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

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[121] e o f t p d a b g k
[122] e o f t p k d a b g
[123] t z e b a g h d
[124] t z e b a g h d
[125] z t n q p i b k f e l a n m g h d
[126] z t n q b k f a e o g h d
[127] k e t o z r l g b x n p f m q d s n a
[128] b o p n g k e f d a q l m
[129] b t o u p n g k e f d a q z m
[130] b u t o p n g k e f d a q z m
[131] u t b p n o g k e f d l a q m z
[132] s g z k t e f d o b r a
[133] t f i k e d m q z x h
[134] k e d q h z
[135] l b k d o
[136] a b n m k l q g d h e
[137] b a b a m f g d n
[138] m t h f b p a g d n
[139] m t h b a g d n
[140] a b l m l t a b m g n d n d
[141] f e t h k o b m a g n d
[142] f e t b m f a g d n
[143] l m a b g n d
[144] e b g q m d a o z h k
[145] a s c p c f d d e b
[146] e b g q l m d o a z n h k
[147] d z b t m l q r p h k f g e a
[148] s z o r x a h k g m u b d e t l f q p n
[149] a b h
[150] a l c q g d b h
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          <p>
            <s xml:id="echoid-s7563" xml:space="preserve">
              <pb o="129" file="0135" n="135" rhead="OPTICAE LIBER V."/>
            cularis & lineæ reflexionis.</s>
            <s xml:id="echoid-s7564" xml:space="preserve"> Puncta autem, quorum imagines citra ſpeculum eomprehenduntur,
              <lb/>
            hoc eſt inter uiſum & ſpeculum, ſunt, cum à quolibet eorum linea ducta ad centrum ſpeculi, ſecat la
              <lb/>
            titudinem uiæ inter uiſum & ſpeculum interiacentis.</s>
            <s xml:id="echoid-s7565" xml:space="preserve"> Et ut uideatur hoc:</s>
            <s xml:id="echoid-s7566" xml:space="preserve"> auferatur pyramis à me-
              <lb/>
            dio ſpeculi:</s>
            <s xml:id="echoid-s7567" xml:space="preserve"> & collocetur in parte, erit uertex centrum ſpeculi:</s>
            <s xml:id="echoid-s7568" xml:space="preserve"> & remotio uiſus ſit maior ſemidiame
              <lb/>
            tro ſphæræ.</s>
            <s xml:id="echoid-s7569" xml:space="preserve"> Deinde ſumatur lignum gracile album, & ſtatuatur in ſpeculo, ut ſit centrum ſpeculi
              <lb/>
            directè medium inter caput ligni & centrum uiſus, & dirigatur intuitus in punctum ſpeculi, à quo
              <lb/>
            linea ad uerticem pyramidis ducta, ſit inter caput ligni & uiſum:</s>
            <s xml:id="echoid-s7570" xml:space="preserve"> & apparebit forma capitis ligni ci-
              <lb/>
            tra ſpeculum, & propin quior uiſui uertice pyramidis:</s>
            <s xml:id="echoid-s7571" xml:space="preserve"> & erunt in eadem linea recta, uertex pyrami-
              <lb/>
            dis, & caput ligni, & imago capitis.</s>
            <s xml:id="echoid-s7572" xml:space="preserve"> Et hæc linea eſt perpendicularis ſuper lineam, contingentem
              <lb/>
            lineam communem ſuperficiei ſpeculi & ſuperficiei reflexionis [per 25 n 4:</s>
            <s xml:id="echoid-s7573" xml:space="preserve">] quoniam ſuperficies
              <lb/>
            reflexionis tranſit per centrum & punctum uiſus.</s>
            <s xml:id="echoid-s7574" xml:space="preserve"> Et linea tranſiens per hæc duo puncta, eſt in
              <lb/>
            ſuperficie reflexionis.</s>
            <s xml:id="echoid-s7575" xml:space="preserve"> Et linea cõmunis eſt circulus:</s>
            <s xml:id="echoid-s7576" xml:space="preserve"> & hæc linea huic circulo erit diameter:</s>
            <s xml:id="echoid-s7577" xml:space="preserve"> quoniã
              <lb/>
            centrum illius circuli, eſt centrum ſphæræ.</s>
            <s xml:id="echoid-s7578" xml:space="preserve"> Quare erit hæc linea perpendicularis ſuper lineam,
              <lb/>
            contingentem circulum in capite huius lineæ [per 18 p 3:</s>
            <s xml:id="echoid-s7579" xml:space="preserve">] & hæc linea tranſit per punctum uiſum,
              <lb/>
            & eius imaginem.</s>
            <s xml:id="echoid-s7580" xml:space="preserve"> Et ita quodlibet punctum citra ſpeculum uiſum, comprehenditur in eadem li-
              <lb/>
            nea cum centro & cum imagine eius:</s>
            <s xml:id="echoid-s7581" xml:space="preserve"> & quodlibet punctum uidetur in linea reflexionis [per 21 n
              <lb/>
            4.</s>
