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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[Figure 211]
Page: 243
[212] a h e d c b k q l g f
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[213] a d c g b e f
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[214] k n m x b l p f s u z y t
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[215] k n b l o q f g u z
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[216] k n m b l d p o q f g u
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[217] k b d o f u g z r e a
Page: 255
[218] k h b m z d e a t i g
Page: 258
[219] h m k o n q e f p g i
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[220] a k h g p d b c l
Page: 262
[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
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[223] a f h p l g o e k d b m c q z n
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[224] a f l p g e o k d b n m c z
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[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
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[229] a n r l c x m h e p z g b b f d o k
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[230] a l g h e z d k b t
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[231] e a g e z b
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[232] k o g e c n a d z f h m l p b
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[233] e o k a c n g d z h m l p b
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[234] a k r q c n g h l m d p z b
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[235] ad m g p h l k q bn z c
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[236] a d e i f p m h l k b z q o c
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[237] a p k d m e l o g h b z c
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[238] a q p k d m e g l o b z f c
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[239] a d p m h e ſ g o k b n z c
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[240] a h m g e n k z b c ſ d
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          <p>
            <s xml:id="echoid-s17806" xml:space="preserve">
              <pb o="256" file="0262" n="262" rhead="ALHAZEN"/>
            motus formæ, quæ mouetur, aut ſuper perpendicularem, quæ eſt ſuper ſuperficiem corporis dia-
              <lb/>
            phani, & deinde translata eſt ab hac perpendiculari alio motu:</s>
            <s xml:id="echoid-s17807" xml:space="preserve"> aut ſuper perpendicularem, quæ exi
              <lb/>
            ſtit ſuper primam perpendicularem, & translata eſt poſt motum ipſius ſuper primam perpendicu-
              <lb/>
            larem motu compoſito ex prædictis duobus motibus.</s>
            <s xml:id="echoid-s17808" xml:space="preserve"> Hoc autem punctum comprehenditur à ui-
              <lb/>
            ſu in rectitudine lineæ, per quam forma peruenit ad uiſum.</s>
            <s xml:id="echoid-s17809" xml:space="preserve"> Forma ergo exiſtens in loco refractio-
              <lb/>
            nis peruenit ad ipſum per motũ formæ, quæ mouetur ſuper lineã perpendicularẽ ſuper ſuperficiẽ
              <lb/>
            corporis diaphani:</s>
            <s xml:id="echoid-s17810" xml:space="preserve"> deinde translata eſt ab hac perpendiculari per motum in rectitudine lineæ, per
              <lb/>
            quam forma peruenit ad uiſum.</s>
            <s xml:id="echoid-s17811" xml:space="preserve"> Forma autem, quæ eſt ſuper perpendicularem exiſtentem ſuper
              <lb/>
            ſuperficiem corporis diaphani:</s>
            <s xml:id="echoid-s17812" xml:space="preserve"> & deinde mouetur in rectitudine lineæ, per quam forma extendi-
              <lb/>
            tur ad uiſum:</s>
            <s xml:id="echoid-s17813" xml:space="preserve"> eſt forma, quæ extenditur à puncto uiſo ſuper ſuperficiem corporis diaphani, donec
              <lb/>
            perueniat ad punctum ſectionis inter hanc perpendicularem, & lineam, per quam forma extendi-
              <lb/>
            turad uiſum.</s>
            <s xml:id="echoid-s17814" xml:space="preserve"> Forma igitur puncti, quam uiſus comprehendit refractè ultra corpus diaphanum, eſt
              <lb/>
            per motum formæ, quæ peruenit ad uiſum à loco imaginis.</s>
            <s xml:id="echoid-s17815" xml:space="preserve"> Viſus autem comprehendit hanc for-
              <lb/>
            mam ex loco imaginis:</s>
            <s xml:id="echoid-s17816" xml:space="preserve"> quia eſt per motum formæ, quam uiſus comprehendit rectè, & ſine refractio
              <lb/>
            ne:</s>
