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
21 15
22 16
23 17
24 18
25 19
26 20
27 21
28 22
29 23
30 24
31 25
32 26
33 27
34 28
35 29
36 30
37 31
38 32
39 33
40 34
41 35
42 36
43 37
44 38
45 39
46 40
47 41
48 42
49 43
50 44
< >
page |< < (131) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div290" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s7686" xml:space="preserve">
              <pb o="131" file="0137" n="137" rhead="OPTICAE LIBER V"/>
            ret continua cum apparente oculo:</s>
            <s xml:id="echoid-s7687" xml:space="preserve"> & ſemper in totali forma apparente eundem tenet locum & ſi-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s7688" xml:space="preserve"> Cuiuſcunq;</s>
            <s xml:id="echoid-s7689" xml:space="preserve"> uerò puncti imago, præter centrũ uiſus, ad ſpeculum accedit, mouetur declinatè:</s>
            <s xml:id="echoid-s7690" xml:space="preserve">
              <lb/>
            quare nõ durat ei ſimilitudo ſitus, reſpectu uiſus:</s>
            <s xml:id="echoid-s7691" xml:space="preserve"> & perpendicularis à puncto uiſo ad ſpeculũ ducta,
              <lb/>
            cadit ſuper centrũ ſphęrę:</s>
            <s xml:id="echoid-s7692" xml:space="preserve"> in qua quidẽ perpẽdiculari obſeruat imago ſimilitu dinẽ ſitus.</s>
            <s xml:id="echoid-s7693" xml:space="preserve"> Nõ eſt ergo
              <lb/>
            punctum, in quo cõprehenſa imago ſeruet ſimilitudinẽ ſitus, niſi in perpendiculari illa.</s>
            <s xml:id="echoid-s7694" xml:space="preserve"> Et cũ opor-
              <lb/>
            teat ipſam comprehendi in linea reflexionis, [per 21 n 4] comprehendetur in concurſu huius lineæ
              <lb/>
            cum hac perpendiculari.</s>
            <s xml:id="echoid-s7695" xml:space="preserve"> Iam ergo aſsignauimus cauſſam huius rei.</s>
            <s xml:id="echoid-s7696" xml:space="preserve"> Verùm rerum naturaliũ ſtatus
              <lb/>
            reſpicit ſitus ſuorum principiorũ, & principia rerum naturaliũ ſunt occulta.</s>
            <s xml:id="echoid-s7697" xml:space="preserve"> Idem erit modus proba
              <lb/>
            tionis in ſpeculo ſphærico concauo.</s>
            <s xml:id="echoid-s7698" xml:space="preserve"> Similiter in pyramidali concauo, uel extrà polito.</s>
            <s xml:id="echoid-s7699" xml:space="preserve"> Et uniuerſali
              <lb/>
            ter erit locus imaginis in perpendiculari in quocunq;</s>
            <s xml:id="echoid-s7700" xml:space="preserve"> ſpeculo:</s>
            <s xml:id="echoid-s7701" xml:space="preserve"> quoniam non eſt locus extra perpen
              <lb/>
            pendicularem, in quo forma obſeruet ſimilitudinem ſitus & identitatem.</s>
            <s xml:id="echoid-s7702" xml:space="preserve"> His explanatis reſtat de-
              <lb/>
            monſtratiuè declarare locum imaginis, in qualibet ſpeculorum ſpecie.</s>
            <s xml:id="echoid-s7703" xml:space="preserve"> Dicimus ergo, quod linea,
              <lb/>
            per quam reflectitur forma puncti cuiuslibet comprehenſi à uiſu in ſpeculo plano, quando ipſum e-
              <lb/>
            greſſum eſt à perpendiculari, quæ à centro uiſus cadit in ſuperficiem ſpeculi plani:</s>
            <s xml:id="echoid-s7704" xml:space="preserve"> concurret cum
              <lb/>
            perpendiculari, producta ab illo puncto ad ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7705" xml:space="preserve"> & erit punctum concurſus (qui eſt
              <lb/>
            locus imaginis) ultra ſpeculum:</s>