            <s xml:id="echoid-s7582" xml:space="preserve">] Quare in loco ſectionis perpendicularis & lineæ reflexionis.</s>
            <s xml:id="echoid-s7583" xml:space="preserve"> Et ea, quorum ueritas in his ſpe-
              <lb/>
            culis comprehenditur, ſunt, quorum imagines apparent ultra ſpeculum uel citra ſuperficiem eius:</s>
            <s xml:id="echoid-s7584" xml:space="preserve">
              <lb/>
            & præter hæc, nulla ſunt, quæ in hoc ſpeculo in ueritate comprehendat uiſus, ipſa enim prohibent
              <lb/>
            imagines ſuas ueras apparere.</s>
            <s xml:id="echoid-s7585" xml:space="preserve"> Imagines, quæ apparent in ſuperficie huius ſpeculi, ſunt ex ultima
              <lb/>
            partitione:</s>
            <s xml:id="echoid-s7586" xml:space="preserve"> & hæc explanabimus, cum erit ſermo de erroribus uiſus.</s>
            <s xml:id="echoid-s7587" xml:space="preserve"> Quodlibet ë
              <unsure/>
            rgo punctum in
              <lb/>
            ueritate in hoc ſpeculo comprehenſum, apparet in concurſu perpendicularis & lineæ reflexionis:</s>
            <s xml:id="echoid-s7588" xml:space="preserve">
              <lb/>
            quæ quidem perpendicularis tranſit à puncto uiſo ad centrum ſphæræ, & cadit orthogonaliter in
              <lb/>
            contingentem, lineam communem.</s>
            <s xml:id="echoid-s7589" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div286" type="section" level="0" n="0">
          <head xml:id="echoid-head310" xml:space="preserve" style="it">7. In ſpeculis cauis cylindraceo, conico, imago uidetur in concurſu perpendicularis inciden-
            <lb/>
          tiæ & lineæ reflexionis. 37 p 5.</head>
          <p>
            <s xml:id="echoid-s7590" xml:space="preserve">IN ſpeculis columnaribus concauis diuerſificatur imago:</s>
            <s xml:id="echoid-s7591" xml:space="preserve"> aliquando enim erit locus eius in ſu-
              <lb/>
            perficie ſpeculi:</s>
            <s xml:id="echoid-s7592" xml:space="preserve"> aliquando ultra:</s>
            <s xml:id="echoid-s7593" xml:space="preserve"> & in his omnibus aliquando in ueritate comprehendetur:</s>
            <s xml:id="echoid-s7594" xml:space="preserve"> ali-
              <lb/>
            quando non.</s>
            <s xml:id="echoid-s7595" xml:space="preserve"> Cum uolueris in his locum imaginis percipere:</s>
            <s xml:id="echoid-s7596" xml:space="preserve"> facias, ſicut feciſti in columnari-
              <lb/>
            bus exterioribus.</s>
            <s xml:id="echoid-s7597" xml:space="preserve"> Adhibeatur enim regula, in qua ſit columna concaua, ſicut adhibita eſt ſuperius,
              <lb/>
            & acus ſimiliter, & corpus modicum, in ſummitate acus:</s>
            <s xml:id="echoid-s7598" xml:space="preserve"> & ponatur uiſus oppoſitus in medio cir-
              <lb/>
            culi, & in medio ſuperficiei annuli:</s>
            <s xml:id="echoid-s7599" xml:space="preserve"> & ſubleuetur uiſus modicum à ſuperficie annuli:</s>
            <s xml:id="echoid-s7600" xml:space="preserve"> & inſpiciat,
              <lb/>
            donec imaginem corporis uideat, & comprehendat formam corporis, & corpus, & punctum in ſpe
              <lb/>
            culo, ſignatum in eadem linea perpendiculari, ſuper ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7601" xml:space="preserve"> & hoc per ſyllogiſmum ſen
              <lb/>
            ſualem.</s>
            <s xml:id="echoid-s7602" xml:space="preserve"> Et erit imago ultra ſpeculum, & erit reflexio ex puncto lineæ rectæ, quæ eſt in medio ſpe-
              <lb/>
            culi.</s>
            <s xml:id="echoid-s7603" xml:space="preserve"> Deinde ſtatuatur uiſus in ſuperficie annuli, ſed extra medium, donec uideat imaginem cor-
              <lb/>
            poris parui:</s>
            <s xml:id="echoid-s7604" xml:space="preserve"> uidebit quidem eam citra ſpeculum:</s>
            <s xml:id="echoid-s7605" xml:space="preserve"> & uidebit corpus, & eius imaginem, & punctum
              <lb/>
            in ſpeculo ſignatum, in una linea recta perpendiculari, ſuper lineam rectam contingentem circu-
              <lb/>
            lum æquidiſtantem baſi ſpeculi, ſuper punctum ſignatum in ſpeculi ſuperficie:</s>
            <s xml:id="echoid-s7606" xml:space="preserve"> & ſuperficies huius,
