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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[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
[251] e d a n b g m q t k z h l
Page: 291
[252] f g k h d c e a b
Page: 292
[253] h d a m e c k z g b
Page: 293
[254] n a d p e q o r f k h g b l c m
Page: 294
[Figure 255]
Page: 295
[256] b a c d
Page: 306
[257] a c b d
Page: 307
[258] c a b d e
Page: 307
[259] a b c d e f
Page: 307
[260] a e b f g
Page: 307
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          <p>
            <s xml:id="echoid-s18895" xml:space="preserve">
              <pb o="272" file="0278" n="278" rhead="ALHAZEN"/>
            ſitis ad l & k per 16 p 1:</s>
            <s xml:id="echoid-s18896" xml:space="preserve"> ſed angulis exterioribus à rectis a b, a c & ſecante k l factis æquantur interio-
              <lb/>
            res ad b & c trianguli a b c per 29 p 1.</s>
            <s xml:id="echoid-s18897" xml:space="preserve"> Anguli igitur ad b & c ſunt maiores angulis a d l & k.</s>
            <s xml:id="echoid-s18898" xml:space="preserve"> Quare per
              <lb/>
            32 p 1 reliquus a b c minor eſt reliquo l a k:</s>
            <s xml:id="echoid-s18899" xml:space="preserve">] & linea l k eſt diameter imaginis b c.</s>
            <s xml:id="echoid-s18900" xml:space="preserve"> Nam omne punctũ
              <lb/>
            lineæ b c refringitur ab aliquo puncto p h.</s>
            <s xml:id="echoid-s18901" xml:space="preserve"> Nam ſi forma b refringitur ex p:</s>
            <s xml:id="echoid-s18902" xml:space="preserve"> punctum, quod eſt inter
              <lb/>
            b & z, refringitur ab aliquo puncto inter p & m:</s>
            <s xml:id="echoid-s18903" xml:space="preserve"> & ponamus ſuper lineam b z punctũ n.</s>
            <s xml:id="echoid-s18904" xml:space="preserve"> Si ergo for-
              <lb/>
            ma n refringeretur ab aliquo puncto extra lineam m p exparte d:</s>
            <s xml:id="echoid-s18905" xml:space="preserve"> tunc linea, per quam extenditur
              <lb/>
            forman, ſecaret lineam b p:</s>
            <s xml:id="echoid-s18906" xml:space="preserve"> & ſic forma puncti ſectionis refringeretur ad a ex duobus punctis [p &
              <lb/>
            g,] quod eſt impoſsibile, ut diximus in capitulo quinto huius libri de imagine:</s>
            <s xml:id="echoid-s18907" xml:space="preserve"> [19 n] n ergo non re
              <lb/>
            fringitur ad a, niſi ex aliquo puncto inter p m.</s>
            <s xml:id="echoid-s18908" xml:space="preserve"> Et ſimiliter omne punctum in z c, non refringetur ad
              <lb/>
            a, niſi ex linea m h.</s>
            <s xml:id="echoid-s18909" xml:space="preserve"> Linea ergo l k eſt diameter imaginis lineę b c:</s>
            <s xml:id="echoid-s18910" xml:space="preserve"> [per 18 n] forma ergo b c uidebitur
              <lb/>
            in l k.</s>
            <s xml:id="echoid-s18911" xml:space="preserve"> Item iam declarauimus [numero præcedente] quòd forma refracta eſt debilior recta:</s>
            <s xml:id="echoid-s18912" xml:space="preserve"> ergo for
              <lb/>
            ma b c, quę comprehenditur refractè, eſt debilior forma eius, quę comprehenditur rectè:</s>
            <s xml:id="echoid-s18913" xml:space="preserve"> & propter
              <lb/>
            debilitatem formæ rei, uiſus aſsimilat eam formæ rei, quæ uidetur à maiore remotione:</s>
            <s xml:id="echoid-s18914" xml:space="preserve"> maior enim
              <lb/>
            diſtantia debilitat formam.</s>
            <s xml:id="echoid-s18915" xml:space="preserve"> Et iam declarauimus in ſecundo libro [38 n] quòd uiſus comprehendit
              <lb/>
            imaginem rei uiſæ ſecundum quantitatem anguli, reſpectu remotionis & poſitionis rei uiſæ apud
              <lb/>
            uiſum:</s>
            <s xml:id="echoid-s18916" xml:space="preserve"> & angulus k a l eſt maior angulo c a b [ex concluſo,] & poſitio l k eſt ſicut poſitio c b, & b c ui
              <lb/>
            detur in l k, & l k comprehenditur in maiore quaſi diſtantia, diſtantia b c, propter debilitatem for-
              <lb/>
            mæ.</s>
            <s xml:id="echoid-s18917" xml:space="preserve"> Viſus ergo comprehendit b c refractè ex comparatione anguli maioris angulo c a b ad diſtan-
