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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        <div xml:id="echoid-div1159" type="section" level="0" n="0">
          <pb o="150" file="0452" n="452" rhead="VITELLONIS OPTICAE"/>
        </div>
        <div xml:id="echoid-div1161" type="section" level="0" n="0">
          <head xml:id="echoid-head921" xml:space="preserve" style="it">73. Viſu hemiſphærio concauo appropinquante, minus ſuperficiei ſphæræ uidebitur: apparet
            <lb/>
          autem plus uideri.</head>
          <p>
            <s xml:id="echoid-s29079" xml:space="preserve">Hęc poteſt demonſtrari, ſicut & 67 huius, de ſphæra cõuexa eſt demonſtrata:</s>
            <s xml:id="echoid-s29080" xml:space="preserve"> eſt enim per omnia
              <lb/>
            idem hinc inde demonſtrandi modus.</s>
            <s xml:id="echoid-s29081" xml:space="preserve"> Vnde hic ſphæra concaua figuretur, ut illic conuexa, & ſub
              <lb/>
            eiſdem literis conſignetur figuratio totalis, & per eadem concludetur.</s>
            <s xml:id="echoid-s29082" xml:space="preserve"> Et hæc quidem de uiſione
              <lb/>
            ſphærarum dicta ſunt, ſuperficie bus ipſarum oppoſitis uiſui totaliter exiſtentibus luminoſis per ſe,
              <lb/>
            uel illuminatis aliun de:</s>
            <s xml:id="echoid-s29083" xml:space="preserve"> quoniam hoc non exiſtente, licet in ſphærarum ſuperficiebus permaneat
              <lb/>
            dictorum modorum uiſibilitas, non tam en actu uidebuntur, niſi luminis interuentu, ut patet per 1
              <lb/>
            th.</s>
            <s xml:id="echoid-s29084" xml:space="preserve"> 3 huius, & ſecundum diuerſitatem lumin oſitatis in partibus ſuperficiei ſphærarum, quæ uiden-
              <lb/>
            tur, nouæ paſsiones uiſibus generantur, quales ſunt hæ, quas nunc intendimus explicare.</s>
            <s xml:id="echoid-s29085" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1162" type="section" level="0" n="0">
          <head xml:id="echoid-head922" xml:space="preserve" style="it">74. Diametro ſphæræ uiſæ illuminatæ maiore diſtantia oculorum exiſtente, & diametro ſphæ
            <lb/>
          ræ illuminantis eidem æquali uel maiore, circulo́ baſis pyr amidis uiſionis æquidiſtante circulo
            <lb/>
          baſis pyr amidis illuminationis uel ipſum intrinſecus contingente: tota ſuperficies baſis pyrami-
            <lb/>
          dis uiſionis illuminata uiſibus occurrit: uidetur autem in maiori diſtantia quaſi plana.</head>
          <p>
            <s xml:id="echoid-s29086" xml:space="preserve">Patet enim per 26 uel 27 th.</s>
            <s xml:id="echoid-s29087" xml:space="preserve"> 2 huius, quoniam tanta exiſtente quantitate diametrorum iſtorum
              <lb/>
            corporum, ut proponitur:</s>
            <s xml:id="echoid-s29088" xml:space="preserve"> tunc baſis pyramidis illuminationis aut eſt circulus magnus ſphæræ illu
              <lb/>
            minatæ, aut æquidiſtans ei.</s>
            <s xml:id="echoid-s29089" xml:space="preserve"> Circulus autem, qui eſt baſis pyramidis uiſionis, ut patet per 70 huius,
              <lb/>
            ſemper eſt minor circulo magno ſphęrę uiſę, quoniam, ut patet ex hypotheſi, diameter ſphęræ uiſæ
              <lb/>
            eſt maior quàm diſtantia oculorum.</s>
            <s xml:id="echoid-s29090" xml:space="preserve"> Si ergo circũferentia circuli minoris ſit ęquidiſtans circum-
              <lb/>
            ferentiæ circuli maioris:</s>
            <s xml:id="echoid-s29091" xml:space="preserve"> tunc per 68 th.</s>
