoid-s12917" xml:space="preserve"> Palàm ex ſuperioribus [18 n 5] quòd proportio a d ad d t, ſicut a m ad m t.</s>
            <s xml:id="echoid-s12918" xml:space="preserve"> Similiter ꝓportio b
              <lb/>
            d ad d q, ſicut proportio b l ad l q:</s>
            <s xml:id="echoid-s12919" xml:space="preserve"> ſed [per 9 ax:</s>
            <s xml:id="echoid-s12920" xml:space="preserve">] a d maior d b, & d t mi
              <lb/>
            nor d q:</s>
            <s xml:id="echoid-s12921" xml:space="preserve"> ergo maior eſt proportio a m ad m t:</s>
            <s xml:id="echoid-s12922" xml:space="preserve"> quàm b l ad l q.</s>
            <s xml:id="echoid-s12923" xml:space="preserve"> [Quia e-
              <lb/>
              <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a" number="154">
                <variables xml:id="echoid-variables144" xml:space="preserve">a f b m
                  <gap/>
                k
                  <gap/>
                q n e t h d
                  <gap/>
                z</variables>
              </figure>
            nim è quatuor lineis a d prima maior eſt b d tertia, & d t ſecunda mi-
              <lb/>
            nor d q quarta:</s>
            <s xml:id="echoid-s12924" xml:space="preserve"> erit ratio a d ad d t maior quàm b d ad d q, ut patet ex
              <lb/>
            8 p 5:</s>
            <s xml:id="echoid-s12925" xml:space="preserve"> & per 11 p 5 ratio a m ad m t maior quàm b l ad l q.</s>
            <s xml:id="echoid-s12926" xml:space="preserve">] Secetur [per
              <lb/>
            12 p 6] a m in pũcto f, ut proportio fm ad m t ſit, ſicut b l ad l q:</s>
            <s xml:id="echoid-s12927" xml:space="preserve"> erit er
              <lb/>
            go minor proportio b m ad m t, quàm b l ad l q.</s>
            <s xml:id="echoid-s12928" xml:space="preserve"> [Nam cum m t ſit ma-
              <lb/>
            ior l q:</s>
            <s xml:id="echoid-s12929" xml:space="preserve"> erit ք 14 p 5 f m maior b l:</s>
            <s xml:id="echoid-s12930" xml:space="preserve"> quare per 8 p 5 ratio f m ad m t maior
              <lb/>
            eſt, quàm b l ad eandem m t:</s>
            <s xml:id="echoid-s12931" xml:space="preserve"> ratio igitur b l ad m t minor eſt, quàm b l
              <lb/>
            ad l q:</s>
            <s xml:id="echoid-s12932" xml:space="preserve"> ergo ratio b m ad m t multo minor erit, ꝗ̃ b l ad l q.</s>
            <s xml:id="echoid-s12933" xml:space="preserve">] Secetur
              <lb/>
            [per 12 p 6] m t in puncto k, ut proportio b m ad m k ſit, ſicut b l ad l q.</s>
            <s xml:id="echoid-s12934" xml:space="preserve">
              <lb/>
            k cadet neceſſariò inter m & q:</s>
            <s xml:id="echoid-s12935" xml:space="preserve"> quia l q minor m q, & b l maior b m.</s>
            <s xml:id="echoid-s12936" xml:space="preserve">
              <lb/>
            Cũ igitur f m ad m t, ſicut b l ad l q, & ſicut b m ad m k:</s>
            <s xml:id="echoid-s12937" xml:space="preserve"> erit [per 19 p 5]
              <lb/>
            proportio f b ad k t, ſicut b l ad l q:</s>
            <s xml:id="echoid-s12938" xml:space="preserve"> ſed b l, maior l q:</s>
            <s xml:id="echoid-s12939" xml:space="preserve"> [concluſum enim
              <lb/>
            eſt ut b d ad d q, ſic b l ad l q:</s>
            <s xml:id="echoid-s12940" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s12941" xml:space="preserve"> cum b d ſit maior d q, erit b l maior
              <lb/>
            l q] ergo f b maior k t.</s>
            <s xml:id="echoid-s12942" xml:space="preserve"> Quare a b maior q t.</s>
            <s xml:id="echoid-s12943" xml:space="preserve"> [quia a b maior eſt f b, quæ
              <lb/>
            maior oſtẽſa eſt k t, & k t maior eſt q t.</s>
            <s xml:id="echoid-s12944" xml:space="preserve"> Quare a b multò maior eſt q t.</s>
            <s xml:id="echoid-s12945" xml:space="preserve">]
              <lb/>
            Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12946" xml:space="preserve"> Si uerò linea a b producta non perueniat ad
              <lb/>
            centrum:</s>
            <s xml:id="echoid-s12947" xml:space="preserve"> ducatur à puncto a linea ad cẽtrum:</s>
            <s xml:id="echoid-s12948" xml:space="preserve"> quæ ſit a d:</s>
            <s xml:id="echoid-s12949" xml:space="preserve"> & ſit d cen-
              <lb/>
            trum:</s>
            <s xml:id="echoid-s12950" xml:space="preserve"> & à puncto b ducatur linea b d:</s>
