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

Page concordance

< >
Scan Original
121 115
122 116
123 117
124 118
125 119
126 120
127 121
128 122
129 123
130 124
131 125
132 126
133 127
134 128
135 129
136 130
137 131
138 132
139 133
140 134
141 135
142 136
143 137
144 138
145 139
146 140
147 141
148 142
149 143
150 144
< >
page |< < (129) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div285" type="section" level="0" n="0">
          <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>
      </text>
    </echo>
Impressum