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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[191.] 64. Perſpicuitas medij immoder ata creat errores in ſingulis uiſibilibus ſpeciebus. In diſtãtia: ſitu: figura: magnitudine: diuiſione: continuatione & numero. 16. 44. 97. 28. 109 p 4.
Page: 106 (100)
[192.] 65. In motu: quiete: aſperitate: lenitate: raritate: denſitate: umbra: tenebris: pulchritudine: deformitate: ſimilitudine & dißimilitudine. 138. 141. 144. 147. 150. 153 p 4.
Page: 106 (100)
[193.] 66. Tempus immoderatum creat errores in ſingulis uiſibilibus ſpeciebus. In diſtantia: ſitu: figura: magnitudine. 16. 44. 97. 28 p 4.
Page: 106 (100)
[194.] 67. In diuiſione: continuatione: numero: quiete & motu. 109. 138 p 4.
Page: 106 (100)
[195.] 68. In aſperitate: lenitate: raritate: denſitate: umbra: tenebris: pulchritudine: deformitate: ſimilitudine: dißimilitudine. 141. 144. 147. 150. 153 p 4.
Page: 107 (101)
[196.] 69. Imbecillit{as} uiſus creat errores in ſingulis uiſibilibus ſpeciebus. In diſtantia: ſitu: magni-tudine: figura: diuiſione: continuatione: numero. 16. 44. 28. 97. 109 p 4.
Page: 107 (101)
[197.] 70. In motu & quiete. 138 p 4.
Page: 107 (101)
[198.] 71. In aſperitate: lenitate: raritate: denſitate: umbra: tenebris: pulchritudine: deformitate: ſimilitudine: dißimilitudine. 141. 144. 147. 150. 153 p 4.
Page: 107 (101)
[199.] 72. In uiſione errores creantur aliàs quidem à ſingulis uiſionẽ perficientibus: aliàs uerò à plu-ribus ſimul, quorum nullum per ſe errorem crearet. 154 p 4.
Page: 108 (102)
[200.] ALHAZEN FILII ALHAYZEN OPTICAE LIBER QVARTVS.
Page: 108 (102)
[201.] PROOEMIVM LIBRI. CAP. I. 1. Viſio fit trifariam: rectè: reflexè: & refr actè. In præf. 1. 3. 10 Libr.
Page: 108 (102)
[202.] QVOD LVCI ACCIDAT REFLEXIO À POLITIS corporibus. Cap. II. 2. Lux & color reflectuntur à quolibet politæ ſuperficiei puncto, lineis rectis. 1 p 5.
Page: 108 (102)
[203.] 3. Lux & color à quolibet ſuperficiei coloratæ puncto ad quodlibet ſuperficiei politæ oppoſitæ punctum permixti confluunt. 2 p 5.
Page: 109 (103)
[204.] 4. Reflexio debilit at lucem & colorem: & omnino totam uiſibilis ſpeciem. 3 p 5.
Page: 109 (103)
[205.] 5. Lux & color reflexi ſunt debiliores luce & colore primis: fortiores autem ſecundis, cum quibus ab eodem ortu æquabiliter diſtant. 4 p 5.
Page: 109 (103)
[206.] DE MODO REFLEXIONIS FORMARVM À POLI-tis corporibus. Cap. III. 6. Lenitatis: politæ ſuperficiei: & perpendicularis incidentiæ definitiones. In def. 5 libr.
Page: 110 (104)
[207.] 7. Fabricatio & uſus organi reflexionis. 9 p 5.
Page: 110 (104)
[208.] 8. Fabricatio ſeptem ſpeculorum regularium. 8 p 5.
Page: 112 (106)
[209.] 9. Sit{us} & collocatio ſpeculorum regulariũ in reflexionis organo.10.12.13.14.15.16.17 p 5.
Page: 113 (107)
[210.] 10. Radi{us} ſpeculo plano obliqu{us}, in oppoſitam partem reflectitur: & æquat angulos inci-dentiæ & reflexionis. 10 p 5.
Page: 114 (108)
[211.] 11. Radi{us} ſpeculo perpendicularis, reflectitur in ſeipſum. 11.12 p 5.
Page: 114 (108)
[212.] 12. In ſpeculis, conuexis, cauis: ſphærico, conico cylindraceo, anguli incidentiæ & reflexio-nis æquantur. 12.13.14.15.16.17.20 p 5.
Page: 114 (108)
[213.] 13. Superficies reflexionis eſt perpendicularis plano ſpeculum in reflexionis puncto tan-genti. 25 p 5.
Page: 115 (109)
[214.] 14. Inter uiſibile & ſpeculũ innumer abiles pyramides fiũt alternis baſib. & uerticib{us}. 22 p 5.
Page: 117 (111)
[215.] 15. Lux à ſuperficie polita longinquiore reflexa, trifariam debilitatur.