            <s xml:id="echoid-s29092" xml:space="preserve"> 1 huius, centra duorum illorum circulorum in eadem ſphæ-
              <lb/>
            rę diametro conſiſtunt, & tota baſis pyramidis uiſionis occurrit uiſibus, quia tota eſt illuminata:</s>
            <s xml:id="echoid-s29093" xml:space="preserve"> ui-
              <lb/>
            detur autem ſuperficies plana per 65 huius.</s>
            <s xml:id="echoid-s29094" xml:space="preserve"> Et hoc proponebatur.</s>
            <s xml:id="echoid-s29095" xml:space="preserve"> Sed etiam ſi centra iſtorum circu
              <lb/>
            lorum uſq;</s>
            <s xml:id="echoid-s29096" xml:space="preserve"> ad punctum contactus circumferentiarum mutentur, quandiu unus circulus alium non
              <lb/>
            ſecat, ſemper tota baſis pyramidis uiſionis uidetur illuminata:</s>
            <s xml:id="echoid-s29097" xml:space="preserve"> & lumen in ſphæræ uiſę ſuperficie ui
              <lb/>
            detur ſemper circulare, & tota baſis pyramidis illuminata:</s>
            <s xml:id="echoid-s29098" xml:space="preserve"> plus tamen tenebreſcit baſis pyramidis
              <lb/>
            uiſionis ad illam partem, ubi fit contactus illorum circulorum per 21 th 3 huius.</s>
            <s xml:id="echoid-s29099" xml:space="preserve"> Patet ergo propo-
              <lb/>
            ſitum.</s>
            <s xml:id="echoid-s29100" xml:space="preserve"> Et quod hic de duobus oculis oſtenſum eſt, euidentius patet, ſi uiſio tantùm uno fiat ocu-
              <lb/>
            lo, per 66 huius.</s>
            <s xml:id="echoid-s29101" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1163" type="section" level="0" n="0">
          <head xml:id="echoid-head923" xml:space="preserve" style="it">75. Si diametro ſphæræ uiſæ illuminatæ maiore diſtantia oculorũ exiſtente, diametro́ ſphæ-
            <lb/>
          ræ illuminantis eidem æquali uel maiore, baſis pyramidis uiſionis inter ſecet baſim pyramidis il-
            <lb/>
          luminationis, it a ut ambo centra baſium ſint ſub ſuperficie communis ſectionis: erit illa commu-
            <lb/>
          nis ſectio pars ſuperficiei ſphæricæ irregularis: uidebitur́ ſuperficies plana gibberoſa, ut duabus
            <lb/>
          curuis lineis inæqualis quantitatis & curuit atis contenta.</head>
          <p>
            <s xml:id="echoid-s29102" xml:space="preserve">Imaginentur enim centra baſium (quę per pręcedentem in eadem diametro ſphęrę uiſę fore diſ-
              <lb/>
            ponuntur) tantùm ab inuicem elongari, ut circuli baſium ſe ſecent quantumcunq;</s>
            <s xml:id="echoid-s29103" xml:space="preserve">, dum tamen cẽ-
              <lb/>
            tra ambarum baſium ſub ſuperficie, quæ eſt communis ambabus illis baſibus, remaneant:</s>
            <s xml:id="echoid-s29104" xml:space="preserve"> tunc illa
              <lb/>
            communis ſectio erit pars ſuperficiei ſphęricæ figurę irregularis:</s>
            <s xml:id="echoid-s29105" xml:space="preserve"> quoniam, ut patet per 26 uel per
              <lb/>
            27 th.</s>
            <s xml:id="echoid-s29106" xml:space="preserve"> 2 huius, & ex 70 huius, & ut oſtenſum eſt in præmiſſa proxima, arcus circuli baſis pyramidis
              <lb/>
            illuminationis eſt maior arcu circuli baſis pyramidis uiſionis:</s>
            <s xml:id="echoid-s29107" xml:space="preserve"> & ſi illius ſuperficiei acciperetur pun
              <lb/>
            ctus medius, lineæ ab illo puncto ad peripherias arcuum ductę, eſſent inęquales.</s>
            <s xml:id="echoid-s29108" xml:space="preserve"> Videtur autem ſu-
              <lb/>
            perficies illa eſſe plana per 65 huius:</s>
