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 contents

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[111.] 61. Similitudo percipitur è uiſibilium inter ſe conuenientia. 151 p 4.
Page: 72 (66)
[112.] 62. Dißimilitudo percipitur è priuatione ſimilitudinis & conuenientiæ uiſibilium inter ſe. 152 p 4.
Page: 72 (66)
[113.] DE DIVERSITATE COMPREHENSIONIS VISVS AB intentionibus particularibus. Cap. III. 63. Viſus plures uiſibiles ſpecies ſimul percipit. 2 p 4.
Page: 73 (67)
[114.] 64. Viſio fit aſpectu, aut obtutu. 51 p 3.
Page: 73 (67)
[115.] 65. Viſio per aſpectum, fit per quemlibet pyramidis opticæ radium: per obtutum uerò fit per ſolum axem. 52 p 3.
Page: 73 (67)
[116.] 66. Obtut{us} iteratio alti{us} imprimit formas uiſibiles animo, certiores́ efficit. 58 p 3.
Page: 75 (69)
[117.] 67. E uiſibili ſæpi{us} uiſo remanet in animo generalis notio: qua quodlibet uiſibile ſimile per cipitur & cognoſcitur. 61 p 3. Idem 14 n.
Page: 75 (69)
[118.] 68. Eſſentia uiſibilis percipitur è ſpecieb{us} uifibilib{us}, beneficio formæ in animo reſiden-tis. 66 p 3.
Page: 76 (70)
[119.] 69. Diſtinctauiſio fit aut obtutu ſolo: aut obtutu & anticipata notione ſimul. 62 p 3.
Page: 76 (70)
[120.] 70. Obtut{us} fit in tempore. 56 p 3.
Page: 77 (71)
[121.] 71. Viſibile obtutu & antegreſſa cognitione ſimul, minore tempore percipitur, quàm ſolo ob-tutu. 64 p 3.
Page: 77 (71)
[122.] 72. Generales uiſibilis ſpecies citi{us} percipiuntur ſingularib{us}. 71 p 3.
Page: 78 (72)
[123.] 73. E uiſibilib{us} communib{us} alia alijs citi{us} percipiuntur. 72 p 3.
Page: 78 (72)
[124.] 74. Temp{us} obtut{us} pro ſpecierum uiſibilium uarietate uariat. 56 p 3.
Page: 79 (73)
[125.] 75. Viſio per anticipatam notionem & breuem obtutum, eſt incerta. 65 p 3.
Page: 79 (73)
[126.] 76. Vera uiſibilis forma percipitur obtutu: accurata conſideratione: & dilig enti omnium uiſibilium ſpecierum diſtinctione. 57 p 3.
Page: 80 (74)
[127.] ALHAZEN FILII ALHAYZEN OPTICAE LIBER TERTIVS.
Page: 81 (75)
[128.] PROOEMIVM LIBRI. CAP. 1. 1. Viſ{us} in perceptione uiſibilium aliquando allucinatur. 1 p 4.
Page: 81 (75)
[129.] DE IIS QVAE DEBENT PRAEPONI SERMONI in deceptionibus uiſus. Cap. II. 2. Axes pyramidum opticarum utriuſ uiſ{us} per centrum foraminis uueæ tranſeuntes, in uno uiſibilis puncto ſemper concurrunt: & ſunt perpendiculares ſuperficiei uiſ{us}. 32. 35 p 3.
Page: 82 (76)
[130.] 3. Sit{us} uiſibilis erga utrun uiſum eſt plerun ſit{us} ſimilis. Ita axes pyramidum optica-rum & lineæ ab utro uiſu ductæ ad cõcurſum duorum axιum, factũ in recta linea adutrun axem perpendiculari, ſunt æquales. 40. 42 p 3.
Page: 82 (76)
[131.] 4. Duærectæ lineæ ab utro uiſu ductæad concurſum duorum axium, factum in recta linea ad utrun axem obliqua, ſunt ferè inæquales. 41 p 3.
Page: 83 (77)
[132.] 5. E plurib. uiſibilib. ordinatim intraopticos axes diſpoſitis: remotiora incertè uidẽtur. 50 p 3.
Page: 83 (77)
[133.] 6. Si duæ rectæ lineæ à medio nerui cõmunis ſint contermi-nærectæ cõnectenti centra for aminum gyrineruorum cauo-rum: conſtituent triangulum æquicrurum. 30 p 3.
