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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[Item 1.]
[2.] Optic ae THE SAVRVS. ALHAZENI ARABIS libri ſeptem, nuncprimùm editi. EIVSDEM liber DE CREPVSCVLIS & Nubium aſcenſionibus. ITEM VITELLONIS THVRINGOPOLONI LIBRI X. Omnes inſtaurati, figuris illuſtrati & aucti, adiectis etiam in Alhazenum commentarijs, A' Federico Risnero.
[3.] Cum priuilegio Cæſareo & Regis Galliæ ad ſexennium BASILE AE, PER EPISCOPIOS. M D LXXII.
[4.] Triplicis uiſus, directi, reflexi & refracti, de quo optica diſputat, ar-gumenta.
[5.] FEDERICI RISNE-RI IN ALHAZENI ARABIS OPTICAM PRAEFATIO A D IL LVSTRISSIMAM REGINAM CA-tharinam Mediceam, matrem regis Galliæ Caroli noni.
[6.] CANDIDO LECTORI
[7.] ALHAZEN FILII ALHAYZEN OPTICAE LIBER PRIMVS.
[8.] QVOD LVX PER SE, ET COLORES ILLVMINATI OPE-renturin uiſum aliquam operationem. Cap. 1. 1. Lux per ſe, & color illuminat{us} feriunt oculos. Vitell. in hypotheſ. 6. 16 p 3.
[9.] QVOD LVX VEHEMENS OCCVLTAT QVAEDAM VI-ſibilia quæ lux debilis manifeſtat: & contrà. Cap. 2. 2. Lux uehemens obſcur at quædam uiſibilia, quæ lux debilis illuſtrat: & contrà. 28. 97. 109. 150. 155. 156 p 4.
[10.] QVOD COLORES CORPORVM DIVERSIFICENTVR APVD VI-ſum ſecundum diuerſitatem lucium ordentium ſuper ipſos. Cap. 3. 3. Color uariatur pro lucis qualitate. 1 p 3.
[11.] DE COMPOSITIONE OCVLI, FORMA ET SI-tu. Caput quartum. 4. Ortus & principium oculi exiſtit è cerebro: & conſtat è tribus humori-bus & quatuor tunicis. 4 p 3.
[12.] 5. In toti{us} oculi ſeu motu ſeu quiete, ſit{us} partium ſtabilis permanet. 25 p 3.
[13.] 6. Ocul{us} tot{us} & ſpher a uuea centris differunt: & oculi centrum ect alti{us}. 8 p 3.
[14.] 7. Rect a connectens centra ſphær arum corneæ & uueæ, continuata tranſit per centrum for aminis uueæ, & medium caui nerui optici. 9 p 3.
[15.] 8. Centrum ſphæræ uueæ eſt inferi{us} centris reliquarum oculi partium. 8 p 3.
[16.] 9. Recta connectẽs centra ſphærarũ cryſtallinæ & uueæ, cõtinuata cadit in centrũ circuli cõglutinãtis cryſtallinã & uitreã ſphær {as} cũ uuea: & eſt ad ipſum perpendicularis. 10 p 3.
[17.] 10. Centrum ſphæræ cryſtallinæ alti{us} eſt centro ſphæræ uitreæ. 11 p 3.
[18.] 11. Rect a connectens centra ſphær arum & uueæ, continuata cadit in centrum ui-treæ, & medium cauinerui optici. 12 p 3.
[19.] 12. Centra ſphær arum toti{us} oculi, cryſtallinæ, utriuſ ſuperficiei corneæ, & con-uexæ humoris albuginei, eſt unum punctum. 7 p 3.
[20.] 13. In toti{us} oculi ſeu motu ſeu quiete ſit{us} partium ſtabilis permanet. 25 p 3. Idem 9 n.
[21.] DE QVALITATE VISIONIS, ET AB ILLA DE-pendentibus. Cap. 5. 14. Viſio fit radijs à uiſibili extrinſec{us} ad uiſum manantib{us}. 6 p 3.
[22.] 15. Viſ{us} è ſingulis ſuæ ſuperficiei punctis ſingula uiſibilis punct a uidet. 17. 18 p 3.
[23.] 16. Humor cryſtallin{us} eſt præcipuum organum facult atis opticæ. 4. 18 p 3.
