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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[151] a g e u m q d o n z h p l
Page: 192
[152] a e u g d o p h q n k z i s t f
Page: 193
[153] f f e a z b h d g
Page: 195
[154] a f b m k q n e t h d z
Page: 196
[155] b a e p g d
Page: 196
[156] a b h z e p g d
Page: 196
[157] o z l h m n q t d a b e
Page: 197
[158] z i l m h n t d z a k g y c f b z r s u p a e x
Page: 198
[159] i u r c z h t m g b n q f a
Page: 201
[160] i u r k c z l b d t m g n q f a
Page: 201
[161] l u r c z o d t m g b n k q f a s p x e s
Page: 202
[162] d t e h s n q b l q m f p a g
Page: 203
[163] e c h m z b d a
Page: 204
[164] e n c z b d g a
Page: 204
[165] c h z b d g a
Page: 205
[166] b e a d h z m g
Page: 205
[167] p o b c e l m t n a q k f d g
Page: 206
[168] b d a e h t z g f
Page: 206
[169] e b f a d m h t z g
Page: 207
[170] q e a b d m h z
Page: 207
[171] l k x s y e t q b a f u r m h o m z g p d
Page: 207
[172] ſ k x b a s t c q f m o h z i g p d
Page: 208
[173] d a b e h z g
Page: 208
[174] d a b e h z g
Page: 209
[175] a d b b g
Page: 209
[176] a d f b ſ m e c z g
Page: 209
[177] h e m c u t s k o b z ſ q r f g a d
Page: 210
[178] h e m c u s t b o q z r f g a d
Page: 210
[179] i h e m c t z u s b o k q r f g a d
Page: 210
[180] n q e ſ g t f m o K d h c a s u p z b
Page: 211
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        <div xml:id="echoid-div351" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s9562" xml:space="preserve">
              <pb o="153" file="0159" n="159" rhead="OPTICAE LIBER V."/>
            re.</s>
            <s xml:id="echoid-s9563" xml:space="preserve"> Etita obſeruatur ſitus partiũ in imaginibus, ſicut fuit in punctis uiſis.</s>
            <s xml:id="echoid-s9564" xml:space="preserve"> Sumpta aũt linea, in qua
              <lb/>
            eſt punctũ eiuſdẽ ſitus:</s>
            <s xml:id="echoid-s9565" xml:space="preserve"> quodlibet punctũ illius lineę eiuſdẽ ſitus erit, reſpectu duorũ oculorũ ſecũ-
              <lb/>
            dũ modũ prędictũ:</s>
            <s xml:id="echoid-s9566" xml:space="preserve"> & unicã habebit imaginẽ, propter æqualitatẽ angulorũ illius lineę cũ lineis ui-
              <lb/>
            ſualibus.</s>
            <s xml:id="echoid-s9567" xml:space="preserve"> Si aũt ſumatur linea, quæ angulũ, quẽ cõtinent duæ lineæ à cẽtris oculorũ ad punctum ui
              <lb/>
            ſum, diuidat per æqualia:</s>
            <s xml:id="echoid-s9568" xml:space="preserve"> ſitus cuiuslibet puncti lineæ quãtumlibet productæ, eritidẽ utriq;</s>
            <s xml:id="echoid-s9569" xml:space="preserve"> uifui
              <gap/>
              <lb/>
            ſicut ſuit uni.</s>
            <s xml:id="echoid-s9570" xml:space="preserve"> Et idẽ eſt probationis modus.</s>
            <s xml:id="echoid-s9571" xml:space="preserve"> Præter has duas lineas nõ eſt ſumere aliã, eundem ob-
              <lb/>
            ſeruantem ſitum.</s>
            <s xml:id="echoid-s9572" xml:space="preserve"> Vnde, cum punctum uiſum comprehendatur in perpendiculari [per 3 n] cadet
              <lb/>
            imago eius in diuerſis punctis illius perpendicularis, ſed imperceptibiliter à ſe remotis:</s>
            <s xml:id="echoid-s9573" xml:space="preserve"> & imago
              <lb/>
            cuiuslibet puncti à quotcunq;</s>
            <s xml:id="echoid-s9574" xml:space="preserve"> uideatur oculis, ſemper obſeruat identitatem partis.</s>
            <s xml:id="echoid-s9575" xml:space="preserve"> Vnde apparet
              <lb/>
            unitas imaginis, ſicut dictum eſt in uiſu directo [27 n 1] quòd formæ, licet in diuerſa cadant loca:</s>
            <s xml:id="echoid-s9576" xml:space="preserve">
              <lb/>
            propter tamen diſtantiã earum inſenſibilem nõ diuerſiſicant apparentiam, niſi diuerſificent partẽ.</s>
