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-div1773" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s46327" xml:space="preserve">
              <pb o="391" file="0693" n="693" rhead="LIBER NONVS."/>
            uerſum ltaq;</s>
            <s xml:id="echoid-s46328" xml:space="preserve"> habebunt ſitum omnes iſtæ imagines.</s>
            <s xml:id="echoid-s46329" xml:space="preserve"> Quod eſt propoſitũ.</s>
            <s xml:id="echoid-s46330" xml:space="preserve"> Patet itaq;</s>
            <s xml:id="echoid-s46331" xml:space="preserve"> exhis quatuor
              <lb/>
            propoſitionibus, quòd lineæ rectæ quandoq;</s>
            <s xml:id="echoid-s46332" xml:space="preserve"> in his ſpeculis pyramidalibus concauis uidẽtur con-
              <lb/>
            uexæ:</s>
            <s xml:id="echoid-s46333" xml:space="preserve"> quandoq;</s>
            <s xml:id="echoid-s46334" xml:space="preserve"> concauæ:</s>
            <s xml:id="echoid-s46335" xml:space="preserve"> quandoq;</s>
            <s xml:id="echoid-s46336" xml:space="preserve"> rectæ:</s>
            <s xml:id="echoid-s46337" xml:space="preserve"> & quandoq;</s>
            <s xml:id="echoid-s46338" xml:space="preserve"> maiores:</s>
            <s xml:id="echoid-s46339" xml:space="preserve"> & quandoq;</s>
            <s xml:id="echoid-s46340" xml:space="preserve"> minores:</s>
            <s xml:id="echoid-s46341" xml:space="preserve"> & quãdo-
              <lb/>
            que æquales rebus uiſis:</s>
            <s xml:id="echoid-s46342" xml:space="preserve"> & ſunt omnes rectæ imagines difformem ſitum habentes, reſpectu ſitus
              <lb/>
            rerum, quarũ ſunt imagines.</s>
            <s xml:id="echoid-s46343" xml:space="preserve"> Et accidit in his ſpeculis, ſicut in alijs ſpeculis, numerari imagines ſe-
              <lb/>
            cundum numerum punctorum reflexionis:</s>
            <s xml:id="echoid-s46344" xml:space="preserve"> & fortè imagines eiuſdem rei diuerſarum erunt forma
              <lb/>
            rum ſecundum diuerſum ſitum ſuarum partium:</s>
            <s xml:id="echoid-s46345" xml:space="preserve"> quæ omnia ex pręmiſsis principijs poſſunt facili-
              <lb/>
            ter declarari.</s>
            <s xml:id="echoid-s46346" xml:space="preserve"> Hæc itaq;</s>
            <s xml:id="echoid-s46347" xml:space="preserve"> de regularibus ſpeculis ſufficiant ad præſens.</s>
            <s xml:id="echoid-s46348" xml:space="preserve"> Deinceps uerò in ſequẽtibus
              <lb/>
            huius libri ad tractatum quorũdam irregularium ſpeculorum & cõburentiũ ingeniũ cõuertemus.</s>
            <s xml:id="echoid-s46349" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1775" type="section" level="0" n="0">
          <head xml:id="echoid-head1315" xml:space="preserve" style="it">35. Poßibile eſt ſpeculum ex conuexo & concauo compoſitum fieri, in quo dextra apparent
            <lb/>
          dextra, & ſiniſtra ſiniſtra, & multa diuerſitas imagιnum occurrit. Euclides 30 th. catoptr. Pto
            <lb/>
          lemæus 3 th. 2 catoptr.</head>
          <p>
            <s xml:id="echoid-s46350" xml:space="preserve">Aſſumatur in illa magnitudine, qua quis conſtruere uoluerit tale ſpeculum, circulus, qui ſit a b g:</s>
            <s xml:id="echoid-s46351" xml:space="preserve">
              <lb/>
            & inſcribatur ei latus pentagoni inſcriptibilis eidem circulo per 11 p 4:</s>
            <s xml:id="echoid-s46352" xml:space="preserve"> quod ſit a b:</s>