            <s xml:id="echoid-s29109" xml:space="preserve"> & erit gibberoſa, ut duabus præmiſsis curuis lineis in æqualis
              <lb/>
            quantitatis & curuitatis contenta:</s>
            <s xml:id="echoid-s29110" xml:space="preserve"> quoniã arcus circuli pyramidis uiſionis eſt curuior & maior por
              <lb/>
            tio ſuę circumferentię, quàm arcus circuli baſis pyramidis ιlluminationis ſit portio ſuę circumferẽ-
              <lb/>
            tię.</s>
            <s xml:id="echoid-s29111" xml:space="preserve"> Quod accidit propter inęqualitatem circulorum.</s>
            <s xml:id="echoid-s29112" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s29113" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1164" type="section" level="0" n="0">
          <head xml:id="echoid-head924" xml:space="preserve" style="it">76. Baſi pyramidis uiſionis ſphæræ interſecante baſim pyramidis illuminationis, ita quòd
            <lb/>
          ipſorum axes angulum rectum contineant: communis earum ſectio est quarta ſuperficiei
            <lb/>
          ſphæricæ: uidetur autem in maiori diftantia plana ſuperficies una recta linea & ſemicircu-
            <lb/>
          lo contenta.</head>
          <p>
            <s xml:id="echoid-s29114" xml:space="preserve">Quòd illuminatio cuiuslibet ſphæræ fiat ſecundum pyramidem, cuius baſis in ſuperficie ſphærę
              <lb/>
            illuminatę eſt circulus, hoc patet per 26 & 27 & 28 th.</s>
            <s xml:id="echoid-s29115" xml:space="preserve"> 2 huius:</s>
            <s xml:id="echoid-s29116" xml:space="preserve"> quòd etiam baſis pyramidis uiſionis
              <lb/>
            omnis ſphęrę ſit circulus, patet per 66 & 68 & 69 & & 70 huius.</s>
            <s xml:id="echoid-s29117" xml:space="preserve"> Et quoniam axes iſtarum pyramidũ
              <lb/>
            ex hypotheſi producti ad inuicem angulũ rectũ continent:</s>
            <s xml:id="echoid-s29118" xml:space="preserve"> tunc patet per 33 p 6, quòd ab illorũ axiũ
              <lb/>
            cõcurſus puncto ſecũdũquantitatẽ ſemidiametri ſphæræ uiſę circũducto circulo, interiacebit quar
              <lb/>
            ta circuli inter axes.</s>
            <s xml:id="echoid-s29119" xml:space="preserve"> Et quoniã uterq;</s>
            <s xml:id="echoid-s29120" xml:space="preserve"> axiũ eſt per pendicularis ſuper ſuperficiẽ ſphæræ illuminatæ
              <lb/>
            uiſæ, palã per 111 th.</s>
            <s xml:id="echoid-s29121" xml:space="preserve"> 1 huius, quòd uterq;</s>
            <s xml:id="echoid-s29122" xml:space="preserve"> axiũ tranſibit per centrum illius ſphęrę:</s>
            <s xml:id="echoid-s29123" xml:space="preserve"> punctus itaq;</s>
            <s xml:id="echoid-s29124" xml:space="preserve"> inter-
              <lb/>
            ſectionis axium eſt in cẽtro illius ſphæræ:</s>
            <s xml:id="echoid-s29125" xml:space="preserve"> & ſolũ ille punctus, qui eſt centrũ ſphærę, ambobus axib.</s>
            <s xml:id="echoid-s29126" xml:space="preserve">
              <lb/>
            erit cõmunis.</s>
            <s xml:id="echoid-s29127" xml:space="preserve"> Axibus itaq;</s>
            <s xml:id="echoid-s29128" xml:space="preserve"> interiacet quarta magni circuli ſphæræ ęqualiter diſtãtis à duobus pun-
              <lb/>
            ctis duarũ interſectionũ circulorũ baſis pyramidis illuminationis & baſis pyramidis uiſionis:</s>
            <s xml:id="echoid-s29129" xml:space="preserve"> cõmu
              <lb/>
            </s>
          </p>
        </div>
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    </echo>
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