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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[221] a p h f l g e o k a n m e z q b
Page: 263
[222] a f h p g o e k d m n c q z b
Page: 263
[223] a f h p l g o e k d b m c q z n
Page: 264
[224] a f l p g e o k d b n m c z
Page: 264
[225] h a b g e f d e z
Page: 265
[226] h a b e d c z
Page: 265
[227] e a b d f c
Page: 265
[228] a r c p e h b z b d
Page: 266
[229] a n r l c x m h e p z g b b f d o k
Page: 267
[230] a l g h e z d k b t
Page: 268
[231] e a g e z b
Page: 269
[232] k o g e c n a d z f h m l p b
Page: 270
[233] e o k a c n g d z h m l p b
Page: 270
[234] a k r q c n g h l m d p z b
Page: 271
[235] ad m g p h l k q bn z c
Page: 277
[236] a d e i f p m h l k b z q o c
Page: 278
[237] a p k d m e l o g h b z c
Page: 279
[238] a q p k d m e g l o b z f c
Page: 279
[239] a d p m h e ſ g o k b n z c
Page: 280
[240] a h m g e n k z b c ſ d
Page: 281
[241] a h g m x e n k z l b c d
Page: 281
[242] a h g f m r e n k b p q d c ſ
Page: 281
[243] a f h m g e n k b p q d c l
Page: 282
[244] a h m g e r o n k b s z c l d
Page: 282
[245] a b g p e d z m h o h l c
Page: 283
[246] k q f b o r c l m e z f g
Page: 285
[247] b g f t n d h k z a m e
Page: 285
[248] b d g q h n k z o a p e m
Page: 286
[249] g a e h c d b z
Page: 290
[250] d a k g e c b z h
Page: 291
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            <s xml:id="echoid-s15683" xml:space="preserve">
              <pb o="221" file="0227" n="227" rhead="OPTICAE LIBER VI."/>
            m, l, f eruntimagines punctiz.</s>
            <s xml:id="echoid-s15684" xml:space="preserve"> Sic ergo z comprehendetur in tribus locis [quia à tribus punctis a,
              <lb/>
            b, d reflectitur ad uiſum e.</s>
            <s xml:id="echoid-s15685" xml:space="preserve">] Item extrahamus ex e lineam ad arcum d z, quomodocunque ſit:</s>
            <s xml:id="echoid-s15686" xml:space="preserve"> &
              <lb/>
            ſit e k:</s>
            <s xml:id="echoid-s15687" xml:space="preserve"> & continuemus g k:</s>
            <s xml:id="echoid-s15688" xml:space="preserve"> & ſecet arcum d z in k:</s>
            <s xml:id="echoid-s15689" xml:space="preserve"> & continuemus lineam k z, Quia ergo arcus
              <lb/>
            e g, g z ſunt æquales:</s>
            <s xml:id="echoid-s15690" xml:space="preserve"> [ex concluſo] erunt [per
              <lb/>
              <figure xlink:label="fig-0227-01" xlink:href="fig-0227-01a" number="198">
                <variables xml:id="echoid-variables187" xml:space="preserve">ſ m s q c d r b n
                  <gap/>
                p t a h e g u i f</variables>
              </figure>
            27 p 3] duo anguli e k g, g k z æquales.</s>
            <s xml:id="echoid-s15691" xml:space="preserve"> Et conti-
              <lb/>
            nuemus g k in r:</s>
            <s xml:id="echoid-s15692" xml:space="preserve"> & extrahamus e r, z r.</s>
            <s xml:id="echoid-s15693" xml:space="preserve"> Ergo an-
              <lb/>
            gulus e r g eſt maior angulo g r z.</s>
            <s xml:id="echoid-s15694" xml:space="preserve"> [Quia enim
              <lb/>
            anguli e k g, z k g æquales ſunt concluſi:</s>
            <s xml:id="echoid-s15695" xml:space="preserve"> æqua-
              <lb/>
            buntur anguli e k r, z k r per 13 p 1.</s>
            <s xml:id="echoid-s15696" xml:space="preserve"> Poſitis igitur