Page: 117 (111)
[216.] 16. Lux & color reflectuntur per line{as} phyſic{as}, latitudine quadam prędit{as}. 3 p 2.6 p 5.
Page: 118 (112)
[217.] 17. Reflexio lucis & coloris à ſuperficie aſper a facta, plerun fugit uiſum. 1 p 5.
Page: 118 (112)
[218.] 18. Radij incidentiæ & reflexionis, ſit{us} ſimilitudine conueniunt. Ita anguli incidentiæ & reflexionis æquantur. 20 p 5.
Page: 118 (112)
[219.] 19. Colorem luci permiſtum reflecti, reflexionis organo ostenditur. 3 p 5.
Page: 119 (113)
[220.] QVOÒD COMPREHENSIO FORMARVM È CORPORIBVS politis fiat reflexione. Cap. 1111. 20. Falſa eſt utra opinio: & radios à uiſu ad ſpeculum miſſos, inde́ ad uiſibile reflexos, ima ginem percipere: & imaginẽ in ſpeculo iam antè impreſſam inde ad uiſum manare. 23. 24 p 5.
Page: 119 (113)
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page |< < (189) of 778 > >|
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            <s xml:id="echoid-s12830" xml:space="preserve">
              <pb o="189" file="0195" n="195" rhead="OPTICAE LIBER VI."/>
            ctionem, quę nullatenus ſunt comprehenſibiles per reflexionem.</s>
            <s xml:id="echoid-s12831" xml:space="preserve"> Palàm ergo, quòd directionem ſu
              <lb/>
            perat reflexio in maioritate errorum & numero.</s>
            <s xml:id="echoid-s12832" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div455" type="section" level="0" n="0">
          <head xml:id="echoid-head412" xml:space="preserve">DE ERRORE, QVI ACCIDIT IN SPECVLIS</head>
          <head xml:id="echoid-head413" xml:space="preserve">planis. Cap. III.</head>
          <head xml:id="echoid-head414" xml:space="preserve" style="it">2. In ſpeculo plano imago æquatur uiſibili. 52 p 5.</head>
          <p>
            <s xml:id="echoid-s12833" xml:space="preserve">IN ſingulis ſpeculis erronea formarum accidit comprehenſio, ſed iuxta uarietatem ſpeculorũ fi
              <lb/>
            uarietas errorum.</s>
            <s xml:id="echoid-s12834" xml:space="preserve"> In ſpeculis planis minor accidit error, quàm in alijs.</s>
            <s xml:id="echoid-s12835" xml:space="preserve"> In his etenim comprehen
              <lb/>
            ditur ueritas figuræ, & quantitatis, ſicut & in directione, quod per probationẽ patebit.</s>
            <s xml:id="echoid-s12836" xml:space="preserve"> Propona
              <lb/>
            tur ſpeculũ planum:</s>
            <s xml:id="echoid-s12837" xml:space="preserve"> & ſit a b linea in ſuperficie illius ſpe-
              <lb/>
            culi, cõmunis ſuperficiei ſpeculi & ſuperficiei orthogona
              <lb/>
              <figure xlink:label="fig-0195-01" xlink:href="fig-0195-01a" number="153">
                <variables xml:id="echoid-variables143" xml:space="preserve">f f e a z b h d g</variables>
              </figure>
            li ſuper ſuperficiem ſpeculi, [id eſt ſuperficiei reflexionis,
              <lb/>
            quę per 13 n 4 perpendicularis eſt plano ſpeculo, uel pla-
              <lb/>
            no ſpeculũ obliquũ in reflexionis puncto tangenti.</s>
            <s xml:id="echoid-s12838" xml:space="preserve">] Sint
              <lb/>
            l, f duo puncta in ſuperficie illa orthogonali:</s>
            <s xml:id="echoid-s12839" xml:space="preserve"> e centrum ui
              <lb/>
            ſus:</s>
            <s xml:id="echoid-s12840" xml:space="preserve"> & à puncto l ducatur perpendicularis ſuper ſuperfi-
              <lb/>
            ciem ſpeculi[per 11 p 11] quæ ſit l h:</s>
            <s xml:id="echoid-s12841" xml:space="preserve"> & producatur, ut h g ſit
              <lb/>
            æqualis l h.</s>
            <s xml:id="echoid-s12842" xml:space="preserve"> Similiter producatur perpendicularis f z, ut d
              <lb/>
            f ſit æqualis z f.</s>
            <s xml:id="echoid-s12843" xml:space="preserve"> Palàm ex ſuperioribus [2.</s>
            <s xml:id="echoid-s12844" xml:space="preserve">3 n 4] quòd l re
              <lb/>
            flectitur ad e ab aliquo puncto ſpeculi:</s>
            <s xml:id="echoid-s12845" xml:space="preserve"> & locus imaginis
              <lb/>
            eſt g [per 2 n 5] tantùm diſtans à ſuperficie ſpeculi, quan-