            <s xml:id="echoid-s17817" xml:space="preserve"> & eſt locus, qui diſtat tantùm à uiſu, quantùm punctum imaginis:</s>
            <s xml:id="echoid-s17818" xml:space="preserve"> cuius ſitus, in reſpectu uiſus,
              <lb/>
            eſt ſitus formæ, quę eſt in loco imaginis:</s>
            <s xml:id="echoid-s17819" xml:space="preserve"> unde uiſus comprehendit illud punctum ſecundum refra-
              <lb/>
            ctionem in loco imaginis.</s>
            <s xml:id="echoid-s17820" xml:space="preserve"> Hęc autem eſt cauſſa, propter quam uiſus comprehendit rem uiſam ultra
              <lb/>
            corpus diaphanum in loco imaginis, & propter quam imago cuiuslibet puncti rei uiſæ comprehen
              <lb/>
            ſæ ſecundum refractionem, eſt in loco, in quo linea, per quam forma peruenit ad uiſum, ſecat per-
              <lb/>
            pendicularem, exeuntem à puncto illo ſuper ſuperficiem corporis diaphani.</s>
            <s xml:id="echoid-s17821" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div580" type="section" level="0" n="0">
          <head xml:id="echoid-head503" xml:space="preserve" style="it">20. Viſibile refractum à medio (quod ſectum plano, facit communem ſectionem lineam re-
            <lb/>
          ctam aut peripheriam) unam habet imaginem. 29. 30 p 10.</head>
          <p>
            <s xml:id="echoid-s17822" xml:space="preserve">HOc autem declarato:</s>
            <s xml:id="echoid-s17823" xml:space="preserve"> dicamus quòd omne uiſum comprehenſum à uiſu ultra aliquod cor-
              <lb/>
            pus diaphanũ, quod differt in diaphanitate à corpore, quod eſt in parte uiſus (ſi corpus fue-
              <lb/>
            rit ex corporibus communibus) non habet, niſi unam imaginem.</s>
            <s xml:id="echoid-s17824" xml:space="preserve"> Corpora autem diaphana
              <lb/>
            aſſueta ſunt cœlum, & aer, & aqua, & uitrum, & lapides diaphani:</s>
            <s xml:id="echoid-s17825" xml:space="preserve"> & ſuperficies cœli, quæ eſt ex par-
              <lb/>
            te uiſus, eſt ſphærica & concaua.</s>
            <s xml:id="echoid-s17826" xml:space="preserve"> Vnde omnis ſuperficies plana, quę ſecat eam, facit in ea lineam cir
              <lb/>
            cularem, cuius concauitas eſt ex parte uiſus.</s>
            <s xml:id="echoid-s17827" xml:space="preserve"> Superficies autem aeris, quæ tangit illam, eſt ſphærica
              <lb/>
            conuexa.</s>
            <s xml:id="echoid-s17828" xml:space="preserve"> Vnde ſi ſecetur à ſuperficie æqualι:</s>
            <s xml:id="echoid-s17829" xml:space="preserve"> fiet in ipſa linea circularis, [per 1 th 1 ſphær.</s>
            <s xml:id="echoid-s17830" xml:space="preserve">] cuius con
              <lb/>
            uexum eſt ex parte cœli.</s>
            <s xml:id="echoid-s17831" xml:space="preserve"> Superficies uerò aquæ, quæ eſt ex parte uiſus, eſt ſphærica conuexa:</s>
            <s xml:id="echoid-s17832" xml:space="preserve"> & ſi
              <lb/>
            ſecetur à ſuperficie æquali, fiet in ipſa linea circularis:</s>
            <s xml:id="echoid-s17833" xml:space="preserve"> cuius conuexum eſt ex parte uiſus.</s>
            <s xml:id="echoid-s17834" xml:space="preserve"> Vitro-
              <lb/>
            rum autem & lapidum diaphanorum figuræ aſſuetæ ſunt rotundæ, aut planæ.</s>
            <s xml:id="echoid-s17835" xml:space="preserve"> Vnde ſi ſecentur à
              <lb/>
            planis ſuperficiebus, fient in illis aut circuli, aut lineæ rectę.</s>
            <s xml:id="echoid-s17836" xml:space="preserve"> Et uniuerſaliter dicimus, quòd omne
              <lb/>
            punctum comprehenſum à uiſu ultra quodcunque corpus diaphanum, (cuius ſuperficies, quæ op
              <lb/>
            ponitur uiſui, eſt unica ſuperficies, & ſi ſecetur à ſuքficie ęquali, fiat in ſuperficie eius linea recta, aut
              <lb/>
            circularis) non habet, niſi unã imaginem:</s>
            <s xml:id="echoid-s17837" xml:space="preserve"> nec comprehenditur à uiſu, niſi unum punctum tantùm.</s>
            <s xml:id="echoid-s17838" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div581" type="section" level="0" n="0">
          <head xml:id="echoid-head504" xml:space="preserve" style="it">21. Si communis ſectio ſuperficierum, refractionis & refractiui fuerit linea recta: uiſibile in
            <lb/>
          perpendiculari ſuper refractiuum à uiſu duct a: rectè, & unum uidebitur. 19 p 10.</head>
          <p>
            <s xml:id="echoid-s17839" xml:space="preserve">SIt ergo uiſus a:</s>
            <s xml:id="echoid-s17840" xml:space="preserve"> & punctum uiſibile b:</s>
            <s xml:id="echoid-s17841" xml:space="preserve"> & corpus diaphanum ul-