              <lb/>
            angulis ad r æqualibus:</s>
            <s xml:id="echoid-s15697" xml:space="preserve"> erunt triangula e k r, z k r
              <lb/>
            æquiangula per 32 p 1:</s>
            <s xml:id="echoid-s15698" xml:space="preserve"> & per 4 p 6 r k ad duasre-
              <lb/>
            ctas k e, k z eandem habebit rationem.</s>
            <s xml:id="echoid-s15699" xml:space="preserve"> Quare
              <lb/>
            ipſæ erunt æquales per 9 p 5:</s>
            <s xml:id="echoid-s15700" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s15701" xml:space="preserve"> & periphe-
              <lb/>
            riæ e a d k & k z ipſis ſubtenſæ per 28 p 3:</s>
            <s xml:id="echoid-s15702" xml:space="preserve"> quod
              <lb/>
            fieri non poteſt.</s>
            <s xml:id="echoid-s15703" xml:space="preserve"> Nam quia rectæ a g, d g æquan-
              <lb/>
            tur per 15 d 1:</s>
            <s xml:id="echoid-s15704" xml:space="preserve"> æquabuntur peripheriæ a g, d g
              <lb/>
            ipſis ſubtenſæ per 28 p 3:</s>
            <s xml:id="echoid-s15705" xml:space="preserve"> & e g æqualis conclu-
              <lb/>
            ſa eſtipſi z g, reliqua igitur a e æquatur reliquæ
              <lb/>
            d z:</s>
            <s xml:id="echoid-s15706" xml:space="preserve"> ergo e a maior eſt k z per 9 ax:</s>
            <s xml:id="echoid-s15707" xml:space="preserve"> ergo e a d k
              <lb/>
            multò maior eſt k z.</s>
            <s xml:id="echoid-s15708" xml:space="preserve"> Quare angulus e r g non
              <lb/>
            eſt æqualis angulo g r z:</s>
            <s xml:id="echoid-s15709" xml:space="preserve"> nec eſt eo minor:</s>
            <s xml:id="echoid-s15710" xml:space="preserve"> quod
              <lb/>
            eodem argumento oſtendetur.</s>
            <s xml:id="echoid-s15711" xml:space="preserve"> Angulus igitur
              <lb/>
            e r g maior eſt angulo g r z] Sit ergo angulus
              <lb/>
            g r n æqualis angulo e r g [per 23 p 1.</s>
            <s xml:id="echoid-s15712" xml:space="preserve">] Duæ er-
              <lb/>
            go lineæ e r, r n reflectentur inter ſe, propter an-
              <lb/>
            gulos æquales [per 12 n 4] & extrahamus e r ad
              <lb/>
            q:</s>
            <s xml:id="echoid-s15713" xml:space="preserve"> erιt ergo q imago n reſpectu e.</s>
            <s xml:id="echoid-s15714" xml:space="preserve"> Et imaginemur
              <lb/>
            ſuperficiem exeuntem à linea m g f, perpendicu-
              <lb/>
            lariter ſuper circulum a b d:</s>
            <s xml:id="echoid-s15715" xml:space="preserve"> & extrahamus ex z
              <lb/>
            lineam in hac ſuperficie, perpendicularem ſuper
              <lb/>
            g z, & tranſeat in utranque partem.</s>
            <s xml:id="echoid-s15716" xml:space="preserve"> Sit ergo c z p:</s>
            <s xml:id="echoid-s15717" xml:space="preserve">
              <lb/>
            & ponamus g centrum:</s>
            <s xml:id="echoid-s15718" xml:space="preserve"> & in longitudine g n fa-
              <lb/>
            ciamus arcum circuli c n p:</s>
            <s xml:id="echoid-s15719" xml:space="preserve"> ſecabit ergo lineam
              <lb/>
            c z p in duobus punctis:</s>