              <lb/>
            eſt ſuperficies reflexionis in hocſitu:</s>
            <s xml:id="echoid-s7607" xml:space="preserve"> & eſt ſuperficies faciei annuli:</s>
            <s xml:id="echoid-s7608" xml:space="preserve"> & punctum reflexionis eſt pun-
              <lb/>
            ctum illius circuli.</s>
            <s xml:id="echoid-s7609" xml:space="preserve"> Poſtea adhibeatur cum manu alia acus, in cuius ſummitate ſit corpus modicum:</s>
            <s xml:id="echoid-s7610" xml:space="preserve">
              <lb/>
            & ſtatuaturin ſuperficiem & axem, hoc modo, ut corpus, & punctum ſignatum ſint in eadem li-
              <lb/>
            nea, ſecundum ſenſualem ſyllogiſmum:</s>
            <s xml:id="echoid-s7611" xml:space="preserve"> & ſit uiſus in ſuperficie annuli, inter caput eius & medium:</s>
            <s xml:id="echoid-s7612" xml:space="preserve">
              <lb/>
            uidebit quidem imaginem corporis, & uidebit hanc imaginem & corpus eius, & punctum ſigna-
              <lb/>
            tum in ſuperficie ſpeculi, in eadem linea recta.</s>
            <s xml:id="echoid-s7613" xml:space="preserve"> Si autem declinetur linea recta cum triangulo par-
              <lb/>
            uo, quod fecimus, & ſit uiſus in medio annuli:</s>
            <s xml:id="echoid-s7614" xml:space="preserve"> uidebit imaginem citra ſpeculum, ſed in eadem linea
              <lb/>
            recta cum corpore, & puncto ſignato.</s>
            <s xml:id="echoid-s7615" xml:space="preserve"> Et hæc reflexio erit ex columnaribus ſectionibus:</s>
            <s xml:id="echoid-s7616" xml:space="preserve"> quoniam
              <lb/>
            ſpeculum eſt declinatum:</s>
            <s xml:id="echoid-s7617" xml:space="preserve"> & ſcimus [è 21 n 4] quòd non percipitur imago, niſi in linea reflexio-
              <lb/>
            nis.</s>
            <s xml:id="echoid-s7618" xml:space="preserve"> Palàm ergo, quòd locus imaginis eſt, ubi ſecat perpendicularis prædictam lineam reflexio-
              <lb/>
            nis, cum comprehenditur ueritas.</s>
            <s xml:id="echoid-s7619" xml:space="preserve"> Et licet non comprehendatur certitudo imaginis, tamen erit
              <lb/>
            modus harum imaginum cum ueritatis imaginibus.</s>
            <s xml:id="echoid-s7620" xml:space="preserve"> Pari modo uidere poteris imaginem in py-
              <lb/>
            ramidalibus concauis in concurſu perpendicularis cum linea reflexionis.</s>
            <s xml:id="echoid-s7621" xml:space="preserve"> Palàm ergo, quòd in o-
              <lb/>
            mnibus ſpeculis comprehenduntur imagines in loco prædicto:</s>
            <s xml:id="echoid-s7622" xml:space="preserve"> qui quidem locus ſimiliter dicitur
              <lb/>
            imaginis locus.</s>
            <s xml:id="echoid-s7623" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div287" type="section" level="0" n="0">
          <head xml:id="echoid-head311" xml:space="preserve" style="it">8. Imago in quocun ſpeculo, uidetur in concurſu perpendicularis incidentiæ & lineæ refle-
            <lb/>
          scionis. 37 p 5.</head>
          <p>
            <s xml:id="echoid-s7624" xml:space="preserve">QVare autem comprehendantur res uiſæ per reflexionem in locis imaginum:</s>
            <s xml:id="echoid-s7625" xml:space="preserve"> & quare ima-
              <lb/>
            go ſit ſuper perpendicularem à re uiſa in ſpeculi ſuperficiem, declarabimus cauſſam.</s>
            <s xml:id="echoid-s7626" xml:space="preserve"> Viſus
              <lb/>
            cum acquirit form am per reflexionẽ, acquirit eam ſtatim ſine certitudine, & acquirit longi-
              <lb/>
            tudinẽ per æſtimationẽ, & hanc longitudinẽ cõprehendet forſitan in ueritate, per diligentiã intui-
              <lb/>
            tus adhibitã, forſitan nõ.</s>
            <s xml:id="echoid-s7627" xml:space="preserve"> Et iſtud explanauimus in libro ſecũdo [24.</s>
            <s xml:id="echoid-s7628" xml:space="preserve"> 25.</s>
            <s xml:id="echoid-s7629" xml:space="preserve"> 38.</s>
            <s xml:id="echoid-s7630" xml:space="preserve"> 39 n:</s>
            <s xml:id="echoid-s7631" xml:space="preserve">] & ibi dictũ eſt, quòd
              <lb/>
            </s>
          </p>
        </div>
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