              <lb/>
              <figure xlink:label="fig-0262-01" xlink:href="fig-0262-01a" number="220">
                <variables xml:id="echoid-variables207" xml:space="preserve">a k h g p d b c l</variables>
              </figure>
            tra, quod eſt b ſit illud, in cuius ſuperficie eſt g:</s>
            <s xml:id="echoid-s17842" xml:space="preserve"> & ſit diaphani
              <lb/>
            tas huius corporis groſsior diaphanitate corporis, quod eſt ex
              <lb/>
            parte uiſus:</s>
            <s xml:id="echoid-s17843" xml:space="preserve"> & ſit ſuperficies eius, quæ eſt ex parte uiſus, æqualis:</s>
            <s xml:id="echoid-s17844" xml:space="preserve"> &
              <lb/>
            [per 11 p 11] extrahamus ſuper ipſam à puncto a perpendicularem
              <lb/>
            a g c.</s>
            <s xml:id="echoid-s17845" xml:space="preserve"> Punctum ergo b aut erit ſuper lineam a g c:</s>
            <s xml:id="echoid-s17846" xml:space="preserve"> aut extra ipſam.</s>
            <s xml:id="echoid-s17847" xml:space="preserve"> Si
              <lb/>
            ergo punctum b fuerit in linea g c:</s>
            <s xml:id="echoid-s17848" xml:space="preserve"> tunc uiſus a comprehendet b re-
              <lb/>
            ctè & ſine refractione [per 13 n.</s>
            <s xml:id="echoid-s17849" xml:space="preserve">] Nam forma b, quando extenditur
              <lb/>
            per b g, exit ad corpus, quod eſt in parte a in rectιtudine b g:</s>
            <s xml:id="echoid-s17850" xml:space="preserve"> nam b g
              <lb/>
            eſt perpendicularis ſuper ſuperficiem corporis diaphani, quod eſt
              <lb/>
            exparte uiſus [per theſin.</s>
            <s xml:id="echoid-s17851" xml:space="preserve">] Viſus ergo a comprehendit b inſuo lo
              <lb/>
            co, & in rectitudine a g b.</s>
            <s xml:id="echoid-s17852" xml:space="preserve"> Dicimus ergo, quòd punctum b extra hãc
              <lb/>
            lineam nunquam refringetur ad a.</s>
            <s xml:id="echoid-s17853" xml:space="preserve"> Quòd ſi ſit poſsibile:</s>
            <s xml:id="echoid-s17854" xml:space="preserve"> refringatur
              <lb/>
            forma b a d a ex puncto p:</s>
            <s xml:id="echoid-s17855" xml:space="preserve"> & extrahamus ſuperficiem, in qua eſt per-
              <lb/>
            pendicularis a g b & punctum p:</s>
            <s xml:id="echoid-s17856" xml:space="preserve"> faciet ergo [per 3 p 11] in ſuperficie
              <lb/>
            corporis diaphani lineam rectam:</s>
            <s xml:id="echoid-s17857" xml:space="preserve"> ſit ergo g p d:</s>
            <s xml:id="echoid-s17858" xml:space="preserve"> & [per 11 p 1] extra-
              <lb/>
            hamus à puncto p perpendicularem ſuper lineam d p g:</s>
            <s xml:id="echoid-s17859" xml:space="preserve"> & ſit k p l:</s>
            <s xml:id="echoid-s17860" xml:space="preserve"> e
              <lb/>
            rit ergo k p l perpendicularis ſuper ſuperficiem corporis diaphani:</s>
            <s xml:id="echoid-s17861" xml:space="preserve">
              <lb/>
            [per conuerſionem 4 d 11.</s>
            <s xml:id="echoid-s17862" xml:space="preserve"> Nam a g p refractionis planum eſt ad per-
              <lb/>
            pendiculum plano refractiui per 9 n:</s>
            <s xml:id="echoid-s17863" xml:space="preserve">] & continuemus b p, & extra-
              <lb/>
            hamus ad h:</s>
            <s xml:id="echoid-s17864" xml:space="preserve"> erit ergo angulus k p h ille, quem continet linea, per quam extenditur forma, & perpen
              <lb/>
            dicularis, exiens à loco refractionis ſuper ſuperficiem corporis diaphani.</s>
            <s xml:id="echoid-s17865" xml:space="preserve"> Quia ergo corpus, quod
              <lb/>
            eſt ex parte a, eſt ſubtilius illo, quod eſt ex parte b:</s>
            <s xml:id="echoid-s17866" xml:space="preserve"> cum b peruenerit ad p, refringetur ad partem con
              <lb/>
            trariam illi, in qua eſt perpendicularis p k, [per 14 n:</s>
            <s xml:id="echoid-s17867" xml:space="preserve">] nõ ergo perueniet forma refracta ad lineã a b:</s>
            <s xml:id="echoid-s17868" xml:space="preserve">
              <lb/>
            ſed [ex hypotheſi] eſt refracta ad punctum a:</s>
            <s xml:id="echoid-s17869" xml:space="preserve"> quod eſt impoſsibile.</s>
            <s xml:id="echoid-s17870" xml:space="preserve"> Non ergo refringetur forma b ad
              <lb/>
            </s>
          </p>
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