            <s xml:id="echoid-s15720" xml:space="preserve"> & ſint c, p:</s>
            <s xml:id="echoid-s15721" xml:space="preserve"> & continue-
              <lb/>
            mus lineas g c, g p.</s>
            <s xml:id="echoid-s15722" xml:space="preserve"> Erunt ergo in ſuperficie per-
              <lb/>
            pendiculari ſuper ſuperficiem a b d:</s>
            <s xml:id="echoid-s15723" xml:space="preserve"> & extraha-
              <lb/>
            mus g c, g p rectè:</s>
            <s xml:id="echoid-s15724" xml:space="preserve"> & ſuper g, & in longitudine
              <lb/>
            g q faciamus arcum circuli:</s>
            <s xml:id="echoid-s15725" xml:space="preserve"> ſecabit ergo duas li-
              <lb/>
            neas g c, g p:</s>
            <s xml:id="echoid-s15726" xml:space="preserve"> ſecet in s, o.</s>
            <s xml:id="echoid-s15727" xml:space="preserve"> Quia ergo ſuperficies
              <lb/>
            a b d circuli eſt perpendicularis ſuper ſuperficiem duarum linearum g c, g p:</s>
            <s xml:id="echoid-s15728" xml:space="preserve"> erunt duo anguli
              <lb/>
            e g s, e g o recti [per 4 d 11] & e g perpendicularis ſuper ſuperficiem g c p:</s>
            <s xml:id="echoid-s15729" xml:space="preserve"> erit ergo [per 18 p 11]
              <lb/>
            utraque ſuperficies e g s, e g o perpendicularis ſuper ſuperficiem s g o:</s>
            <s xml:id="echoid-s15730" xml:space="preserve"> & utraque iſtarum dua-
              <lb/>
            rum ſuperficierum facit in ſpeculo circulum magnum, [per 1 th.</s>
            <s xml:id="echoid-s15731" xml:space="preserve"> 1 ſphær.</s>
            <s xml:id="echoid-s15732" xml:space="preserve">] comparem circulo a b d.</s>
            <s xml:id="echoid-s15733" xml:space="preserve">
              <lb/>
            Punctum ergo circuli compar puncto r, eſt, quod facit ſuperficies e g s.</s>
            <s xml:id="echoid-s15734" xml:space="preserve"> Ergo concurrunt ex ipſo
              <lb/>
            ſecundum angulos æquales duæ lineæ inter duo puncta e, c:</s>
            <s xml:id="echoid-s15735" xml:space="preserve"> & ſimiliter inter duo puncta e, p:</s>
            <s xml:id="echoid-s15736" xml:space="preserve"> & li-
              <lb/>
            neæ g c, g p ſunt æquales [per 15 d 1] & lineæ g s, g q, g o ſunt æquales:</s>
            <s xml:id="echoid-s15737" xml:space="preserve"> & q eſt imago n:</s>
            <s xml:id="echoid-s15738" xml:space="preserve"> & s ima-
              <lb/>
            go c:</s>
            <s xml:id="echoid-s15739" xml:space="preserve"> & o imago p.</s>
            <s xml:id="echoid-s15740" xml:space="preserve"> Imago ergo arcus c n p conuexi ex parte ſpeculi, eſt arcus s q o concauus ex
              <lb/>
            parte uiſus:</s>
            <s xml:id="echoid-s15741" xml:space="preserve"> & leſt imago z:</s>
            <s xml:id="echoid-s15742" xml:space="preserve"> & duo puncta s, o ſunt imagines c, p.</s>
            <s xml:id="echoid-s15743" xml:space="preserve"> Imago ergo lineæ c z p eſt linea
              <lb/>
            tranſiens per puncta s, l, o:</s>
            <s xml:id="echoid-s15744" xml:space="preserve"> & talis eſt concaua ex parte uiſus.</s>
            <s xml:id="echoid-s15745" xml:space="preserve"> Et ſignemus lineam tranſeuntem
              <lb/>
            per puncta s, l, o:</s>