            <s xml:id="echoid-s7706" xml:space="preserve"> & erit longitudo illius à ſuperficie ſpeculi, æqualis longitudini pun
              <lb/>
            cti uiſi à ſuperficie ſpeculi:</s>
            <s xml:id="echoid-s7707" xml:space="preserve"> & uiſus non acquirit imaginem puncti uiſi, niſi in loco illo.</s>
            <s xml:id="echoid-s7708" xml:space="preserve"> Et quodcunq;</s>
            <s xml:id="echoid-s7709" xml:space="preserve">
              <lb/>
            punctum acquirit uiſus in hoc ſpeculo:</s>
            <s xml:id="echoid-s7710" xml:space="preserve"> non apparebit ex eo, niſi unica imago.</s>
            <s xml:id="echoid-s7711" xml:space="preserve"> Quodcunq;</s>
            <s xml:id="echoid-s7712" xml:space="preserve"> autẽ pun
              <lb/>
            ctum comprehendit uiſus in ſpeculo ſphærico extrà polito, quando egreditur forma à perpendicu-
              <lb/>
            lari, ducta à centro uiſus ad centrum ſpeculi:</s>
            <s xml:id="echoid-s7713" xml:space="preserve"> linea, per quã reflectitur imago ad oculum, concurret
              <lb/>
            cum linea producta à puncto illo ad centrum ſpeculi:</s>
            <s xml:id="echoid-s7714" xml:space="preserve"> quæ linea eſt perpendicularis, ducta à puncto
              <lb/>
            illo orthogonaliter ſuper lineã, contingentẽ lineam cõmunem ſuperficiei reflexionis, & ſuperficiei
              <lb/>
            ſpeculi.</s>
            <s xml:id="echoid-s7715" xml:space="preserve"> Et ſitus puncti concurſus, qui eſt locus imaginis, à ſuperficie ſpeculi erit ſecundũ ſitum ui-
              <lb/>
            ſus à ſuperficie ſpeculi.</s>
            <s xml:id="echoid-s7716" xml:space="preserve"> Et forſitan erit punctum concurſus ultra ſpeculum, forſitan in ſuperficie ſpe
              <lb/>
            culi, forſitan intra ſpeculum.</s>
            <s xml:id="echoid-s7717" xml:space="preserve"> Et uiſus comprehendit imagines omnes ultra ſpeculum, licet diuerſa
              <lb/>
            ſint earum loca:</s>
            <s xml:id="echoid-s7718" xml:space="preserve"> & non comprehendit locum cuiuslibet imaginis, niſi ſyllogiſticè in ſuperficie ſpe-
              <lb/>
            culi.</s>
            <s xml:id="echoid-s7719" xml:space="preserve"> Et quodlibet punctum comprehenſum in hoc ſpeculo, non prætendit, niſi unam imaginem.</s>
            <s xml:id="echoid-s7720" xml:space="preserve"> In
              <lb/>
            ſpeculo columnari extrà polito, & pyramidali extrà polito, quodcunq;</s>
            <s xml:id="echoid-s7721" xml:space="preserve"> punctum comprehendit ui-
              <lb/>
            ſus, cum fuerit extra perpendicularem, ductam à centro uiſus, orthogonalem ſuper ſuperficiem con
              <lb/>
            tingentem ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7722" xml:space="preserve"> linea, per quam reflectitur forma ad uiſum, concurret cum perpendi
              <lb/>
            culari, ducta ab illo puncto ſuper rectam lineam, contingentem lineam communem ſuperficiei re-
              <lb/>
            flexionis, & ſpeculi.</s>
            <s xml:id="echoid-s7723" xml:space="preserve"> Et loca imagihum horum ſpeculorum quædam ſunt ultra ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7724" xml:space="preserve">
              <lb/>
            quædam in ſuperficie:</s>
            <s xml:id="echoid-s7725" xml:space="preserve"> quædam citra.</s>
            <s xml:id="echoid-s7726" xml:space="preserve"> Et uiſus acquirit omnes imagines horum ſpeculorum ultra ſu
              <lb/>
            perficiem ſpeculi.</s>
