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]
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[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
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[218] k h b m z d e a t i g
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[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
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[221] a p h f l g e o k a n m e z q b
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[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
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[226] h a b e d c z
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[227] e a b d f c
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[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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            <s xml:id="echoid-s17716" xml:space="preserve">
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            aquæ, & diameter, quæ erat perpendicularis, fiat decliuis:</s>
            <s xml:id="echoid-s17717" xml:space="preserve"> deinde dimittat uiſum ſuum, & intueatur
              <lb/>
            centrum:</s>
            <s xml:id="echoid-s17718" xml:space="preserve"> & tunc inueniet formam centri in rectitudine diametri, quæ nunc eſt perpendicularis ſu-
              <lb/>
            per ſuperficiem aquę, extra cuius rectitudinem erat forma centri, quando erat decliuis:</s>
            <s xml:id="echoid-s17719" xml:space="preserve"> & inueniet
              <lb/>
            formam extra rectitudinem diametri, quæ eſt nunc decliuis, quæ prius erat perpendicularis ſuper
              <lb/>
            ſuperficiem aquæ:</s>
            <s xml:id="echoid-s17720" xml:space="preserve"> & inueniet diametrum decliuem incuruatam apud ſuperficiem aquæ:</s>
            <s xml:id="echoid-s17721" xml:space="preserve"> & angulus
              <lb/>
            incuruationis erit ex parte diametri decliuis.</s>
            <s xml:id="echoid-s17722" xml:space="preserve"> Et ſi fuerint in circulo plures diametri, & reuoluerit
              <lb/>
            experimentator circulum, quouſque unaquęque earum fuerit perpendicularis ſuper ſuperficiem
              <lb/>
            aquæ ſucceſsiuè, & fuerit diameter, quæ ſequitur illam diametrum, decliuis, & aliqua pars eius fue-
              <lb/>
            rit extra aquam:</s>
            <s xml:id="echoid-s17723" xml:space="preserve"> tunc inueniet formam puncti, quod eſt centrum circuli, ſemper in rectitudine dia-
              <lb/>
            metri perpendicularis, & eleuatam à rectitudine diametri decliuis, & ſemper inueniet illud, quod
              <lb/>
            eſt intra aquam, rectum.</s>
            <s xml:id="echoid-s17724" xml:space="preserve"> Ex omnibus ergo iſtis patet, quòd forma cuiuslibet puncti comprehenſi à
              <lb/>
            uiſu in corpore diaphano groſsiore corpore aeris:</s>
            <s xml:id="echoid-s17725" xml:space="preserve"> comprehenditur extra ſuum locum & eleuatum
              <lb/>
            à ſuo loco, & in rectitudine perpendicularis exeuntis ab illo puncto ſuper ſuperficiem corporis dia
              <lb/>
            phani:</s>
            <s xml:id="echoid-s17726" xml:space="preserve"> cum linea, quæ continuat centrum uiſus cum illo puncto, non fuerit perpendicularis ſuper
              <lb/>
            ſuperficiem corporis diaphani:</s>
            <s xml:id="echoid-s17727" xml:space="preserve"> omne autem punctum comprehenditur à uiſu in eius oppoſitio-
              <lb/>
            ne, & in rectitudine lineæ rectæ, per quam extenditur forma ad uiſum, [per 19.</s>
            <s xml:id="echoid-s17728" xml:space="preserve"> 21.</s>
            <s xml:id="echoid-s17729" xml:space="preserve"> 38 n 1.</s>
            <s xml:id="echoid-s17730" xml:space="preserve"> 13 n.</s>
            <s xml:id="echoid-s17731" xml:space="preserve">] Pun-
              <lb/>
            cta ergo, quę comprehendit uiſus refractè, comprehenduntur in eius oppoſitione, & in rectitudine
              <lb/>
            lineæ rectę, per quam forma peruenit ad uiſum.</s>
            <s xml:id="echoid-s17732" xml:space="preserve"> Hoc autem declarabitur per experimentationem
              <lb/>
            comprehenſionis rerum uiſibilium ſecundum refractionem per illud inſtrumentum prædictum.</s>
            <s xml:id="echoid-s17733" xml:space="preserve">
              <lb/>
            Nam ſi experimentator clauſerit ſecundum foramen, quod eſt in inſtrumento:</s>
            <s xml:id="echoid-s17734" xml:space="preserve"> tunc non compre-
              <lb/>
            hendet rem uiſam, quam comprehendebat ſecundum refractionem:</s>
            <s xml:id="echoid-s17735" xml:space="preserve"> & cum clauſerit ſecundum fo-
              <lb/>
            ramen, nihil aliud facit, niſi ſecare lineam rectam imaginabilem, quæ exit à centro uiſus ad locum
              <lb/>
            refractionis.</s>
            <s xml:id="echoid-s17736" xml:space="preserve"> Ex quo patet, quòd forma, quæ extenditur à uiſu in corpore diaphano, in quo res ui-
              <lb/>
            ſa eſt, & refringitur in corpore diaphano, in quo eſt uiſus:</s>
            <s xml:id="echoid-s17737" xml:space="preserve"> extenditur per lineam rectam, quæ exit à
              <lb/>
            centro uiſus ad locum refractionis:</s>
            <s xml:id="echoid-s17738" xml:space="preserve"> & quod omne punctum, quod comprehenditur à uiſu in corpo
              <lb/>
            re diaphano magis groſſo, quàm ſit corpus aeris (ſi centrum uiſus fuerit extra perpendicularem,