            <s xml:id="echoid-s46353" xml:space="preserve"> & ſimiliter in-
              <lb/>
              <figure xlink:label="fig-0693-01" xlink:href="fig-0693-01a" number="826">
                <variables xml:id="echoid-variables803" xml:space="preserve">b e z a g z m h t f k l x o p a b g</variables>
              </figure>
            ſcribatur eidẽ circulo latus hexagoni per 15 p 4,
              <lb/>
            quod ſit b g:</s>
            <s xml:id="echoid-s46354" xml:space="preserve"> eritq́;</s>
            <s xml:id="echoid-s46355" xml:space="preserve"> per eádem 15 p 4 linea b g ę-
              <lb/>
            qualis ſemidiametro circuli.</s>
            <s xml:id="echoid-s46356" xml:space="preserve"> Et abſcindatur ab
              <lb/>
            illo circulo portio a e b, cuius arcus a b ք 28 p 3
              <lb/>
            eſt æqualis quintæ parti peripheriæ circuli.</s>
            <s xml:id="echoid-s46357" xml:space="preserve"> Et
              <lb/>
            ſimiliter abſcindatur ab eodem circulo portio
              <lb/>
            g z b, cuius arcus b g eſt æqualis ſextæ parti
              <lb/>
            circuli.</s>
            <s xml:id="echoid-s46358" xml:space="preserve"> Fiant quoq;</s>
            <s xml:id="echoid-s46359" xml:space="preserve"> formæ regulares ad quanti-
              <lb/>
            tatem illarum duarum portionum:</s>
            <s xml:id="echoid-s46360" xml:space="preserve"> quarum una
              <lb/>
            fiat ſecundum quantitatem portionis a e b, quæ
              <lb/>
            ſit concaua, ut eſt figura, quam deſcripſimus,
              <lb/>
            z h t f k m l:</s>
            <s xml:id="echoid-s46361" xml:space="preserve"> altera uerò facta ad quantitatem
              <lb/>
            portionis, quę eſt g z b, ſit conuexa, ut eſt fi-
              <lb/>
            gura x o p.</s>
            <s xml:id="echoid-s46362" xml:space="preserve"> Et aſſumatur petia uel pars ferri re-
              <lb/>
            ctangula, cuius longitudo ſit maior quàm am-
              <lb/>
            bę chordę a b, & b g, latitudo quoque ſit maior
              <lb/>
            quàm chorda b g:</s>
            <s xml:id="echoid-s46363" xml:space="preserve"> & incuruetur ferrũ taliter, ut
              <lb/>
            eius longitudo ſit conuexitatis portionis a e b,
              <lb/>
            ita ut ſuperficies cõcaua, quæ eſt k f t, ſibi extrin
              <lb/>
            ſecus applicetur:</s>
            <s xml:id="echoid-s46364" xml:space="preserve"> & eius latitudo ſit in parte lon
              <lb/>
            gitudinis reſiduæ concauitatis portionis g z b,
              <lb/>
            ita ut cóuexitas ſuperficiei x o p ſibi intrinſecus
              <lb/>
            applicetur.</s>
            <s xml:id="echoid-s46365" xml:space="preserve"> Taliter uerò fiat, ne forma cóuexita
              <lb/>
            tis impedimentum accipiat ex forma concaui-
              <lb/>
            tatis, ſed in eadem ſuperficie ſpeculi ipſarũ quę-
              <lb/>
            libet imprimatur:</s>
            <s xml:id="echoid-s46366" xml:space="preserve"> poliaturq́;</s>
            <s xml:id="echoid-s46367" xml:space="preserve"> ſpeculum ex parti-
              <lb/>
            bus ambabus:</s>
            <s xml:id="echoid-s46368" xml:space="preserve"> propter quod oportet ut lamina
              <lb/>
            ſpeculanda ſit conuenienter ſpiſſa, ut ex utra-
              <lb/>
            que parte ſalua diſpoſitione reliqua ualeat poli-
              <lb/>