              <lb/>
            tùm l [per 11 n 5.</s>
            <s xml:id="echoid-s12846" xml:space="preserve">] Similiter f reflectitur ad e:</s>
            <s xml:id="echoid-s12847" xml:space="preserve"> & locus ima-
              <lb/>
            ginis eſt d [per 2 n 5.</s>
            <s xml:id="echoid-s12848" xml:space="preserve">] Ducta autẽ linea f l:</s>
            <s xml:id="echoid-s12849" xml:space="preserve"> & ſimiliter g d:</s>
            <s xml:id="echoid-s12850" xml:space="preserve">
              <lb/>
            quodcunq;</s>
            <s xml:id="echoid-s12851" xml:space="preserve"> punctum lineæ f l reflectetur ad e:</s>
            <s xml:id="echoid-s12852" xml:space="preserve"> locus ima-
              <lb/>
            ginis eius eſt tantùm diſtans à ſuperficie ſpeculi, quantũ
              <lb/>
            ipſum punctũ.</s>
            <s xml:id="echoid-s12853" xml:space="preserve"> Et ita quo dlibet punctũ linéæ f l tantùm
              <lb/>
            uidetur diſtare, quantùm diſtat! Vnde ſi linea f l fuerit re
              <lb/>
            cta:</s>
            <s xml:id="echoid-s12854" xml:space="preserve"> erit linea d g recta:</s>
            <s xml:id="echoid-s12855" xml:space="preserve"> ſi fuerit arcus:</s>
            <s xml:id="echoid-s12856" xml:space="preserve"> erit d g arcus & eiuſdem curuitatis.</s>
            <s xml:id="echoid-s12857" xml:space="preserve"> Quare linea l fapparebit e-
              <lb/>
            iuſdem quantitatis, eiuſdem figuræ, cuius fuerit.</s>
            <s xml:id="echoid-s12858" xml:space="preserve"> Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12859" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div457" type="section" level="0" n="0">
          <head xml:id="echoid-head415" xml:space="preserve" style="it">3. Viſus in reflexione præcipuè allucinatur propter lucis immoderationẽ: ſitus diuerſitatem:
            <lb/>
          uiſus & uiſibilis à ſpeculo diſtantiam. 7 p 5.</head>
          <p>
            <s xml:id="echoid-s12860" xml:space="preserve">VErùm ſi in punctis lineæ f l fuerit uarietas colorum minutim uariata:</s>
            <s xml:id="echoid-s12861" xml:space="preserve"> forſitan nõ diſcernetur
              <lb/>
            uariatio, ſed una prætendetur uiſui coloris conſuſio.</s>
            <s xml:id="echoid-s12862" xml:space="preserve"> Vnde error erit in luce & colore.</s>
            <s xml:id="echoid-s12863" xml:space="preserve"> Et hoc
              <lb/>
            in numero, propter reflexionẽ.</s>
            <s xml:id="echoid-s12864" xml:space="preserve"> Illa etenim colorum & lucium uarietas forſitan comprehen-
              <lb/>
            di poſſet directè, ſed egreſſus eſt color à tẽperantia reſpectu reflexionis, nõ reſpectu directionis.</s>
            <s xml:id="echoid-s12865" xml:space="preserve"> Si-
              <lb/>
            militer particulæ minutæ occultantur, aut confunduntur in reflexione, quæ diſcerni poſſent in dire
              <lb/>
            ctione.</s>
            <s xml:id="echoid-s12866" xml:space="preserve"> Et propter debilitatẽ lucis uel coloris ex reflexione, accidit error in longitudine, qui quidẽ
              <lb/>
            nõ accideret directè.</s>
            <s xml:id="echoid-s12867" xml:space="preserve"> In ſitu manifeſtè accidit error ex reflexione ſola.</s>
            <s xml:id="echoid-s12868" xml:space="preserve"> In imagine enim, ſiniſtra com
              <lb/>
            prehendimus ea, quæ in corpore uiſo (ſi eſſet in loco imaginis) dextra uideremus.</s>
            <s xml:id="echoid-s12869" xml:space="preserve"> Cũ enim aliquid
              <lb/>
            alij opponitur, contrarius eis ſitus eſt ad inuicem:</s>
            <s xml:id="echoid-s12870" xml:space="preserve"> quod enim uni fuerit dextrum, alij erit ſiniſtrum.</s>
            <s xml:id="echoid-s12871" xml:space="preserve">
              <lb/>
            Igitur quod rei uiſæ dextrum, eſt imagini ſiniſtrum:</s>
            <s xml:id="echoid-s12872" xml:space="preserve"> & ſiniſtrum in imagine, dextrum eſt uidenti.</s>
            <s xml:id="echoid-s12873" xml:space="preserve"> Et
              <lb/>