Page: 84 (78)
[134.] 7. Si recta linea ſit à medio nerui communis admedium rectæ lineæ connectentis centra fo-raminum gyrineruorum cauorum: erit ad ipſam perpendicularis. 33 p 3.
Page: 84 (78)
[135.] 8. Si axes, communis & duo optici, in uno uiſibilis puncto concurrant: erunt in eodem plano cum rectis, connectente centra foraminum gyrineruorum cauorum, & duab{us} à medio nerui communis connectenti conterminis. 34 p 3.
Page: 85 (79)
[136.] 9. Vtro uiſu uiſibile unum plerun uidetur. 28 p 3. Idem 27 n 1.
Page: 85 (79)
[137.] 10. Concurſiis axium opticorum in axe communifacit uiſionem certißimam: extrà, tantò certiorem, quantò axi propinquior fuerit. 44 p 3.
Page: 86 (80)
[138.] 11. Viſibile intra axes opticos ſitum: ueluni uiſui rectè, reliquo obliquè oppoſitum: uidetur geminum. 104.103 p 4.
Page: 87 (81)
[139.] 12. Viſibile aliàs unum: aliàs geminum uideri organo ostenditur. 108 p 4.
Page: 87 (81)
[140.] 13. Viſibile medio unius uiſus rectè, reliquo obliquè oppoſitum, uidetur geminum. 103 p 4. Idem II n.
Page: 89 (83)
< >
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          <p>
            <s xml:id="echoid-s14094" xml:space="preserve">
              <pb o="203" file="0209" n="209" rhead="OPTICAE LIBER VI."/>
            uiſum à duobus punctis arcus:</s>
            <s xml:id="echoid-s14095" xml:space="preserve"> quod eſt impoſsibile [& contra 29 n 5.</s>
            <s xml:id="echoid-s14096" xml:space="preserve">] Licet autẽ reflectatur pun-
              <lb/>
            ctum illud à puncto primùm ſumpto:</s>
            <s xml:id="echoid-s14097" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0209-01" xlink:href="fig-0209-01a" number="174">
                <variables xml:id="echoid-variables164" xml:space="preserve">d a b e h z g</variables>
              </figure>
              <figure xlink:label="fig-0209-02" xlink:href="fig-0209-02a" number="175">
                <variables xml:id="echoid-variables165" xml:space="preserve">a d b b g</variables>
              </figure>
            non tamen ũidetur, cum ſit in linea re
              <lb/>
            flexionis, quæ occultatur per præce-
              <lb/>
            dentia puncta.</s>
            <s xml:id="echoid-s14098" xml:space="preserve"> Et ita linea adiacens li-
              <lb/>
            neæ reflexionis non uidetur.</s>
            <s xml:id="echoid-s14099" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div484" type="section" level="0" n="0">
          <head xml:id="echoid-head433" xml:space="preserve" style="it">20. Si uiſ{us} ſit in ſuperficie inci-
            <lb/>
          dentiæ: imago lineæ rectæ infinitæ,
            <lb/>
          peripheriam circuli (qui eſt commu-
            <lb/>
          nis ſectio ſuperficierũ reflexionis &
            <lb/>
          ſpeculi ſphærici conuexi) ſiue tangen
            <lb/>
          tis, ſiue non, & ad uiſ{us} partemobli-
            <lb/>
          quatæ, nulla uidebitur. 55 p 6.</head>
          <p>
            <s xml:id="echoid-s14100" xml:space="preserve">SI uerò ſumatur linea declinata,
              <lb/>
            cuius declinatio ſit ex parte ui-
              <lb/>
            ſus, iacẽs ſub linea reflexionis, &
              <lb/>
            ſecans ipſam in puncto circuli Dico,
              <lb/>
            quòd nullũ punctum illius lineæ uide
              <lb/>
            bitur.</s>
            <s xml:id="echoid-s14101" xml:space="preserve"> Sumpto enim pũcto:</s>
            <s xml:id="echoid-s14102" xml:space="preserve"> ſi dicatur,
              <lb/>
            quòd punctum illud poſsit reflecti ab
              <lb/>
            aliquo puncto arcus, interiacentis lineam reflexionis, & lineam à centro uiſus ad centrum ſpeculi
              <lb/>
            ductam:</s>
            <s xml:id="echoid-s14103" xml:space="preserve"> & ducatur linea ab illo puncto ad punctũ arcus ſumptum:</s>
            <s xml:id="echoid-s14104" xml:space="preserve"> hæc ſecabit lineam reflexionis:</s>