            ri.</s>
            <s xml:id="echoid-s46369" xml:space="preserve"> Hoc itaque ſpeculum ſi ſuper ſedem uolubi-
              <lb/>
            lem ad hoc præparatam componatur, & ſuper
              <lb/>
            ipſam uoluatur, ita quòd nunc conuexa, nunc
              <lb/>
            concaua ſuperficies uiſui ſe offerat:</s>
            <s xml:id="echoid-s46370" xml:space="preserve"> tunc appa-
              <lb/>
            rebunt dextra dextra, & ſiniſtra ſiniſtra:</s>
            <s xml:id="echoid-s46371" xml:space="preserve"> & di-
              <lb/>
            ſtanti quaſi duobus cubitis apparet imago commenſurata & ſimilis ueræ formę:</s>
            <s xml:id="echoid-s46372" xml:space="preserve"> magis uerò diſtan
              <lb/>
            ti protenditur imago in anterius:</s>
            <s xml:id="echoid-s46373" xml:space="preserve"> propius uerò accedenti ad conuexam ſuperficiem ſpeculi, fit i-
              <lb/>
            mago penitus informis:</s>
            <s xml:id="echoid-s46374" xml:space="preserve"> & magis accedenti informitas plus augetur, & contraria ei, quod uidetur,
              <lb/>
            fit imago, magisq́;</s>
            <s xml:id="echoid-s46375" xml:space="preserve"> accedẽti prolixior apparet, & fit facies uidentis cõſimilis formæ equi:</s>
            <s xml:id="echoid-s46376" xml:space="preserve"> & ſemper
              <lb/>
            magis inclinato ſpeculo, imago apparet plus inclinata.</s>
            <s xml:id="echoid-s46377" xml:space="preserve"> Permutato quoque ſpeculo, imago quan-
              <lb/>
            doque habet caput ſurſum & pedes deorſum:</s>
            <s xml:id="echoid-s46378" xml:space="preserve"> & quandoque pedes ſurſum & caput deorſum:</s>
            <s xml:id="echoid-s46379" xml:space="preserve"> &
              <lb/>
            plus experientia, quàm ſcriptura, docebit imaginum diuerſitates:</s>
            <s xml:id="echoid-s46380" xml:space="preserve"> quia ſi connectantur duo ſpe-
              <lb/>
            cula ſphærica, quorum unum ſit concauum, reliquum conuexum, non moto etiam ſpeculo, ua-
              <lb/>
            riatur diſpoſitio imaginum.</s>
            <s xml:id="echoid-s46381" xml:space="preserve"> Propter reuerberationem enim formæ reflexæ ab uno ſpeculo in al-
              <lb/>
            terum, dextra apparebunt dextra, & ſiniſtra ſiniſtra:</s>
            <s xml:id="echoid-s46382" xml:space="preserve"> & in parte conuexa non mutabitur ſitus i-
              <lb/>
            maginis ſecundum ſurſum & deorſum:</s>
            <s xml:id="echoid-s46383" xml:space="preserve"> ſed in parte concaua uidebitur imago ſupercapitalis, ue-
              <lb/>
            lut antipodes.</s>
            <s xml:id="echoid-s46384" xml:space="preserve"> Cauſſa uerò omnium horum in ſimplicibus ſpeculis dicta eſt per præmiſſa:</s>
            <s xml:id="echoid-s46385" xml:space="preserve"> mo-
              <lb/>
            do quoq;</s>
            <s xml:id="echoid-s46386" xml:space="preserve"> tali in præmiſſo ſpeculo permiſcentur imaginies.</s>
            <s xml:id="echoid-s46387" xml:space="preserve"> Et ſi in eadem continuitate ſit ſpeculum
              <lb/>
            planum ipſis ſpeculis ſphęricis conuexis & cõcauis interpoſitum:</s>
            <s xml:id="echoid-s46388" xml:space="preserve"> uaria bitur imaginum quátitas:</s>
            <s xml:id="echoid-s46389" xml:space="preserve">
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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