[24.] 17. Lux perpendicularis penetr at per qualibet diuerſa media: obliqua refringitur. 42. 43. 44. 45. 47 p 2.
[25.] 18. Viſio diſtincta fit rectis lineis à uiſibili ad ſuperficiem uiſ{us} perpẽdicularibus. Ita ſin-gula uiſibilis punct a eundem obtinent ſitum in ſuperficie uiſ{us}, quem in uiſibili. 17 p 3.
[26.] 19. Viſio fit per pyramidem, cui{us} uertex eſt in uiſu, baſis in uiſibili. 18. 21. 22 p 3.
[27.] 20. Oculus & ſphæra cryſtallina habent idem centrum. 7 p 3. Idem 12 n.
[28.] 21. Viſibile uiſui oppoſitum uidetur. 2 p 3.
[29.] 22. Viſibile per medium perſpicuum uidetur. 13 p 3.
[30.] 23. Viſio non fit radijs à uiſu emißis. s p 3.
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        <div xml:id="echoid-div331" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s8534" xml:space="preserve">
              <pb o="143" file="0149" n="149" rhead="OPTICAE LIBER V."/>
            ſecet in puncto d:</s>
            <s xml:id="echoid-s8535" xml:space="preserve"> & ducatur linea a d:</s>
            <s xml:id="echoid-s8536" xml:space="preserve"> quæ ſecabit neceſſariò circũlum.</s>
            <s xml:id="echoid-s8537" xml:space="preserve"> Si enim contingeretin
              <lb/>
            puncto a:</s>
            <s xml:id="echoid-s8538" xml:space="preserve"> eſſet æquidiſtans b g, & nunquam concurreret cum ea.</s>
            <s xml:id="echoid-s8539" xml:space="preserve"> [Nam ex theſi g a, b a æ-
              <lb/>
            quantur.</s>
            <s xml:id="echoid-s8540" xml:space="preserve"> Itaque ſemidiameter à centro ad a ducta, efficiet per 8 p.</s>
            <s xml:id="echoid-s8541" xml:space="preserve"> 10 d 1 angulos cum b g rectos.</s>
            <s xml:id="echoid-s8542" xml:space="preserve">
              <lb/>
            Similiter angulus lineæ d a tãgentis & ſemidiametri rectus eſt per 18 p 3:</s>
            <s xml:id="echoid-s8543" xml:space="preserve"> ergo per 28 p 1 b d, a d eſ-
              <lb/>
            ſent parallelæ:</s>
            <s xml:id="echoid-s8544" xml:space="preserve"> quæ tamen concurrunt in puncto d, è fabricatione.</s>
            <s xml:id="echoid-s8545" xml:space="preserve">] Secet ergo in puncto h:</s>
            <s xml:id="echoid-s8546" xml:space="preserve"> & du-
              <lb/>
            catur linea g h.</s>
            <s xml:id="echoid-s8547" xml:space="preserve"> Palàm [per 22 p 3] cum a b g h ſit quadrangulum intra circulum:</s>
            <s xml:id="echoid-s8548" xml:space="preserve"> a b g, a h g an-
              <lb/>
            gulos oppoſitos ualere duos rectos:</s>
            <s xml:id="echoid-s8549" xml:space="preserve"> ſed [per 5 p 1] a g b eſt æqualis angulo a b g, cum reſpiciant
              <lb/>
            æqualia latera ex hypotheſi.</s>
            <s xml:id="echoid-s8550" xml:space="preserve"> Erit igitur angulus a h g æqualis angulo d g a:</s>
            <s xml:id="echoid-s8551" xml:space="preserve"> [per 13 p 1] & angu-
              <lb/>
            lus h a g communis triangulo totali a d g, & partiali a h g:</s>
            <s xml:id="echoid-s8552" xml:space="preserve"> reſtat ergo [per 32 p 1] ut angulus
              <lb/>
            h d g ſit æqualis angulo h g a:</s>
            <s xml:id="echoid-s8553" xml:space="preserve"> & triangulum ſimile triangulo [per 4 p.</s>
            <s xml:id="echoid-s8554" xml:space="preserve"> 1 d 6.</s>
            <s xml:id="echoid-s8555" xml:space="preserve">] Quare proportio
              <lb/>
            d a ad a g, ſicut a g ad a h:</s>
            <s xml:id="echoid-s8556" xml:space="preserve"> ergo [per 17 p 6] quod fit ex ductu d a in a h, eſt æquale quadrato a g:</s>