            <s xml:id="echoid-s9577" xml:space="preserve">
              <lb/>
            Similiter hic, quando remotio puncti ab uno uiſu fuerit modicò maior, quàm ab alio:</s>
            <s xml:id="echoid-s9578" xml:space="preserve"> eruntlocai-
              <lb/>
            maginum imperceptibiliter remota.</s>
            <s xml:id="echoid-s9579" xml:space="preserve"> Vnde apparent ſimul, & ex eis una imago compacta:</s>
            <s xml:id="echoid-s9580" xml:space="preserve"> quando-
              <lb/>
            quidem imaginum loca aliquando non totaliter diſtant, ſed partialiter.</s>
            <s xml:id="echoid-s9581" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div352" type="section" level="0" n="0">
          <head xml:id="echoid-head346" xml:space="preserve" style="it">43. Si cõmunis ſectio ſuperficierũ reſlexiõis & ſpeculi cylindracei cõuexi fuerit latus cylindri,
            <lb/>
          uel circul{us}: loca, tum reflexionum tum imaginum eodem modo ſehabebunt, ut in ſpeculis pla-
            <lb/>
          no & ſphærico conuexo. 42. 43 p 7.</head>
          <p>
            <s xml:id="echoid-s9582" xml:space="preserve">IN ſpeculis columnaribus exterioribus aliquãdo linea cõmunis ſuperficiei reflexiõis & ſuperfi-
              <lb/>
            ciei ſpeculi, eſt linea recta:</s>
            <s xml:id="echoid-s9583" xml:space="preserve"> aliquãdo circulus:</s>
            <s xml:id="echoid-s9584" xml:space="preserve"> aliquãdo ſectio columnaris.</s>
            <s xml:id="echoid-s9585" xml:space="preserve"> Cũ fuerit linea cõmu-
              <lb/>
            nis, linea recta:</s>
            <s xml:id="echoid-s9586" xml:space="preserve"> erit locus imaginis in perpendiculari à puncto uiſo ducta ſuper ſuperficiem ſpe-
              <lb/>
            culi, tantum diſtans à linea communi, quantum punctum uiſum ab eadem.</s>
            <s xml:id="echoid-s9587" xml:space="preserve"> Et eadem eſt probatio,
              <lb/>
            quæ dicta eſt in ſpeculo plano [11 n.</s>
            <s xml:id="echoid-s9588" xml:space="preserve">] Cum autem communis linea fuerit circulus:</s>
            <s xml:id="echoid-s9589" xml:space="preserve"> erit aliquando
              <lb/>
            imaginis locus intra circulum:</s>
            <s xml:id="echoid-s9590" xml:space="preserve"> aliquando extra:</s>
            <s xml:id="echoid-s9591" xml:space="preserve"> aliquando in ipſa circumferentia.</s>
            <s xml:id="echoid-s9592" xml:space="preserve"> Eius rei eadem
              <lb/>
            penitus aſsignatio, quæ in ſpeculo exteriore ſphærico [22 n.</s>
            <s xml:id="echoid-s9593" xml:space="preserve">]</s>
          </p>
        </div>
        <div xml:id="echoid-div353" type="section" level="0" n="0">
          <head xml:id="echoid-head347" xml:space="preserve" style="it">44. Siperpendicularis incidentiæ ſecetur à lineis: reflexionis, intra ellipſin (quæ est communis
            <lb/>
          ſectio ſuperficierum reflexionis & ſpeculi cylindracei conuexi) & tangente in reflexionis pun-
            <lb/>
          cto: erit ut tota perpendicularis adinferum ſegmentum, ſic ſuperum adintermedium. Et infe-
            <lb/>
          rum mai{us} erit ſegmento lineæ reflexionis. 47.48 p 7.</head>
          <p>
            <s xml:id="echoid-s9594" xml:space="preserve">SIuerò linea cõmunis fuerit ſectio colũnaris:</s>
            <s xml:id="echoid-s9595" xml:space="preserve"> dico, quòd imaginũ quędã ſunt intra ſpeculũ:</s>
            <s xml:id="echoid-s9596" xml:space="preserve"> quę
              <lb/>
            dã in ſuքficie ſpeculi:</s>
            <s xml:id="echoid-s9597" xml:space="preserve"> quędã extra ſpeculũ:</s>
            <s xml:id="echoid-s9598" xml:space="preserve"> quę in ſingulari explanabũtur.</s>
            <s xml:id="echoid-s9599" xml:space="preserve"> Sit a b c ſectio colũ-