            <s xml:id="echoid-s15746" xml:space="preserve"> & extrahamus lineam e g a d h.</s>
            <s xml:id="echoid-s15747" xml:space="preserve"> Si ergo ſpeculum non peruenit ad duo puncta b,
              <lb/>
            h, ſed alter ſuorum terminorum fuerit inter duo puncta b, h, & reliquus fuerit infra h, & uiſus fue-
              <lb/>
            rit in e:</s>
            <s xml:id="echoid-s15748" xml:space="preserve"> & duæ lineæ p z c, p n c fuerint in aliquo uiſibili:</s>
            <s xml:id="echoid-s15749" xml:space="preserve"> tunc forma lineæ p z c rectæ, erit conca-
              <lb/>
            ua, ſcilicet s l o:</s>
            <s xml:id="echoid-s15750" xml:space="preserve"> & forma arcus p n c conuexi erit etiam linea concaua, ſcilicet s q o.</s>
            <s xml:id="echoid-s15751" xml:space="preserve"> Et p z c re-
              <lb/>
            cta habebit unam imaginem:</s>
            <s xml:id="echoid-s15752" xml:space="preserve"> & arcus p n c habebit unam imaginem.</s>
            <s xml:id="echoid-s15753" xml:space="preserve"> Item extrahamus b g ad i:</s>
            <s xml:id="echoid-s15754" xml:space="preserve">
              <lb/>
            & continuemus lineas e i, i z:</s>
            <s xml:id="echoid-s15755" xml:space="preserve"> iſtæ ergo duæ lineæ reflectuntur ſecundum angulos æquales:</s>
            <s xml:id="echoid-s15756" xml:space="preserve"> [Quia
              <lb/>
            enim e b, z b æquales ſunt concluſæ, & communis eſt b i:</s>
            <s xml:id="echoid-s15757" xml:space="preserve"> anguliq́ue e b i, z b i æquales per 27
              <lb/>
            p 3, ut patuit:</s>
            <s xml:id="echoid-s15758" xml:space="preserve"> æquabuntur per 4 p 1 anguli e i b, z i b] & e i ſecabit f g:</s>
            <s xml:id="echoid-s15759" xml:space="preserve"> ſecet ergo in u:</s>
            <s xml:id="echoid-s15760" xml:space="preserve"> u ergo
              <lb/>
            erit imago z [per 6 n 5.</s>
            <s xml:id="echoid-s15761" xml:space="preserve">] Puncta ergo m, l, u, f ſunt imagines z.</s>
            <s xml:id="echoid-s15762" xml:space="preserve"> Et ſi ſpeculum exceſſerit duo pun-
              <lb/>
            cta a, d, & uiſus fuerit in e, & dorſum aſpicientis fuerit ex parte arcus a i, & comprehenderit to-
              <lb/>
            tum arcum i d a:</s>
            <s xml:id="echoid-s15763" xml:space="preserve"> tunc z uidebitur in quatuor locis, ſcilicet l, m, u, f:</s>
            <s xml:id="echoid-s15764" xml:space="preserve"> & uidebit duo puncta p, cin
              <lb/>
            duobus punctis s, o:</s>
            <s xml:id="echoid-s15765" xml:space="preserve"> & ſic linea recta p z c habebit quatuor imagines concauas:</s>
            <s xml:id="echoid-s15766" xml:space="preserve"> una tranſibit per
              <lb/>
            puncta s, m, o, ſcilicet linea s m o:</s>
            <s xml:id="echoid-s15767" xml:space="preserve"> ſecunda tranſibit per puncta s, l, o, ſcilicet linea s l o:</s>
            <s xml:id="echoid-s15768" xml:space="preserve"> tertia tran-
              <lb/>
            ſibit per puncta s, u, o, ſcilicet linea s u o:</s>
            <s xml:id="echoid-s15769" xml:space="preserve"> quarta tranſibit per puncta s, f, o, linea ſcilicet s f o.</s>
            <s xml:id="echoid-s15770" xml:space="preserve"> Pa-
              <lb/>
            </s>
          </p>
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