            <s xml:id="echoid-s7727" xml:space="preserve"> Et quodcunq;</s>
            <s xml:id="echoid-s7728" xml:space="preserve"> punctum comprehendit uiſus in his ſpeculis, non efficit, niſi unam
              <lb/>
            imaginem tantùm.</s>
            <s xml:id="echoid-s7729" xml:space="preserve"> In ſpeculo ſphærico concauo lineæ, per quas reflectuntur formæ punctorũ uiſo-
              <lb/>
            rum:</s>
            <s xml:id="echoid-s7730" xml:space="preserve"> quædam concurrunt cum perpendicularibus, ductis à punctis illis ſuper lineas, contingentes
              <lb/>
            lineas communes ſuperficiei ſpeculi & ſuperficiei reflexionis:</s>
            <s xml:id="echoid-s7731" xml:space="preserve"> quædam ſunt æquidiſtantes his per-
              <lb/>
            pendicularibus.</s>
            <s xml:id="echoid-s7732" xml:space="preserve"> Et earum, quæ concurrunt cum perpendicularibus, quædam habent locum con-
              <lb/>
            curſus (qui eſt locus imaginis) ultra ſpeculum:</s>
            <s xml:id="echoid-s7733" xml:space="preserve"> quædam citra ſpeculum.</s>
            <s xml:id="echoid-s7734" xml:space="preserve"> Et quæ citra ſpeculum ha-
              <lb/>
            bent:</s>
            <s xml:id="echoid-s7735" xml:space="preserve"> quædam inter uiſum & ſpeculum:</s>
            <s xml:id="echoid-s7736" xml:space="preserve"> quædam ſuper ipſum centrũ uiſus:</s>
            <s xml:id="echoid-s7737" xml:space="preserve"> quædam ultra centrum
              <lb/>
            uiſus.</s>
            <s xml:id="echoid-s7738" xml:space="preserve"> Et uiſus quaſdam formarum rerum uiſarum, quas acquirit in his ſpeculis, comprehendit in lo
              <lb/>
            co imaginis, qui eſt punctum concurſus:</s>
            <s xml:id="echoid-s7739" xml:space="preserve"> & hæ ſunt, quas uiſus certò comprehendit:</s>
            <s xml:id="echoid-s7740" xml:space="preserve"> quaſdam com-
              <lb/>
            prehendit extra locum concurſus:</s>
            <s xml:id="echoid-s7741" xml:space="preserve"> & eſt comprehenſio ſine certitudine.</s>
            <s xml:id="echoid-s7742" xml:space="preserve"> Et res uiſæ, quas acquirit ui
              <lb/>
            ſus in hoc ſpeculo, quædam unam præ ſe ferunt imaginem tantùm:</s>
            <s xml:id="echoid-s7743" xml:space="preserve"> quædam duas:</s>
            <s xml:id="echoid-s7744" xml:space="preserve"> quædam tres:</s>
            <s xml:id="echoid-s7745" xml:space="preserve">
              <lb/>
            quædã quatuor.</s>
            <s xml:id="echoid-s7746" xml:space="preserve"> Nec poteſt eſſe, quod una res prætendat plures.</s>
            <s xml:id="echoid-s7747" xml:space="preserve"> In ſpeculo pyramidali cõcauo & co
              <lb/>
            lumnari concauo lineæ, per quas reflectuntur formæ ad uiſum:</s>
            <s xml:id="echoid-s7748" xml:space="preserve"> quædam concurrunt cum perpendi
              <lb/>
            cularibus, ductis à punctis uiſis ſuper lineas, contingentes lineas communes:</s>
            <s xml:id="echoid-s7749" xml:space="preserve"> & quædam ſunt æqui
              <lb/>
            diſtantes perpendιcularibus.</s>
            <s xml:id="echoid-s7750" xml:space="preserve"> Quæ concurrunt cum perpendicularibus:</s>
            <s xml:id="echoid-s7751" xml:space="preserve"> quædam habent concur-
              <lb/>
            ſum ultra ſpeculum:</s>
            <s xml:id="echoid-s7752" xml:space="preserve"> quædam citra.</s>
            <s xml:id="echoid-s7753" xml:space="preserve"> Quæ autem citra:</s>