            <s xml:id="echoid-s8557" xml:space="preserve">
              <lb/>
            Sed [per 15 d 1] d a eſt æqualis t a:</s>
            <s xml:id="echoid-s8558" xml:space="preserve"> igitur [per 1 ax] eſt æqualis q z:</s>
            <s xml:id="echoid-s8559" xml:space="preserve"> & erit a h æqualis e z:</s>
            <s xml:id="echoid-s8560" xml:space="preserve"> [quia
              <lb/>
            è prima fabricatione oblongum comprehenſum ſub q z & e z æquatur quadrato a g:</s>
            <s xml:id="echoid-s8561" xml:space="preserve"> cui æquale o-
              <lb/>
            ſtenſum eſt oblongum comprehenſum ſub d a & a h:</s>
            <s xml:id="echoid-s8562" xml:space="preserve"> & d a æquaturipſi q z] & [per 3 ax] d h æqua-
              <lb/>
            lis q e:</s>
            <s xml:id="echoid-s8563" xml:space="preserve"> quæ eſt data linea.</s>
            <s xml:id="echoid-s8564" xml:space="preserve"> Et ita eſt propoſitum.</s>
            <s xml:id="echoid-s8565" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div333" type="section" level="0" n="0">
          <head xml:id="echoid-head336" xml:space="preserve" style="it">33. À
            <unsure/>
          puncto dimidiatæ peripheriæ non medio, ducere lineam rectam: ut ſegmentum ei{us}
            <lb/>
          conterminum continuatæ diametro, æquetur datæ lineæ rectæ. 130 p 1.</head>
          <p>
            <s xml:id="echoid-s8566" xml:space="preserve">SI uerò a b & a g non ſint æquales:</s>
            <s xml:id="echoid-s8567" xml:space="preserve"> protrahatur [per 31 p 1] à puncto g linea æquidiſtans a b:</s>
            <s xml:id="echoid-s8568" xml:space="preserve">
              <lb/>
            quæ ſit g n:</s>
            <s xml:id="echoid-s8569" xml:space="preserve"> & ſumatur linea, quæcunque ſit:</s>
            <s xml:id="echoid-s8570" xml:space="preserve"> z t:</s>
            <s xml:id="echoid-s8571" xml:space="preserve"> & [per 23 p 1] ſuper punctum z fiat angulus ę-
              <lb/>
            qualis angulo a g d per lineam z f:</s>
            <s xml:id="echoid-s8572" xml:space="preserve"> & [per 31 p 1] ducatur à puncto t linea æquidiſtans z f:</s>
            <s xml:id="echoid-s8573" xml:space="preserve"> & ſit
              <lb/>
            t m:</s>
            <s xml:id="echoid-s8574" xml:space="preserve"> & [per 23 p 1] ex angulo t z f ſecetur angulus æqualis angulo d g n per lineam z m.</s>
            <s xml:id="echoid-s8575" xml:space="preserve"> Hæc
              <lb/>
              <figure xlink:label="fig-0149-01" xlink:href="fig-0149-01a" number="65">
                <variables xml:id="echoid-variables55" xml:space="preserve">k t o z m u y f c l z</variables>
              </figure>
              <figure xlink:label="fig-0149-02" xlink:href="fig-0149-02a" number="66">
                <variables xml:id="echoid-variables56" xml:space="preserve">q d
                  <gap/>
                g e a b</variables>
              </figure>
            igitur linea neceſſariò cõcurrit cum
              <lb/>
            t m:</s>
            <s xml:id="echoid-s8576" xml:space="preserve"> [per lemma Procli ad 29 p 1]
              <lb/>
            cum ſit inter æquidiſtantes.</s>
            <s xml:id="echoid-s8577" xml:space="preserve"> Sit pun-
              <lb/>
            ctum concurſus m:</s>
            <s xml:id="echoid-s8578" xml:space="preserve"> reſtat ergo [per
              <lb/>
            3 ax] angulus m z f æqualis angu-
              <lb/>
            lo a g n.</s>