              <lb/>
            naris:</s>
            <s xml:id="echoid-s9600" xml:space="preserve"> b ſit pũctũ reflexionis:</s>
            <s xml:id="echoid-s9601" xml:space="preserve"> e pũctũ uiſum:</s>
            <s xml:id="echoid-s9602" xml:space="preserve"> d cẽtrũ uiſus:</s>
            <s xml:id="echoid-s9603" xml:space="preserve"> & [ք 12 p 11] ducatur à puncto b per-
              <lb/>
            pendicularis ſuper ſuperficiẽ cõtingentẽ ſpeculũ:</s>
            <s xml:id="echoid-s9604" xml:space="preserve"> quæ ſit g b q:</s>
            <s xml:id="echoid-s9605" xml:space="preserve"> & [ք 11 p 11] ducatur à puncto e per-
              <lb/>
            pendicularis ſuper ſuperficiẽ, cõtingentẽ ſpeculũ:</s>
            <s xml:id="echoid-s9606" xml:space="preserve"> quę ſit e k q:</s>
            <s xml:id="echoid-s9607" xml:space="preserve"> & linea cõtingẽs ſpeculũ in pũcto b:</s>
            <s xml:id="echoid-s9608" xml:space="preserve">
              <lb/>
            ſit t u:</s>
            <s xml:id="echoid-s9609" xml:space="preserve"> linea cõtingẽs ſpeculũ in pũcto k:</s>
            <s xml:id="echoid-s9610" xml:space="preserve"> ſit k m.</s>
            <s xml:id="echoid-s9611" xml:space="preserve"> Dico, quòd duę perpẽdiculares g b q, e k q cõcurrẽt.</s>
            <s xml:id="echoid-s9612" xml:space="preserve">
              <lb/>
            Ducãtur lineę e b, d b:</s>
            <s xml:id="echoid-s9613" xml:space="preserve"> & ducatur linea k b.</s>
            <s xml:id="echoid-s9614" xml:space="preserve"> Palàm, qđ k m cadet in figurã e k b, & linea b t in figurã
              <lb/>
            eandẽ [quia recta linea ſecãs angulũ trianguli, ſecat baſim angulo ſubtẽſam:</s>
            <s xml:id="echoid-s9615" xml:space="preserve"> ſecus nõ ſecaret angu
              <lb/>
            lũ.</s>
            <s xml:id="echoid-s9616" xml:space="preserve">] Igitur b t ſecabite k:</s>
            <s xml:id="echoid-s9617" xml:space="preserve"> ſecetin pũcto t.</s>
            <s xml:id="echoid-s9618" xml:space="preserve"> Palàm, quòd angulus g b k eſt maior recto, & angulus e k b
              <lb/>
            ſimiliter maior recto [quia g b q, e k q ſunt քpendiculares ipſis t u, k m.</s>
            <s xml:id="echoid-s9619" xml:space="preserve">] Quare [per 13 p 1.</s>
            <s xml:id="echoid-s9620" xml:space="preserve"> 11 ax.</s>
            <s xml:id="echoid-s9621" xml:space="preserve">] g b,
              <lb/>
            e k cõcurrẽt.</s>
            <s xml:id="echoid-s9622" xml:space="preserve"> Sit cõcurſus punctũ q.</s>
            <s xml:id="echoid-s9623" xml:space="preserve"> Similiter d b k maior recto:</s>
            <s xml:id="echoid-s9624" xml:space="preserve"> igitur d b, e k cõcurrẽt.</s>
            <s xml:id="echoid-s9625" xml:space="preserve"> Sit cõcurſus
              <lb/>
            punctũ h.</s>
            <s xml:id="echoid-s9626" xml:space="preserve"> Igitur h eſt locus imaginis [ք 4 n.</s>
            <s xml:id="echoid-s9627" xml:space="preserve">] Dico
              <lb/>
              <figure xlink:label="fig-0159-01" xlink:href="fig-0159-01a" number="85">
                <variables xml:id="echoid-variables75" xml:space="preserve">e g d t m b u k h f q a c</variables>
              </figure>
            etiã, quòd proportio e q ad q h, ſicut e t ad th:</s>
            <s xml:id="echoid-s9628" xml:space="preserve"> & etiã
              <lb/>
            quòd q h eſt maior h b.</s>
            <s xml:id="echoid-s9629" xml:space="preserve"> Ducatur [ք 31 p 1] h f æquidi
              <lb/>
            ſtãs e b.</s>
            <s xml:id="echoid-s9630" xml:space="preserve"> Palàm, quòd angulus e b t eſt ę qualis angulo
              <lb/>
            d b u [ք 12 n 4:</s>
            <s xml:id="echoid-s9631" xml:space="preserve">] eſt igitur [ք 15 p 1.</s>