            <s xml:id="echoid-s7754" xml:space="preserve"> quædam inter ſpeculum & uiſum:</s>
            <s xml:id="echoid-s7755" xml:space="preserve"> quædam ſu
              <lb/>
            per centrum uiſus:</s>
            <s xml:id="echoid-s7756" xml:space="preserve"> quædam ultra centrum uiſus.</s>
            <s xml:id="echoid-s7757" xml:space="preserve"> Et comprehenſio rerum uiſarum in hoc ſpeculo
              <lb/>
            per uiſum, quædam fit in loco imaginis (qui eſt locus concurſus) quædam extra locum concurſus.</s>
            <s xml:id="echoid-s7758" xml:space="preserve">
              <lb/>
            Et eorum, quæ comprehenduntur, aliud prætendit unam imaginem tantùm:</s>
            <s xml:id="echoid-s7759" xml:space="preserve"> aliud duas:</s>
            <s xml:id="echoid-s7760" xml:space="preserve"> aliud tres:</s>
            <s xml:id="echoid-s7761" xml:space="preserve">
              <lb/>
            alind quatuor.</s>
            <s xml:id="echoid-s7762" xml:space="preserve"> Nec aliquod eſt, quod poſsit prætendere plures, quàm quatuor.</s>
            <s xml:id="echoid-s7763" xml:space="preserve"> Et nos declarabi-
              <lb/>
            mus hæc omnia demonſtratiuè.</s>
            <s xml:id="echoid-s7764" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div291" type="section" level="0" n="0">
          <head xml:id="echoid-head314" xml:space="preserve" style="it">11. Viſibile & imago à ſpeculi plani ſuperficie in oppoſit {as} partes æquabiliter distant. 49 p 5.</head>
          <p>
            <s xml:id="echoid-s7765" xml:space="preserve">SIt a punctum uiſum:</s>
            <s xml:id="echoid-s7766" xml:space="preserve"> b centrum uiſus:</s>
            <s xml:id="echoid-s7767" xml:space="preserve"> c d e ſpeculum planum:</s>
            <s xml:id="echoid-s7768" xml:space="preserve"> & ſit d punctum reflexionis:</s>
            <s xml:id="echoid-s7769" xml:space="preserve"> c d e
              <lb/>
            linea communis ſuperficiei reflexionis & ſuperficiei ſpeculi.</s>
            <s xml:id="echoid-s7770" xml:space="preserve"> A puncto d ducatur d f perpendi-
              <lb/>
            cularis ſuper lineã cõmunẽ:</s>
            <s xml:id="echoid-s7771" xml:space="preserve"> [per 11 p 1] & à puncto a ducatur perpendicularis ſuper ſpeculi ſu
              <lb/>
            perficiẽ, [per 11 p 11] quæ ſit a c, & producatur ultra ſpeculũ:</s>
            <s xml:id="echoid-s7772" xml:space="preserve"> & a d ſit linea, per quã forma accedit ad
              <lb/>
            ſpeculũ:</s>
            <s xml:id="echoid-s7773" xml:space="preserve"> b d, per quã reflectitur ad uiſum.</s>
            <s xml:id="echoid-s7774" xml:space="preserve"> Igitur b d, f d, a d, ſunt in ſuperficie reflexionis [per 23 n 4.</s>
            <s xml:id="echoid-s7775" xml:space="preserve">]
              <lb/>
            Et cũ f d ſit æquidiſtãs a c [per 28 p 1:</s>
            <s xml:id="echoid-s7776" xml:space="preserve"> quia cũ a c ſit քpẽdicularis ſuperficiei ſpeculi per fabricatiõem:</s>
            <s xml:id="echoid-s7777" xml:space="preserve">
              <lb/>
            erit perpẽdicularis lineę c d e per 3 d 11] & [per 13 p 11] d b declinata ſit ſuper f d, cõcurret [per lemma
              <lb/>
            Procli ad 29 p 1] b d cũ a c.</s>
            <s xml:id="echoid-s7778" xml:space="preserve"> Cõcurrat ergo in puncto g.</s>
            <s xml:id="echoid-s7779" xml:space="preserve"> Dico, quòd g c eſt æqualis c a.</s>
            <s xml:id="echoid-s7780" xml:space="preserve"> Quoniã enim
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum