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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[451.] 36. Vtro uiſu una refracti uiſibilis imago uidetur. 47 p 10.
[452.] 37. Viſio diſtincta fit rectis lineis à uiſibili ad uiſum perpendicularib{us}. Et uiſio omnis fit re-fractè. 17. 18 p 3.
[453.] DE FALLACIIS VISVS, QVAE ACCIDVNT ex refractione. Cap. VII. 38. Refractio debilit at lucem & colorem uiſibilis: ita totam imaginem confuſam uiſui of-fert. 10 p 10.
[454.] 39. Si communis ſectio ſuperficierum, refractionis & refractiui fuerit linea recta, & uiſ{us} ſit in perpendiculari duct a à medio uiſibilis par alleli communi ſectioni: imago maior uidebitur uiſibili. 31 p 10.
[455.] 40. Si communis ſectio ſuperficierum, refractionis & refractiui fuerit linea recta, & uiſ{us} ſit in perpendiculari duct a à medio uiſibilis obliqui ad communem ſectionem: imago maior ui-debitur uiſibili. 32 p 10.
[456.] 41. Si communis ſectio ſuperficierum, refractionis & refractiui fuerit linea recta: & uiſ{us} ſit extra planum perpendicularium à terminis uiſibilis, par alleli communiſectioni ſuper refra-ctiuum duct arum: imago uidebitur maior uiſibili. 33 p 10.
[457.] 42. Si communis ſectio ſuperficierum, refractionis et refractiui fuerit linea recta: & uiſ{us} ſit extr a planum perpendicularium à terminis uiſibilis obliqui ad com- munem ſectionem, ſuper refractiuum ductarum: ima- go maior uidebitur uiſibili. 34 p 10.
[458.] 43. Si tota imago refracti uiſibilis à refractiuo plano, uideatur maior uiſibili: uidebitur & pars imaginis maior parte uiſibilis proportionali. 35 p 10.
[459.] 44. Si uiſ{us} ſit in continuat a diametro circuli (qui eſt communis ſectio ſuperficierum, re-fractionis & refractiui conuexi denſioris) uiſibile uerò inter ipſi{us} centrum & uiſum, ab eodem centro æquabiliter diſtet: imago uidebitur maior uiſibili. 36 p 10.
[460.] 45. Si uiſ{us} ſit in continuata diametro circuli (quieſt cõmunis ſectio ſuperficierum refractio-nis et refractiui cõuexi dẽſioris) uiſibile uerò inter ipſi{us} centrũ & uiſum ab eodẽ cẽtro inæqua-biliter diſtet: imago uιdebi tur maior uiſi bili. 37 p 10.
[461.] 46. Si cõmu nis ſectio ſuք-ficierũ refra-ctionis & re-fractiui cõue-xi dẽſioris fue rit քipheria: et uiſ{us} ſit extra planum perpendicularium duct arũ à terminis uiſibilis inter cen trũ refractiui & uiſum, ab eodem centro ſiue æquabiliter ſiue in æquabiliter diſtantis: imago ui-debitur maior uiſibili. 38. 39 p 10.
[462.] 47. Si tota imago refracti uiſibilis à refractiuo conuexo, uideatur maior uiſibili: uidebitur & pars imaginis maior parte uiſibilis proportionali. 41 p 10.
[463.] 48. Imago refracti uiſibilis ab aqua ad aerem, uidetur maior uiſibili. 42 p 10.
[464.] 49. Siuiſ{us}, centrum refractiui conuexi denſioris & uiſibile ultra refractiuum poſitum, fue-rint in e adem recta linea: imago uidebitur corona ſeu armilla: & maior uiſibili. 43 p 10.
[465.] 50. Siuiſ{us}, centrum circuli in refractiuo cylindraceo conuexo denſiore, & uiſibιle ultra re-
[466.] 51. Stella in horizonte ut plurimum uidetur maior, quàm in medio cæli. 54 p 10.
[467.] 52. Diameter ſtellæ uertici propinquæ, & duarum inter ſe diſtantia, refractè uiſa, minor: rectè, maior uidetur. 51 p 10.
[468.] 53. Diameter ſtellæ, uel duarum ſtellarum diſtantia in horizonte, aut inter horizontem & meridianum, ad horizontem parallela, refractè uiſa, minor: rectè, maior uidetur. 52 p 10.
[469.] 54. Diameter ſtellæ, uel duarum ſtellarum dιſtantia in circulo altitudinis refractè uiſa, mi-nor: rectè, maior uidetur. 53 p 10.
[470.] 55. Stella uidetur circularis: maior in horizonte, quàm in medio cæli: ſimiliter́ duarum ſio ſitarum inter ſe diſtantia. 54 p 10. Idem 51 n.
[471.] ALHAZEN FILII ALHAYZEN OPTICAE FINIS.
[472.] ALHAZEN FILII ALHAYZEN DE CREPVSCVLIS ET NVBIVM ASCENSIONIBVS LIBER VNVS. Gerardo Cremonenſi interprete. NVMERI. 1. Crepuſculum matutinum incipit, ac ueſpertinum deſinit, ſole ante ortum & poſt occaſum ſuum 19 partib{us}, in peripheria circuli per uerticem regionis ſolis́ locum tranſeuntis, ſub horizontem demerſo.
[473.] 2. Si ſphæricũ luminoſum illuminet opacum æquale: hemiſphæriũ illuminabit. Vitell. 26 p 2.
[474.] 3. Si ſphæricum luminoſum illuminet opacum min{us}: pl{us} hemiſphærio illuminabit. Vi-tell. 27 p 2.
[475.] 4. Si peripheri{as} duorum circulorum æqualium duæ rectæ lιneæ tangant: punct a ſemiperi-pheriarum cõuexis partib{us} ſe reſpicientium ſingula ſingulis appa- rent, reliquarum uerò ſemiperipheriarum conuexis partib{us} ſenon reſpicientium latent.
[476.] 5. Deperipheria maximi in terra circuli ſol illuminat partes 180, ſcrupula prima 27, ſcru-pula ſecunda 52. Vitell. 59 p 10.
[477.] 6. Poſit a peripheria maximi in terra circuli 2 4000 milliarium Italicorum: erit ſumma ua-porum in nubem coactorum à terra altιtudo 5 2000 paſſuum. Vitell. 60 p 10.
[478.] FINIS.
[479.] VITELLONIS THV-RINGOPOLONI OPTI-CAE LIBRI DECEM. Inſtaurati, figuris nouis illuſtrati atque aucti: infinitis q́; erroribus, quibus antea ſcatebant, expurgati. À Federico Risnero.
[480.] BASILEAE.
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page |< < (127) of 778 > >|
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          <pb o="127" file="0429" n="429" rhead="LIBER QVARTVS."/>
          <p>
            <s xml:id="echoid-s27668" xml:space="preserve">Eſto centrum uiſus in puncto a:</s>
            <s xml:id="echoid-s27669" xml:space="preserve"> & ſit res, quę f e, uiſa ſub angulo f a e:</s>
            <s xml:id="echoid-s27670" xml:space="preserve"> productis quoq;</s>
            <s xml:id="echoid-s27671" xml:space="preserve"> lineis a f &
              <lb/>
            a e, producatur inter ipſas linea g b æ quidiſtanter lineæ f e:</s>
            <s xml:id="echoid-s27672" xml:space="preserve"> uidebitur ergo linea g b ſub angulo f a e,
              <lb/>
            quam fortè accidet uideri eſſe æqualem lineæ f e per præmiſſam, ut ſi lineas g f & b e non contingat
              <lb/>
            uideri, ſed uiſis lineis g f & b e, uidetur minor, quia eſt ſecundum ueritatem per 4 p 6 linea g b mi-
              <lb/>
            nor, quàm ſit linea f e, cum linea a g ſit minor quàm linea a f ex hypotheſi.</s>
            <s xml:id="echoid-s27673" xml:space="preserve"> Ducatur itaq;</s>
            <s xml:id="echoid-s27674" xml:space="preserve"> à puncto
              <lb/>
            e linea æquidiſtans lineæ a g per 31 p 1, quæ ſecet protractam lineam g b in puncto d:</s>
            <s xml:id="echoid-s27675" xml:space="preserve"> erit ergo per
              <lb/>
            34 p 1 linea g d æqualis lineæ f e:</s>
            <s xml:id="echoid-s27676" xml:space="preserve"> ducaturq́;</s>
            <s xml:id="echoid-s27677" xml:space="preserve"> linea a d, ſecans protractam lineam e f in puncto h:</s>
            <s xml:id="echoid-s27678" xml:space="preserve"> e
              <lb/>
            ritq́;</s>
            <s xml:id="echoid-s27679" xml:space="preserve"> linea h f maior quàm linea e f:</s>
            <s xml:id="echoid-s27680" xml:space="preserve"> & angulus f a h
              <lb/>
              <figure xlink:label="fig-0429-01" xlink:href="fig-0429-01a" number="459">
                <variables xml:id="echoid-variables439" xml:space="preserve">f g k e b a h d</variables>
              </figure>
            eſt maior angulo f a e per 29 th.</s>
            <s xml:id="echoid-s27681" xml:space="preserve"> 1 huius.</s>
            <s xml:id="echoid-s27682" xml:space="preserve"> Et quoniam
              <lb/>
            angulus f a e eſt pars anguli f a h, linea uerò f h uide-
              <lb/>
            tur maior quàm linea e f, & linea d g uidetur maior
              <lb/>
            quàm linea b g:</s>
            <s xml:id="echoid-s27683" xml:space="preserve"> quia uiſus partem à toto dijudicat:</s>
            <s xml:id="echoid-s27684" xml:space="preserve">
              <lb/>
            quod ergo ſub minori angulo uidetur, minus uide-
              <lb/>
            tur:</s>
            <s xml:id="echoid-s27685" xml:space="preserve"> ſed & quandoq;</s>
            <s xml:id="echoid-s27686" xml:space="preserve"> f e per præcedentem uidetur æ-
              <lb/>
            qualis lineæ g b:</s>
            <s xml:id="echoid-s27687" xml:space="preserve"> ergo poteſt uideri linea e f minor
              <lb/>
            quàm linea g d, quæ eſt æqualis lineæ f e, ut patet ex
              <lb/>
            pręmiſsis:</s>
            <s xml:id="echoid-s27688" xml:space="preserve"> quod ergo ſub maiori angulo uidetur, ma-
              <lb/>
            ius uidetur, & quod uidetur ſub minori, uidetur mi-
              <lb/>
            nus.</s>
            <s xml:id="echoid-s27689" xml:space="preserve"> Conus itaq;</s>
            <s xml:id="echoid-s27690" xml:space="preserve"> pyramidis uiſualis, quæ eſt f a e, ſe-
              <lb/>
            cundum quam uidetur res remotior, quæ eſt f e, mi-
              <lb/>
            nor & acutior eſt quàm conus pyramidis g a d.</s>
            <s xml:id="echoid-s27691" xml:space="preserve"> Et
              <lb/>
            quoniam ſuperficies oculi ſecat ambas iſtas pyrami-
              <lb/>
            des, cum ipſarum ambarum conus ſit quaſi in centro
              <lb/>
            oculi per 18 th.</s>
            <s xml:id="echoid-s27692" xml:space="preserve"> 3 huius, neceſſe eſt ergo baſim pyrami
              <lb/>
            dis abſciſſæ à pyramide f a e minorem eſſe baſi pyramidis abſciſſæ à totali pyramide g a d per 109
              <lb/>
            th.</s>
            <s xml:id="echoid-s27693" xml:space="preserve"> 1 huius, cum illæ duæ a bſciſſæ pyramides æ qualis ſint altitudinis:</s>
            <s xml:id="echoid-s27694" xml:space="preserve"> quoniam linea producta à cen
              <lb/>
            tro foraminis gyrationis nerui concaui ad ſuperficiem oculi extrinſecam eſt axis ambarum illa-
              <lb/>
            rum pyramidum abſciſſarum.</s>
            <s xml:id="echoid-s27695" xml:space="preserve"> Pars ergo ſuperficiei uiſus ibi figurata per formam rei uiſæ, quæ eſt
              <lb/>
            g d, eſt maior quàm pars eiuſdem ſuperficiei figurata per formam rei uiſæ, quæ eſt f e:</s>
            <s xml:id="echoid-s27696" xml:space="preserve"> uidetur
              <lb/>
            ergo linea g d maior quàm linea fe.</s>
            <s xml:id="echoid-s27697" xml:space="preserve"> Et quoniam ſecundum quantitatem illarum partium ſuperfi-
              <lb/>
            ciei ipſius uiſus uirtus ſenſitiua comprehendit angulum, quem lineæ radiales continentin centro
              <lb/>
            per 73 th.</s>
            <s xml:id="echoid-s27698" xml:space="preserve"> 3 huius:</s>
            <s xml:id="echoid-s27699" xml:space="preserve"> patet quòd rei, quæ uidetur maior, correſpondet angulus maior, & rei, quæ uide-
              <lb/>
            tur minor, correſpondet angulus minor:</s>
            <s xml:id="echoid-s27700" xml:space="preserve"> quoniam ſecundum quod forma rei uiſæ recipitur in ſu-
              <lb/>
            perficie organi uiſiui, ſecundum hoc accipitur quantitas anguli, ſub quo fit uiſio, & ſecundum hoc
              <lb/>
            idem etiam fit iudicium quantitatis rei uiſæ.</s>
            <s xml:id="echoid-s27701" xml:space="preserve"> Omnis ergo res ſub maiori angulo uiſa maior uidetur
              <lb/>
            ſe ipſa uiſa ſub angulo minori.</s>
            <s xml:id="echoid-s27702" xml:space="preserve"> Et uniuerſaliter in rebus directè uiſis ſecundum excrem entum angu
              <lb/>
            li fit excrementum quantitatis rei uiſæ:</s>
            <s xml:id="echoid-s27703" xml:space="preserve"> unde ſub duplo angulo uiſum duplum uidetur, & ſub triplo
              <lb/>
            triplum, & ſic ſecundum proportionem angulorum.</s>
            <s xml:id="echoid-s27704" xml:space="preserve"> In obliquè tamen uiſis, uel in his, quorum u-
              <lb/>
            num uidetur directè, & aliud obliquè, non ſic.</s>
            <s xml:id="echoid-s27705" xml:space="preserve"> Si enim trigonum a e f fit orthogonium, ita ut
              <lb/>
            eius angulus a e f ſit rectus, diuidaturq́;</s>
            <s xml:id="echoid-s27706" xml:space="preserve"> angulus f a e per æ qualia, producta linea a k, ſecante lineam
              <lb/>
            f e in puncto k:</s>
            <s xml:id="echoid-s27707" xml:space="preserve"> non propter hoc diuidetur linea e f per æqualia in puncto k:</s>
            <s xml:id="echoid-s27708" xml:space="preserve"> quoniã, ut patet per 35
              <lb/>
            th.</s>
            <s xml:id="echoid-s27709" xml:space="preserve"> 1 huius, minor eſt proportio anguli f a k ad angulũ k a e, quàm lineæ f k ad lineam k e:</s>
            <s xml:id="echoid-s27710" xml:space="preserve"> & ſic ſecun-
              <lb/>
            dum proportionem anguli ad angulum, non ſemper fit proportio quantitatis uiſæ ad quantitatem
              <lb/>
            uiſam:</s>
            <s xml:id="echoid-s27711" xml:space="preserve"> neq;</s>
            <s xml:id="echoid-s27712" xml:space="preserve"> enim talia uiſa ſecundum eandem uidentur diſpoſitionem & ſitum reſpectu ipſius ui-
              <lb/>
            ſus.</s>
            <s xml:id="echoid-s27713" xml:space="preserve"> In conformibus autem uiſibilibus ſecundum diſtantiam & ſitum & alia accidentia, quæ requi-
              <lb/>
            runtur ad conditionem & circunſtantiam uidendi, quæ patent per 1 the.</s>
            <s xml:id="echoid-s27714" xml:space="preserve"> huius, ſemper ſecundum
              <lb/>
            proportionem anguli uidetur proportionaliter quantitas rei uiſæ:</s>