            <s xml:id="echoid-s14105" xml:space="preserve">
              <lb/>
            & punctum ſectionis reflectetur ad uiſum, à duobus punctis arcus ſpeculi:</s>
            <s xml:id="echoid-s14106" xml:space="preserve"> quod eſt impoſsibile [&
              <lb/>
            contra 29 n 5.</s>
            <s xml:id="echoid-s14107" xml:space="preserve">] Si uerò dicatur, quòd punctum ſumptum in linea, reflectatur à puncto arcus circuli,
              <lb/>
            qui eſt ſub ipſa linea:</s>
            <s xml:id="echoid-s14108" xml:space="preserve"> erit impoſsibile:</s>
            <s xml:id="echoid-s14109" xml:space="preserve"> quia ille totus arcus occultatur à linea.</s>
            <s xml:id="echoid-s14110" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div485" type="section" level="0" n="0">
          <head xml:id="echoid-head434" xml:space="preserve" style="it">21. Si uiſ{us} ſit in ſuperficie incidentiæ: ιmago lιneæ rectæ infinitæ; peripheriam circuli (qui
            <lb/>
          eſt communis ſectio ſuperficierum, reflexionis & ſpeculi ſphærici conuexi) nec tangentis nec per
            <lb/>
          centrum ſecantis, & ad partem uιſuι oppoſitam obliquatæ, uidebitur curua. 56 p 6.</head>
          <p>
            <s xml:id="echoid-s14111" xml:space="preserve">SI uerò linea ſumpta nõ attingat circulum:</s>
            <s xml:id="echoid-s14112" xml:space="preserve"> poterit quidem uideri:</s>
            <s xml:id="echoid-s14113" xml:space="preserve"> ſed modicum eſt.</s>
            <s xml:id="echoid-s14114" xml:space="preserve"> Si uerò ſu-
              <lb/>
            matur linea declinata prædicta inter lineam reflexionis, & lineam per punctũ reflexionis pri-
              <lb/>
            mò ſumptum tranſeuntem ad centrum:</s>
            <s xml:id="echoid-s14115" xml:space="preserve"> poterit quidem uideri hæclinea:</s>
            <s xml:id="echoid-s14116" xml:space="preserve"> & imminuetur cur-
              <lb/>
            uitas imaginis huius lineæ, ſecundum quod magis acceſſerit ad lineã tranſeuntem ad centrum, per
              <lb/>
            punctum reflexionis.</s>
            <s xml:id="echoid-s14117" xml:space="preserve"> Si uerò ſumantur lineæ inter lineam ad centrũ
              <lb/>
              <figure xlink:label="fig-0209-03" xlink:href="fig-0209-03a" number="176">
                <variables xml:id="echoid-variables166" xml:space="preserve">a d f b ſ m e
                  <gap/>
                c z g</variables>
              </figure>
            tranſeuntem per punctum reflexionis:</s>
            <s xml:id="echoid-s14118" xml:space="preserve"> uidebuntur quidem, ſiue de-
              <lb/>
            clinatio earum ſit ex parte uiſus, ſiue non:</s>
            <s xml:id="echoid-s14119" xml:space="preserve"> & modus uiſus earũ, ſimi-
              <lb/>
            lis modo uiſus linearum inter lineam reflexionis & lineam ad cen-
              <lb/>
            trum tranſeuntem.</s>
            <s xml:id="echoid-s14120" xml:space="preserve"> Et hæc quidem intelligenda ſunt de lineis con-
              <lb/>
            currentibus in arcu circuli, qui apparet uiſui, id eſt, in arcu, qui inter-
              <lb/>
            iacet duas contingentes, ductas à centro uiſus ad circulum.</s>
            <s xml:id="echoid-s14121" xml:space="preserve"> Linearũ
              <lb/>
            autem concurrentium cum circulo in parte circuli occulta uiſui:</s>
            <s xml:id="echoid-s14122" xml:space="preserve"> ali-
              <lb/>
            qua erit æquidiſtans lineæ reflexionis:</s>
            <s xml:id="echoid-s14123" xml:space="preserve"> & illa quidem non uidebitur.</s>
            <s xml:id="echoid-s14124" xml:space="preserve">
              <lb/>
            Similiter conterminalis æquidiſtanti, quæ eſt ſub æquidiſtante, oc-
              <lb/>
            cultabitur:</s>
            <s xml:id="echoid-s14125" xml:space="preserve"> ſed conterminalis æquidiſtanti, ſupra ipſam exiſtens, po-