            <s xml:id="echoid-s12951" xml:space="preserve"> & locus imaginis a ſit punctum
              <lb/>
            g:</s>
            <s xml:id="echoid-s12952" xml:space="preserve"> locus imaginis b ſit p:</s>
            <s xml:id="echoid-s12953" xml:space="preserve"> & ducatur linea g p:</s>
            <s xml:id="echoid-s12954" xml:space="preserve"> quæ quidem eſt imago lineæ a b.</s>
            <s xml:id="echoid-s12955" xml:space="preserve"> Dico quòd a b maior
              <lb/>
            eſt g p:</s>
            <s xml:id="echoid-s12956" xml:space="preserve"> quoniam g p aut eſt æquidiſtans a b, aut nõ.</s>
            <s xml:id="echoid-s12957" xml:space="preserve"> Si fuerit æquidiſtans, planum:</s>
            <s xml:id="echoid-s12958" xml:space="preserve"> quòd eſt minor.</s>
            <s xml:id="echoid-s12959" xml:space="preserve">
              <lb/>
            [Nam per 29.</s>
            <s xml:id="echoid-s12960" xml:space="preserve">32 p 1 triangula a d b, & g d p ſunt æquiangula:</s>
            <s xml:id="echoid-s12961" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s12962" xml:space="preserve"> per 4 p 6, ut a d ad d g, ſic a b ad
              <lb/>
              <figure xlink:label="fig-0196-02" xlink:href="fig-0196-02a" number="155">
                <variables xml:id="echoid-variables145" xml:space="preserve">b a e p g d</variables>
              </figure>
              <figure xlink:label="fig-0196-03" xlink:href="fig-0196-03a" number="156">
                <variables xml:id="echoid-variables146" xml:space="preserve">a b h z e p g d</variables>
              </figure>
            g p:</s>
            <s xml:id="echoid-s12963" xml:space="preserve"> ſed per 9 ax.</s>
            <s xml:id="echoid-s12964" xml:space="preserve"> a d maior eſt d g:</s>
            <s xml:id="echoid-s12965" xml:space="preserve"> ergo a b maior eſt g p.</s>
            <s xml:id="echoid-s12966" xml:space="preserve">] Si non fuerit æquidiſtans, producatur,
              <lb/>
            quouſque concurrat cum ea:</s>
            <s xml:id="echoid-s12967" xml:space="preserve"> ſit concurſus z:</s>
            <s xml:id="echoid-s12968" xml:space="preserve"> & [per 31 p 1] à puncto p producatur æquidiſtans
              <lb/>
            a b:</s>
            <s xml:id="echoid-s12969" xml:space="preserve"> quæ ſit p h.</s>
            <s xml:id="echoid-s12970" xml:space="preserve"> Angulus p g h aut eſt acutus:</s>
            <s xml:id="echoid-s12971" xml:space="preserve"> aut rectus:</s>
            <s xml:id="echoid-s12972" xml:space="preserve"> aut maior.</s>
            <s xml:id="echoid-s12973" xml:space="preserve"> Sit rectus uel maior:</s>
            <s xml:id="echoid-s12974" xml:space="preserve"> erit
              <lb/>
            [per 19 p 1] latus p h maius p g:</s>
            <s xml:id="echoid-s12975" xml:space="preserve"> ſed [per 29.</s>
            <s xml:id="echoid-s12976" xml:space="preserve"> 32 p 1.</s>
            <s xml:id="echoid-s12977" xml:space="preserve"> 4 p 6] p h minus a b:</s>
            <s xml:id="echoid-s12978" xml:space="preserve"> [ideoq́;</s>
            <s xml:id="echoid-s12979" xml:space="preserve"> recta p g multò mi-
              <lb/>
            nor eſt a b.</s>
            <s xml:id="echoid-s12980" xml:space="preserve">] Et ita eſt propoſitũ.</s>
            <s xml:id="echoid-s12981" xml:space="preserve"> Si fuerit acutus:</s>
            <s xml:id="echoid-s12982" xml:space="preserve"> poteſt accidere ut forma ſit maior ipſa re, cuius eſt
              <lb/>
            forma:</s>
            <s xml:id="echoid-s12983" xml:space="preserve"> [quando nimirum angulus p g h minor eſt angulo p h g] quam licet, excedat:</s>
            <s xml:id="echoid-s12984" xml:space="preserve"> rarò accidet.</s>
            <s xml:id="echoid-s12985" xml:space="preserve">
              <lb/>
            Et ſi acciderit, forſitan comprehendetur forma à longitudine tali, quòd minor uidebitur quàm ſit:</s>
            <s xml:id="echoid-s12986" xml:space="preserve">
              <lb/>
            quoniam ipſum corpus ab hac longitudine forſitan uidebitur minus.</s>
            <s xml:id="echoid-s12987" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div461" type="section" level="0" n="0">
          <head xml:id="echoid-head419" xml:space="preserve" style="it">6. In ſpeculo ſphærico conuexo, imagouiſibilis, cuius uera magnitudo uiſione directa propter
            <lb/>
          immoder at am diſtantiam percipi non poteſt: aliâs eſt æquabilis uiſibili: aliâs maior. 38 p 6.</head>
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