            generabter in modo lucis, uel coloris, uel ſitus ſemper error accidit ex ſola reflexione.</s>
            <s xml:id="echoid-s12874" xml:space="preserve"> Et in alijs,
              <lb/>
            quæ errorem inducunt directè:</s>
            <s xml:id="echoid-s12875" xml:space="preserve"> inducunt ſimiliter in reflexione:</s>
            <s xml:id="echoid-s12876" xml:space="preserve"> & facilius:</s>
            <s xml:id="echoid-s12877" xml:space="preserve"> quoniam temperamen-
              <lb/>
            tum ſingulorum minus eſt in uiſu reflexo, quàm in directo.</s>
            <s xml:id="echoid-s12878" xml:space="preserve"> Horum omniũ unum proponatur exem
              <lb/>
            plum, & idem in cæteris intelligatur.</s>
            <s xml:id="echoid-s12879" xml:space="preserve"> In uiſu directo cum fuerit corpus uiſum, remotum ab axibus
              <lb/>
            uiſualibus, accidit ipſum uider
              <gap/>
            duo:</s>
            <s xml:id="echoid-s12880" xml:space="preserve"> [ut demonſtratum eſt 11 n 3] idem euenit in ſpeculis, re uiſa ab
              <lb/>
            axibus elongata.</s>
            <s xml:id="echoid-s12881" xml:space="preserve"> In ſpeculis ab aliqua lõgitudine uidebitur corpus minus, quàm ſit, quod forſan di-
              <lb/>
            rectè à tanta longitudine uideretur etiã minus, quàm eſſet in ueritate, ſed non adeò minus.</s>
            <s xml:id="echoid-s12882" xml:space="preserve"> Et hoe
              <lb/>
            minoritatis additamentum in ſpeculis, prouenit propter minus in longitudine temperamentũ.</s>
            <s xml:id="echoid-s12883" xml:space="preserve"> In
              <lb/>
            figura nonnunquam accidit error in ſpeculis propter cauſſas, propter quas in uiſu directo:</s>
            <s xml:id="echoid-s12884" xml:space="preserve"> ſed ma-
              <lb/>
            ior & frequentior propter ſitum.</s>
            <s xml:id="echoid-s12885" xml:space="preserve"> Si aliquid ab aliqua longitudine opponatur ſpeculo, & eius capita
              <lb/>
            non percipiantur à uiſu, ut funis, del aliquid tale:</s>
            <s xml:id="echoid-s12886" xml:space="preserve"> uidebitur forſitan continuũ ſpeculo.</s>
            <s xml:id="echoid-s12887" xml:space="preserve"> Idem accidit
              <lb/>
            in uiſu directo, ſi opponatur funis aliquιs foramini, & non uideantur capita funis:</s>
            <s xml:id="echoid-s12888" xml:space="preserve"> non apparebit di
              <lb/>
            ſtantia inter funem & foramen, licet magna ſit.</s>
            <s xml:id="echoid-s12889" xml:space="preserve"> Et eſt propter ſitum.</s>
            <s xml:id="echoid-s12890" xml:space="preserve"> Si autem alterum capitum ui-
              <lb/>
            deatur, alterum uerò non:</s>
            <s xml:id="echoid-s12891" xml:space="preserve"> uidebitur fortaſsis illud caput continuum.</s>
            <s xml:id="echoid-s12892" xml:space="preserve"> Et in ſingulis ubi directè er-
              <lb/>
            ror accidit:</s>
            <s xml:id="echoid-s12893" xml:space="preserve"> ſimiliter in reflexione.</s>
            <s xml:id="echoid-s12894" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div458" type="section" level="0" n="0">
          <head xml:id="echoid-head416" xml:space="preserve">DE ERRORE, QVI ACCIDIT IN SPECVLIS SPHAE-
            <lb/>
          ricis conuexis. Cap. IIII.</head>
          <head xml:id="echoid-head417" xml:space="preserve" style="it">4. In ſpeculo ſphærico cõuexo idẽ eſt ſitus, eadem́ diſpoſitio partiũ imaginis & uiſibilis. 35 p 6.</head>
          <p>
            <s xml:id="echoid-s12895" xml:space="preserve">VNiuerſitas errorũ in ſpeculis planis accidentiũ, euenit ſimiliter in ſphæricis exterioribus.</s>
            <s xml:id="echoid-s12896" xml:space="preserve"> Et
              <lb/>
            præter hoc res uiſa uidetur minor ꝗ̃ ſit.</s>
            <s xml:id="echoid-s12897" xml:space="preserve"> Et generaliter in his ſpeculis nihil exre uiſa compre-
              <lb/>
            </s>
          </p>
        </div>
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    </echo>
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