            <s xml:id="echoid-s27715" xml:space="preserve"> unde etiam illud, quod ſub mi-
              <lb/>
            nimo angulo uidetur, minimum uidetur, & quod ſub nullo uel inſenſibili angulo peruenit ad uiſus
              <lb/>
            ſuperficiem, nullo modo uldetur, ut patet per 19 th.</s>
            <s xml:id="echoid-s27716" xml:space="preserve"> 3 huius.</s>
            <s xml:id="echoid-s27717" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s27718" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1079" type="section" level="0" n="0">
          <head xml:id="echoid-head869" xml:space="preserve" style="it">21. Parallelæ lineæ ſecundum remotiores à uiſu partes quaſi concurrere uidentur: nunquam
            <lb/>
          tamen uidebuntur concurrentes. Euclides 6 the. opt.</head>
          <p>
            <s xml:id="echoid-s27719" xml:space="preserve">Vniuerſale eſt quod proponitur, uiſu quocunq;</s>
            <s xml:id="echoid-s27720" xml:space="preserve"> modo ſe habente ad illas lineas parallelas:</s>
            <s xml:id="echoid-s27721" xml:space="preserve"> ſiue
              <lb/>
            enim uiſus ſit in illarum ſuperficie, ſiue ſupra illam, ſiue ſub illa, ſemper eadem paſsio uiſui accidit.</s>
            <s xml:id="echoid-s27722" xml:space="preserve">
              <lb/>
            Sit ergo primò uiſus in illarum ſuperficie, & ſint duæ parallelæ lineæ a b & g d:</s>
            <s xml:id="echoid-s27723" xml:space="preserve"> hæ ergo per 1 th.</s>
            <s xml:id="echoid-s27724" xml:space="preserve"> 1
              <lb/>
            huius neceſſariò erunt in eadem ſuperficie:</s>
            <s xml:id="echoid-s27725" xml:space="preserve"> ſit ergo in ipſarum ſuperficie uiſus, qui ſit e, uel prope
              <lb/>
            illam.</s>
            <s xml:id="echoid-s27726" xml:space="preserve"> Dico, quòd ſuperficiei interiacentis lineas a b & g d, in æqualis apparebit latitudo:</s>
            <s xml:id="echoid-s27727" xml:space="preserve"> & quòd
              <lb/>
            pars ſui propinquior uiſui apparebit latior, quàm pars eius à uiſu remotior, & ita lineæ a b & g d
              <lb/>
            quaſi concurrere uidebuntur.</s>
            <s xml:id="echoid-s27728" xml:space="preserve"> Signentur enim puncta æquidiſtanter & ſimiliter in lineis a b & g
              <lb/>
            d, quæ ſint in linea a b puncta z & t, & in linea d g pucta l & k:</s>
            <s xml:id="echoid-s27729" xml:space="preserve"> & coniungantur illa puncta, & pun-
              <lb/>
            cta terminalia ductis lineis b d, z l, t k, a g:</s>
            <s xml:id="echoid-s27730" xml:space="preserve"> quæ omnes erunt æ quidiſtantes ex hypotheſi & per 33 p 1:</s>
            <s xml:id="echoid-s27731" xml:space="preserve">
              <lb/>
            & producantur lineæ e b, e z, e t, e a:</s>
            <s xml:id="echoid-s27732" xml:space="preserve"> e d, e l, e k, e g.</s>
            <s xml:id="echoid-s27733" xml:space="preserve"> Et quoniam angulus b e d maior eſt angulo z e
              <lb/>
            l.</s>
            <s xml:id="echoid-s27734" xml:space="preserve"> ſicut totum parte (quod patet per 34 theo.</s>
            <s xml:id="echoid-s27735" xml:space="preserve"> 1 huius) palàm per præmiſſam quia maior uidebitur
              <lb/>
            </s>
          </p>
        </div>
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