            <s xml:id="echoid-s8579" xml:space="preserve"> Et à puncto t ducatur li-
              <lb/>
            nea æquidiſtans lineæ z m:</s>
            <s xml:id="echoid-s8580" xml:space="preserve"> [per 31
              <lb/>
            p 1] quæ ſit t o:</s>
            <s xml:id="echoid-s8581" xml:space="preserve"> quæ quidem neceſſa-
              <lb/>
            riò concurret cum f z:</s>
            <s xml:id="echoid-s8582" xml:space="preserve"> [per lemma
              <lb/>
            Procli ad 29 p 1] & ſit concurſus in
              <lb/>
            puncto k:</s>
            <s xml:id="echoid-s8583" xml:space="preserve"> & ſumatur [per 12 p 6] li-
              <lb/>
            nea, cuius proportio ad lineam z t, ſi-
              <lb/>
            cut b g ad q e lineam datam:</s>
            <s xml:id="echoid-s8584" xml:space="preserve"> & ſit
              <lb/>
            i.</s>
            <s xml:id="echoid-s8585" xml:space="preserve"> Deinde fiat ſuper punctum m ſe-
              <lb/>
            ctio pyramidalis, quemadmodũ do-
              <lb/>
            cet Apollonius in libro ſecundo de
              <lb/>
            pyramidalibus, propoſitiõe quarta:</s>
            <s xml:id="echoid-s8586" xml:space="preserve">
              <lb/>
            & ſit u c m:</s>
            <s xml:id="echoid-s8587" xml:space="preserve"> quæ quidem ſectio non
              <lb/>
            ſecat lineas k o, k f:</s>
            <s xml:id="echoid-s8588" xml:space="preserve"> & in hac ſectione
              <lb/>
            ducatur linea æqualis lineę i:</s>
            <s xml:id="echoid-s8589" xml:space="preserve"> ſcilicet
              <lb/>
            m c:</s>
            <s xml:id="echoid-s8590" xml:space="preserve"> & producatur uſque ad lineas k t, k f:</s>
            <s xml:id="echoid-s8591" xml:space="preserve"> & ſint puncta ſectio num o, l.</s>
            <s xml:id="echoid-s8592" xml:space="preserve"> Igitur, ſicut ibidem [8 th 2
              <lb/>
            coni conicorum] probatur:</s>
            <s xml:id="echoid-s8593" xml:space="preserve"> erit o m æqualis c l:</s>
            <s xml:id="echoid-s8594" xml:space="preserve"> & à puncto t ducatur linea æquidiſtans c m:</s>
            <s xml:id="echoid-s8595" xml:space="preserve"> [per
              <lb/>
            31 p 1,] quæ ſit t f:</s>
            <s xml:id="echoid-s8596" xml:space="preserve"> & [per 23 p 1] ſuper punctum a fiat angulus æqualis angulo z f t per lineam a n
              <lb/>
            d.</s>
            <s xml:id="echoid-s8597" xml:space="preserve"> Palàm, quòd hæc linea concurret cum g d:</s>
            <s xml:id="echoid-s8598" xml:space="preserve"> cum angulus a g n ſit ęqualis f z m angulo:</s>
            <s xml:id="echoid-s8599" xml:space="preserve"> [per con-
              <lb/>
            cluſionem] & angulus g a n angulo z f t [per fabricationem:</s>
            <s xml:id="echoid-s8600" xml:space="preserve"> & totus angulus f z t æquatus ſit toti
              <lb/>
            angulo d g a:</s>
            <s xml:id="echoid-s8601" xml:space="preserve"> & per 32 p 1 anguli ad z & f ſint minores duobus rectis.</s>
            <s xml:id="echoid-s8602" xml:space="preserve"> Ergo anguli ad g & a ipſis æ-
              <lb/>
            quales, minores erunt duobus rectis.</s>
            <s xml:id="echoid-s8603" xml:space="preserve"> Itaque per 11 ax.</s>
            <s xml:id="echoid-s8604" xml:space="preserve"> g d, a d concurrent.</s>
            <s xml:id="echoid-s8605" xml:space="preserve">] Igitur a d linea aut tan-
              <lb/>
            get circulum:</s>