              <lb/>
            tiam maiorem diſtantia b c, & ad poſitionem æqualem poſitioni b c.</s>
            <s xml:id="echoid-s18918" xml:space="preserve"> Quapropter b c comprehendi-
              <lb/>
            tur refractè maior:</s>
            <s xml:id="echoid-s18919" xml:space="preserve"> & hoc duabus de cauſsis, ſcilicet magnitudine anguli, & debilitate formæ.</s>
            <s xml:id="echoid-s18920" xml:space="preserve"> Cauſ-
              <lb/>
            ſa autem magnitudinis anguli, eſt propinquitas anguli ad uiſum:</s>
            <s xml:id="echoid-s18921" xml:space="preserve"> & cauſſa propin quitatis anguli eſt
              <lb/>
            refractio.</s>
            <s xml:id="echoid-s18922" xml:space="preserve"> Cauſſa ergo, qua b c comprehenditur maior, eſt refractio.</s>
            <s xml:id="echoid-s18923" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div609" type="section" level="0" n="0">
          <head xml:id="echoid-head525" xml:space="preserve" style="it">40. Si communis ſectio ſuperficierum, refractionis & refractiui fuerit linea recta, & uiſ{us}
            <lb/>
          ſit in perpendiculari duct a à medio uiſibilis obliqui ad communem ſectionem: imago maior ui-
            <lb/>
          debitur uiſibili. 32 p 10.</head>
          <p>
            <s xml:id="echoid-s18924" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s18925" xml:space="preserve"> iteremus figurã:</s>
            <s xml:id="echoid-s18926" xml:space="preserve"> & ſit b c nõ æquidiſtans lineę d e:</s>
            <s xml:id="echoid-s18927" xml:space="preserve"> & extrahamus à remotiore extremitatũ
              <lb/>
            b c lineam æquidiſtantẽ lineæ d e:</s>
            <s xml:id="echoid-s18928" xml:space="preserve"> [per 31 p 1] & ſit c q:</s>
            <s xml:id="echoid-s18929" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0278-01" xlink:href="fig-0278-01a" number="236">
                <variables xml:id="echoid-variables223" xml:space="preserve">a d e i f p m h l k b z q o c</variables>
              </figure>
            & extrahamus a z ad o:</s>
            <s xml:id="echoid-s18930" xml:space="preserve"> erit ergo o in medio c q.</s>
            <s xml:id="echoid-s18931" xml:space="preserve"> [Quia
              <lb/>
            enim per fabricationem a z parallela d b, continuata eſt
              <lb/>
            in o, & d b in q:</s>
            <s xml:id="echoid-s18932" xml:space="preserve"> erit ք 2 p 6, ut b z ad z c, ſic q o ad o c:</s>
            <s xml:id="echoid-s18933" xml:space="preserve"> ſed b
              <lb/>
            z ęquatur z c ex theſi:</s>
            <s xml:id="echoid-s18934" xml:space="preserve"> ergo q o ęquabitur o c:</s>
            <s xml:id="echoid-s18935" xml:space="preserve"> o igitur erit
              <lb/>
            medium punctũ lineę q c:</s>
            <s xml:id="echoid-s18936" xml:space="preserve">] quare z eſt in medio b c:</s>
            <s xml:id="echoid-s18937" xml:space="preserve"> quia
              <lb/>
            b q eſt æ quidiſtans z o:</s>
            <s xml:id="echoid-s18938" xml:space="preserve"> & [per 2 p 6] proportio q o ad o c,
              <lb/>
            ſicut b z ad z c.</s>
            <s xml:id="echoid-s18939" xml:space="preserve"> Et refringatur forma q ad a exp:</s>
            <s xml:id="echoid-s18940" xml:space="preserve"> & forma
              <lb/>
            c ad a ex h:</s>
            <s xml:id="echoid-s18941" xml:space="preserve"> & continuemus a p, & pertranſeat uſque ad l:</s>
            <s xml:id="echoid-s18942" xml:space="preserve">
              <lb/>
            & continuemus a h, & pertranſeat uſque ad k:</s>
            <s xml:id="echoid-s18943" xml:space="preserve"> & conti-
              <lb/>
            nuemus l k:</s>
            <s xml:id="echoid-s18944" xml:space="preserve"> erit ergo l k diameter imaginis q c:</s>
            <s xml:id="echoid-s18945" xml:space="preserve"> eritq́;</s>
            <s xml:id="echoid-s18946" xml:space="preserve"> an-
              <lb/>
            gulus k a l maior angulo c a q:</s>
            <s xml:id="echoid-s18947" xml:space="preserve"> [ut oſtenſum eſt pręceden
              <lb/>
            te numero] a ergo comprehendet imaginem q c maiorẽ