            <s xml:id="echoid-s9632" xml:space="preserve"> 1 ax.</s>
            <s xml:id="echoid-s9633" xml:space="preserve">] æqualis an-
              <lb/>
            gulo t b h:</s>
            <s xml:id="echoid-s9634" xml:space="preserve"> reſtat e b g æqualis angulo h b q:</s>
            <s xml:id="echoid-s9635" xml:space="preserve"> cũ g b t, t
              <lb/>
            b q ſint recti.</s>
            <s xml:id="echoid-s9636" xml:space="preserve"> Cũ igitur t b diuidat angulũ e b h ք æ-
              <lb/>
            qualia:</s>
            <s xml:id="echoid-s9637" xml:space="preserve"> erit [ք 3 p 6] et ad t h, ſicut e b ad b h:</s>
            <s xml:id="echoid-s9638" xml:space="preserve"> Sed an-
              <lb/>
            gulus e b g eſt æqualis angulo h ſb [ք 29 p 1:</s>
            <s xml:id="echoid-s9639" xml:space="preserve">] quare
              <lb/>
            h f, h b ſunt æqualia.</s>
            <s xml:id="echoid-s9640" xml:space="preserve"> [angulus enim e b g ęqualis con
              <lb/>
            cluſus eſt angulo h b f:</s>
            <s xml:id="echoid-s9641" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s9642" xml:space="preserve"> anguli h f b, h b f æquan-
              <lb/>
            tur:</s>
            <s xml:id="echoid-s9643" xml:space="preserve"> quare ք 6 p 1 latera h f, h b ęquantur:</s>
            <s xml:id="echoid-s9644" xml:space="preserve"> ergo ք 7 p 5,
              <lb/>
            ut e t ad th, ſic e b ad h f] Sed e b ad h f, ſicut e q ad q h
              <lb/>
            [ք 4 p 6:</s>
            <s xml:id="echoid-s9645" xml:space="preserve"> ꝗa enim h f parallela ducta eſt ipſi e b:</s>
            <s xml:id="echoid-s9646" xml:space="preserve"> ſunt
              <lb/>
            trιangula e b q, h f q æquiãgula ք 29.</s>
            <s xml:id="echoid-s9647" xml:space="preserve"> 32 p 1.</s>
            <s xml:id="echoid-s9648" xml:space="preserve">] Erit ergo
              <lb/>
            [per 11 p 5] et ad th, ſicute q ad q h.</s>
            <s xml:id="echoid-s9649" xml:space="preserve"> Qđ eſt propoſi-
              <lb/>
            tũ.</s>
            <s xml:id="echoid-s9650" xml:space="preserve"> Et ex hoc:</s>
            <s xml:id="echoid-s9651" xml:space="preserve"> cũ ſit ꝓportio e q ad q h, ſicut e b ad h
              <lb/>
            f [& h f æquetur ipſi h b:</s>
            <s xml:id="echoid-s9652" xml:space="preserve"> erit ք 7 p 5, e q ad q h, ſicute
              <lb/>
            b ad b h] & e q ſit maior e b [ք 19 p 1:</s>
            <s xml:id="echoid-s9653" xml:space="preserve"> ꝗa angulus e b q recto maior eſt] erit [ք 14 p 5] q h maior h b
              <lb/>
            Quod eſt ꝓpoſitũ.</s>
            <s xml:id="echoid-s9654" xml:space="preserve"> Palàm exhoc, quòd ſi ſuper ſectionẽ a b c ducatur քpendicul aris ſuք ſuperficiẽ
              <lb/>
            cõtingentẽ ſectionẽ:</s>
            <s xml:id="echoid-s9655" xml:space="preserve"> cõcurret cũ g b.</s>
            <s xml:id="echoid-s9656" xml:space="preserve"> Et hęc quidẽ patẽt, cũpunctũ uiſum nõ fuerit in քpẽdiculari
              <lb/>
            uiſuali.</s>
            <s xml:id="echoid-s9657" xml:space="preserve"> Palàm enim ex ſuperioribus [19 n] quòd unius ſolius pũcti forma ք perpẽdicularẽ accedit
              <lb/>
            ad ſpeculũ, & ſecũdũ eundẽ reflectitur.</s>
            <s xml:id="echoid-s9658" xml:space="preserve"> Et eſt pũctũ քpendicularis, exiſtẽs in ſuքficie uiſus:</s>
            <s xml:id="echoid-s9659" xml:space="preserve"> punctũ
              <lb/>
            enim ultra uiſum ſumptũ nõ poteſt reflecti ſuք hãc քpendicularẽ:</s>
            <s xml:id="echoid-s9660" xml:space="preserve"> ꝗa nõ põt accedere ad ſpeculũ ſu
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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