              <lb/>
            terit uideri.</s>
            <s xml:id="echoid-s14126" xml:space="preserve"> Si uerò ſumatur linea inter æquidiſtantes, nõ contermi-
              <lb/>
            nalis alicui earum:</s>
            <s xml:id="echoid-s14127" xml:space="preserve"> ſi fuerit eius declinatio ex parte uiſus, uidebitur:</s>
            <s xml:id="echoid-s14128" xml:space="preserve">
              <lb/>
            ſi ex alia parte, aliquando uidebitur, aliquãdo non Quoniam ſi à ter-
              <lb/>
            mino eius ducatur æquidiſtans lineæ reflexionis:</s>
            <s xml:id="echoid-s14129" xml:space="preserve"> ſi fuerit linea ſub
              <lb/>
            æquidiſtante:</s>
            <s xml:id="echoid-s14130" xml:space="preserve"> non uidebitur:</s>
            <s xml:id="echoid-s14131" xml:space="preserve"> ſi ſupra eã, uideri poterit.</s>
            <s xml:id="echoid-s14132" xml:space="preserve"> Si uerò lineæ
              <lb/>
            non concurrant cum circulo, aut ſecabunt lineam ductam à centro
              <lb/>
            uiſus ad cẽtrum ſpeculi:</s>
            <s xml:id="echoid-s14133" xml:space="preserve"> aut æquidiſtabunt ei.</s>
            <s xml:id="echoid-s14134" xml:space="preserve"> Si ſecet aliqua earum:</s>
            <s xml:id="echoid-s14135" xml:space="preserve">
              <lb/>
            linea illa aut ſecabit illam ex parte uiſus, id eſt, inter uiſum & ſpecu-
              <lb/>
            lum:</s>
            <s xml:id="echoid-s14136" xml:space="preserve"> aut ultra ſpeculũ.</s>
            <s xml:id="echoid-s14137" xml:space="preserve"> Si ultra:</s>
            <s xml:id="echoid-s14138" xml:space="preserve"> occultabitur linea illa, ſed forſan ap-
              <lb/>
            parebunt eius capita.</s>
            <s xml:id="echoid-s14139" xml:space="preserve"> Si uerò ſecet lineam uiſualem ex parte uiſus, apparebit quidem ſimiliter.</s>
            <s xml:id="echoid-s14140" xml:space="preserve"> Si
              <lb/>
            fuerit æquidιſtans lineæ uiſuali:</s>
            <s xml:id="echoid-s14141" xml:space="preserve"> poterit uideri.</s>
            <s xml:id="echoid-s14142" xml:space="preserve"> Omnium autem harum linearum imagines curuæ.</s>
            <s xml:id="echoid-s14143" xml:space="preserve">
              <lb/>
            Vιſu autem exiſtente in eadem ſuperficie cum centro ſpeculi & lineis uiſis, diminuta eſt apparẽtia:</s>
            <s xml:id="echoid-s14144" xml:space="preserve">
              <lb/>
            & quæ ſit, quæ manifeſtius apparet, eſt illa, quæ declinata eſt maxima declinatione, & illa uiſum re-
              <lb/>
            ſpiciente.</s>
            <s xml:id="echoid-s14145" xml:space="preserve"> Pari modo arcuum in his ſpeculis apparentium, & in eadem ſuperficie cum cẽtro ſpecu-
              <lb/>
            li, & uiſu exiſtẽtium, imagines quidẽ curuæ ſunt curuitate ſpeculũ reſpiciente.</s>
            <s xml:id="echoid-s14146" xml:space="preserve"> Hæc aũt intelligẽda
              <lb/>
            ſunt duplici uiſu exiſtẽte in eadẽ ſuperficie cũ cẽtro ſpeculi, & re uiſa.</s>
            <s xml:id="echoid-s14147" xml:space="preserve"> Si enim alter uiſus modicùm
              <lb/>
            declinetur, quò ad ipſum, alio modo res uiſa comprehendetur.</s>
            <s xml:id="echoid-s14148" xml:space="preserve"> Et uiſu exiſtente extra ſuperficiem
              <lb/>
            rei uiſæ & centrum ſpeculi, certior erit ipſius rei comprehenſio, quam exiſtente in ea.</s>
            <s xml:id="echoid-s14149" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div487" type="section" level="0" n="0">
          <head xml:id="echoid-head435" xml:space="preserve" style="it">22. Si uiſ{us} ſit in ſuperficie incidentiæ: imago lineæ rectæ infinitæ, quæ uel non concurrens
            <lb/>
          </head>
        </div>
      </text>
    </echo>
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