              <lb/>
            q c, ut prius diximus.</s>
            <s xml:id="echoid-s18948" xml:space="preserve"> Linea autem q p ſecab it lineam b c
              <lb/>
            in r:</s>
            <s xml:id="echoid-s18949" xml:space="preserve"> r ergo refringetur ad a ex p:</s>
            <s xml:id="echoid-s18950" xml:space="preserve"> ergo b refringetur ad a
              <lb/>
            ex puncto inter duo puncta p, d.</s>
            <s xml:id="echoid-s18951" xml:space="preserve"> Nam ſi refrin geretur ex
              <lb/>
            puncto inter p, m:</s>
            <s xml:id="echoid-s18952" xml:space="preserve"> accideret prædictum impoſsibile [nu
              <lb/>
            mero pręcedente:</s>
            <s xml:id="echoid-s18953" xml:space="preserve"> quod erat, idem punctũ uiſibilis à duo
              <lb/>
            bus refractiui punctis refringi non poſſe.</s>
            <s xml:id="echoid-s18954" xml:space="preserve">] Refringatur
              <lb/>
            ergo b ad a ex f, & continuemus a f, & pertranſeat ad i, &
              <lb/>
            cõtinuemus i k:</s>
            <s xml:id="echoid-s18955" xml:space="preserve"> ergo i k erit diameter imaginis b c:</s>
            <s xml:id="echoid-s18956" xml:space="preserve"> & po-
              <lb/>
            ſitio i k in reſpectu a, eſt ſimilis poſitioni b c, quia i k aut
              <lb/>
            erit ęquidiſtans ad b c, aut non erit inter illam & æ quidi-
              <lb/>
            ſtantem diuerſitas, quæ mutet poſitionem:</s>
            <s xml:id="echoid-s18957" xml:space="preserve"> non eſt enim
              <lb/>
            inter diſtantiam i k & diſtantiã b c à uiſu grandis diuerſi-
              <lb/>
            tas:</s>
            <s xml:id="echoid-s18958" xml:space="preserve"> quare declinatio i k à linea æquidiſtante b c, quę exit
              <lb/>
            ex k, erit ualde parua.</s>
            <s xml:id="echoid-s18959" xml:space="preserve"> Ergo angulus i a k eſt maior angu-
              <lb/>
            lo b a c:</s>
            <s xml:id="echoid-s18960" xml:space="preserve"> & poſitio i k eſt ſimilis poſitioni b c:</s>
            <s xml:id="echoid-s18961" xml:space="preserve"> & i k comprehenditur quaſi remotior, propter debilita-
              <lb/>
            tem formæ eius.</s>
            <s xml:id="echoid-s18962" xml:space="preserve"> Linea ergo k i uidetur maior, quã b c, utin præcedente figura declarauimus:</s>
            <s xml:id="echoid-s18963" xml:space="preserve"> Sed
              <lb/>
            i k eſt imago b c:</s>
            <s xml:id="echoid-s18964" xml:space="preserve"> ergo b c uidebitur maior, quàm ſit:</s>
            <s xml:id="echoid-s18965" xml:space="preserve"> & hoc eſt quod uoluimus.</s>
            <s xml:id="echoid-s18966" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div611" type="section" level="0" n="0">
          <head xml:id="echoid-head526" xml:space="preserve" style="it">41. Si communis ſectio ſuperficierum, refractionis & refractiui fuerit linea recta: & uiſ{us}
            <lb/>
          ſit extra planum perpendicularium à terminis uiſibilis, par alleli communiſectioni ſuper refra-
            <lb/>
          ctiuum duct arum: imago uidebitur maior uiſibili. 33 p 10.</head>
          <p>
            <s xml:id="echoid-s18967" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s18968" xml:space="preserve"> ſit uiſus a:</s>
            <s xml:id="echoid-s18969" xml:space="preserve"> & res uiſa b c:</s>
            <s xml:id="echoid-s18970" xml:space="preserve"> extrahamus perpendiculares b d, c e:</s>
            <s xml:id="echoid-s18971" xml:space="preserve"> & continuemus d e:</s>
            <s xml:id="echoid-s18972" xml:space="preserve"> & ſit
              <lb/>
            b c æquidiſtans d e:</s>
            <s xml:id="echoid-s18973" xml:space="preserve"> & ſit a extra, ſuperficiem b d c e, cum co quod continuatur cum ipſa:</s>
            <s xml:id="echoid-s18974" xml:space="preserve"> &
              <lb/>
            [per 10 p 1] diuidamus b c in duo æqualia in z:</s>
            <s xml:id="echoid-s18975" xml:space="preserve"> & extrahamus perpendicularem a h ſuper ſuperfi
              <lb/>
            </s>
          </p>
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