            <s xml:id="echoid-s8606" xml:space="preserve"> aut ſecabit ipſum.</s>
            <s xml:id="echoid-s8607" xml:space="preserve"> Quoniam ſi non tetigerit, & arcus a b fuerit maior arcu a g:</s>
            <s xml:id="echoid-s8608" xml:space="preserve"> ſeca-
              <lb/>
            bit arcum a b:</s>
            <s xml:id="echoid-s8609" xml:space="preserve"> & ſi a b fuerit minor:</s>
            <s xml:id="echoid-s8610" xml:space="preserve"> ſecabit arcum a g.</s>
            <s xml:id="echoid-s8611" xml:space="preserve"> Tangat igitur in puncto a.</s>
            <s xml:id="echoid-s8612" xml:space="preserve"> Cum igitur [per
              <lb/>
            fabricationem] angulus g a n ſit æqualis angulo z f t, & angulus a g n angulo f z y:</s>
            <s xml:id="echoid-s8613" xml:space="preserve"> erit [per
              <lb/>
            32 p 1] tertius tertio æqualis:</s>
            <s xml:id="echoid-s8614" xml:space="preserve"> & erit triangulum a g n ſimile triangulo z f y.</s>
            <s xml:id="echoid-s8615" xml:space="preserve"> Similiter cum [per
              <lb/>
            fabricationem] a g d ſit æqualis angulo f z t:</s>
            <s xml:id="echoid-s8616" xml:space="preserve"> erit [per 32 p 1.</s>
            <s xml:id="echoid-s8617" xml:space="preserve"> 4 p.</s>
            <s xml:id="echoid-s8618" xml:space="preserve"> 1 d 6] triangulum a g d ſimile
              <lb/>
            triangulo f z t.</s>
            <s xml:id="echoid-s8619" xml:space="preserve"> Igitur quæ eſt proportio a n ad a g, ea eſt proportio f y ad f z:</s>
            <s xml:id="echoid-s8620" xml:space="preserve"> & quæ eſt propor-
              <lb/>
            tio a g ad g d, ea eſt f z ad z t.</s>
            <s xml:id="echoid-s8621" xml:space="preserve"> Quare [per 22 p 5] quæ eſt proportio a n ad g d, ea eſt f y ad
              <lb/>
            z t.</s>
            <s xml:id="echoid-s8622" xml:space="preserve"> Verùm cum [per fabricationem] t m ſit æquidiſtans f l, & f t ſit æquidiſtans l m:</s>
            <s xml:id="echoid-s8623" xml:space="preserve"> eſt
              <gap/>
            per
              <lb/>
            34 p 1] f t æqualis l m.</s>
            <s xml:id="echoid-s8624" xml:space="preserve"> Quare [per 2 ax] erit æqualis c o:</s>
            <s xml:id="echoid-s8625" xml:space="preserve"> cum [per 8 th 2 conicorum Apol-
              <lb/>
            lonij] m o ſit æqualis l c:</s>
            <s xml:id="echoid-s8626" xml:space="preserve"> ſed [per 34 p 1] m o eſt æqualis y t:</s>
            <s xml:id="echoid-s8627" xml:space="preserve"> cum [per fabricationem] ſit ipſt
              <lb/>
            æquidiſtans, & y m æquidiſtans t o.</s>
            <s xml:id="echoid-s8628" xml:space="preserve"> Reſtat ergo [per 3 ax] f y æqualis c m:</s>
            <s xml:id="echoid-s8629" xml:space="preserve"> ſed [per fabrica-
              <lb/>
            tionem] c m eſt æqualis i.</s>
            <s xml:id="echoid-s8630" xml:space="preserve"> Quare [per 1 ax] f y eſt æqualis i:</s>
            <s xml:id="echoid-s8631" xml:space="preserve"> ſed [per fabricationem] propor-
              <lb/>
            tio i [id eſt, per 7 p 5 f y] ad z t, ſicut b g ad e q.</s>
            <s xml:id="echoid-s8632" xml:space="preserve"> Igitur [per 11 p 5] proportio a n ad g d, ſi-
              <lb/>
            cut b g ad e q.</s>
            <s xml:id="echoid-s8633" xml:space="preserve"> Verùm angulus g a n eſt æqualis angulo g b a:</s>
            <s xml:id="echoid-s8634" xml:space="preserve"> ſicut probat Euclides in ter-
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>