              <lb/>
            exeuntem ab illo puncto ſuper corpus diaphanum) comprehenditur in puncto, quod eſt differen-
              <lb/>
            tia communis lineę, ſuper quam peruenit forma ad uiſum, & perpendiculari, exeunti à puncto ui-
              <lb/>
            ſo ſuper ſuperficiem corporis diaphani, quod eſt ex parte uiſus.</s>
            <s xml:id="echoid-s17739" xml:space="preserve"> Si autem experimentator uolue-
              <lb/>
            rit experiri imaginem rei uiſæ, cuius forma refrin-
              <lb/>
              <figure xlink:label="fig-0260-01" xlink:href="fig-0260-01a" number="219">
                <variables xml:id="echoid-variables206" xml:space="preserve">h m k o n q e f p g i</variables>
              </figure>
            gitur à corpore ſubtiliore ad corpus groſsius:</s>
            <s xml:id="echoid-s17740" xml:space="preserve"> acci-
              <lb/>
            piat fruſtum uitri, cuius ſuperficies ſint æquatæ &
              <lb/>
            æquidiſtantes, habens in longitudine octo digi-
              <lb/>
            tos, & in altitudine quatuor, & in ſpiſsitudine qua-
              <lb/>
            tuor:</s>
            <s xml:id="echoid-s17741" xml:space="preserve"> & accipiat circulum ligneum prædictum, &
              <lb/>
            ſignet in dorſo eius chordam in longitudine decẽ
              <lb/>
            digitorum, & diuidat illam in duo æqualia, & con-
              <lb/>
            tinuet locum diuiſionis cum cẽtro cιrculi linea re
              <lb/>
            cta, quæ tranſeat in utram que partem:</s>
            <s xml:id="echoid-s17742" xml:space="preserve"> hæc ergo li
              <lb/>
            nea erit perpẽdicularis ſuper lineam primam [per
              <lb/>
            3 p 3.</s>
            <s xml:id="echoid-s17743" xml:space="preserve">] Deinde continuet alteram extremitatem
              <lb/>
            chordæ cum centro circuli linea recta, quæ etiam
              <lb/>
            tranſeat in utramque partem.</s>
            <s xml:id="echoid-s17744" xml:space="preserve"> Et hæ duæ diame-
              <lb/>
            tri ſint ſignatę ferro, quarum alteram impleat cor-
              <lb/>
            pore albo, & aliam alterius modi colore.</s>
            <s xml:id="echoid-s17745" xml:space="preserve"> Deinde
              <lb/>
            ponat uitrum longum ſuper dorſum inſtrumenti
              <lb/>
            circuli lignei, & ſuperponat alteram extremitatem
              <lb/>
            longitudinis e
              <gap/>
            us medietati chordæ, & diſtinguat de uitro tres digitos, ex quibus duo erunt ex par
              <lb/>
            te diametri decliuis extra circulum, & remanebit de longitudine uitri unus digitus:</s>
            <s xml:id="echoid-s17746" xml:space="preserve"> qui erit ultra
              <lb/>
            diametrum perpendicularem ſuper chordam:</s>
            <s xml:id="echoid-s17747" xml:space="preserve"> & ſit corpus uitri ex parte centri:</s>
            <s xml:id="echoid-s17748" xml:space="preserve"> & applicet uitrum
              <lb/>
            ſecundum hunc ſitum circulo ligneo applicatione fixa.</s>
            <s xml:id="echoid-s17749" xml:space="preserve"> Sic ergo diameter perpendicularis ſuper
              <lb/>
            chordam, erit perpendicularis ſuper extremitates uitri ęquidiſtantes, & altera diameter erit decli-
              <lb/>
            uis ſuper has duas ſuperficies.</s>
            <s xml:id="echoid-s17750" xml:space="preserve"> Deinde oportet, ut experimentator ponat oram circuli, in qua eſt
              <lb/>
            extremitas uitri eminens ex parte ſui uiſus, & ponat alterum uiſum in differentia communi circũ-
              <lb/>
            ferentiæ & extremitati uitri, quæ eſt extremitas diametri decliuis, & appropinquet uiſum ſuum ui-
              <lb/>
            tro, quantum poterit, ita, ut non poſsit per illum uidere ex ſuperficie aliquid, pręter extremitatem
              <lb/>
            diametri decliuis:</s>
            <s xml:id="echoid-s17751" xml:space="preserve"> reliquus autem uiſus ſit in parte, in qua eſt uitrum & circulus:</s>
            <s xml:id="echoid-s17752" xml:space="preserve"> deinde cooperiat
              <lb/>
            illud, quod opponitur alteri uiſui ex ſuperficie uitri cum bombace:</s>
            <s xml:id="echoid-s17753" xml:space="preserve"> quam applicet ſuper aliquam
              <lb/>
            partem uitri, ita ut comprehendat diametrum decliuem, quæ eſt ultima linea per unum uiſum, qui
              <lb/>
            contingit uitrum:</s>
            <s xml:id="echoid-s17754" xml:space="preserve"> & non uideat ultra hanc lineam, & uideat lineam albam perpendicularem utro-
              <lb/>
            que uiſu.</s>
            <s xml:id="echoid-s17755" xml:space="preserve"> Ipſo autem exiſtente in hoc ſitu, intueatur centrum circuli, & inueniet illud in rectitudi-
              <lb/>
            nelineæ albæ, quę eſt perpendicularis ſuper ſuperficiem uitri:</s>
            <s xml:id="echoid-s17756" xml:space="preserve"> & intueatur diametrum decliuem,
              <lb/>
            apud cuius extremitatem tenet uiſum ſuum:</s>
            <s xml:id="echoid-s17757" xml:space="preserve"> & tunc uidebit eam incuruatam apud ſuperficiem ui-
              <lb/>
            tri, quæ eſt ex parte centri, & inueniet angulum incuruationis ex parte circumferentiæ:</s>
            <s xml:id="echoid-s17758" xml:space="preserve"> uiſus au-
              <lb/>
            </s>
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