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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            lis eſt g h.</s>
            <s xml:id="echoid-s10729" xml:space="preserve"> Similiter angulus b g q ęqualis eſt angulo a g z.</s>
            <s xml:id="echoid-s10730" xml:space="preserve"> [Nã cũ angulus e g q æquetur angulo e g z:</s>
            <s xml:id="echoid-s10731" xml:space="preserve">
              <lb/>
            ꝗa ք 18 p 3 uterq;</s>
            <s xml:id="echoid-s10732" xml:space="preserve"> rectus eſt, & e g b ipſi e g a, ut patuit:</s>
            <s xml:id="echoid-s10733" xml:space="preserve"> reliquus igitur b g q ęquatur reliquo a g z ք 3
              <lb/>
            ax.</s>
            <s xml:id="echoid-s10734" xml:space="preserve">] & angulus a g z ęqualis eſt angulo g q b [exterior interiori oppoſito ք 29 p 1:</s>
            <s xml:id="echoid-s10735" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s10736" xml:space="preserve"> b g q ęquatur
              <lb/>
            g q b:</s>
            <s xml:id="echoid-s10737" xml:space="preserve"> & ita [ք 6 p 1] b q ęqualis eſt b g.</s>
            <s xml:id="echoid-s10738" xml:space="preserve"> Quare [ք 7 p 5] ꝓportio b g ad h l, ſicut b q ad h g.</s>
            <s xml:id="echoid-s10739" xml:space="preserve"> Sed quoniã
              <lb/>
            angulus g h t eſt ęqualis angulo t b q:</s>
            <s xml:id="echoid-s10740" xml:space="preserve"> [per 29 p 1] erit triangulũ t b q ſimile triãgulo g h t.</s>
            <s xml:id="echoid-s10741" xml:space="preserve"> [Nã anguli
              <lb/>
            ad t æquãtur ք 15 p 1, & ք 32 p 1 tertius tertio.</s>
            <s xml:id="echoid-s10742" xml:space="preserve"> Quare ք 4 p.</s>
            <s xml:id="echoid-s10743" xml:space="preserve"> 1 d 6 triãgula t b q.</s>
            <s xml:id="echoid-s10744" xml:space="preserve"> g h t ſunt ſimilia.</s>
            <s xml:id="echoid-s10745" xml:space="preserve">] Igitur
              <lb/>
            ꝓportio q b ad h g, ſicut b t ad t h:</s>
            <s xml:id="echoid-s10746" xml:space="preserve"> & ita [per 7 p 5] b g ad h l, ſicut b t ad t h.</s>
            <s xml:id="echoid-s10747" xml:space="preserve"> Sed cũ triangulũ b g e ſit
              <lb/>
            ſimile triangulo h e l:</s>
            <s xml:id="echoid-s10748" xml:space="preserve"> [angulus enim ad e cõmunis eſt, & exteriores ad g & b ęquãtur interiorib, op
              <lb/>
            poſitis ad l & h per 29 p 1.</s>
            <s xml:id="echoid-s10749" xml:space="preserve"> Quare ք 4 p.</s>
            <s xml:id="echoid-s10750" xml:space="preserve"> 1 d 6 triangula b g e, h e l ſunt ſimilia] erit ꝓportio b g ad h l,
              <lb/>
              <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a" number="100">
                <variables xml:id="echoid-variables90" xml:space="preserve">b l a e h q g f z</variables>
              </figure>
              <figure xlink:label="fig-0170-02" xlink:href="fig-0170-02a" number="101">
                <variables xml:id="echoid-variables91" xml:space="preserve">l t b e a q g z</variables>
              </figure>
            ſicut e b ad e h:</s>
            <s xml:id="echoid-s10751" xml:space="preserve"> & ita [ք 11 p 5] e b ad e h, ſicut b
              <lb/>
              <figure xlink:label="fig-0170-03" xlink:href="fig-0170-03a" number="102">
                <variables xml:id="echoid-variables92" xml:space="preserve">t f g q a c b</variables>
              </figure>
            t ad t h.</s>
            <s xml:id="echoid-s10752" xml:space="preserve"> Qđ eſt ꝓpoſitũ.</s>
            <s xml:id="echoid-s10753" xml:space="preserve"> Eadẽ erit ꝓbatio, ſi lo
              <lb/>
            cus imaginis fuerit inter a & g:</s>
            <s xml:id="echoid-s10754" xml:space="preserve"> aut in a:</s>
            <s xml:id="echoid-s10755" xml:space="preserve"> aut ul
              <lb/>
            tra.</s>
            <s xml:id="echoid-s10756" xml:space="preserve"> Si uerò linea cõtingẽtiæ z g ſit æquidiſtãs
              <lb/>
            perpẽdiculari, q̃ eſt b e h:</s>
            <s xml:id="echoid-s10757" xml:space="preserve"> ducatur perpẽdicu-
              <lb/>
            laris g e:</s>
            <s xml:id="echoid-s10758" xml:space="preserve"> [à pũcto g ſuper z g] quę cũ ſit քpen-
              <lb/>
            dicularis ſuper g z:</s>
            <s xml:id="echoid-s10759" xml:space="preserve"> erit perpẽdicularis ſuք b h
              <lb/>
              <figure xlink:label="fig-0170-04" xlink:href="fig-0170-04a" number="103">
                <variables xml:id="echoid-variables93" xml:space="preserve">z g q h c b</variables>
              </figure>
            [per 29 p 1] & erit angulus b e g ęqualis angu
              <lb/>
            lo h e g:</s>
            <s xml:id="echoid-s10760" xml:space="preserve"> & [per 12 n 4] angulus b g e æqualis
              <lb/>
            eſt angulo e g h:</s>
            <s xml:id="echoid-s10761" xml:space="preserve"> reſtat triãgulũ b g e ſimile triã
              <lb/>
            gulo e g h.</s>
            <s xml:id="echoid-s10762" xml:space="preserve"> [ęquabitur.</s>
            <s xml:id="echoid-s10763" xml:space="preserve"> n.</s>
            <s xml:id="echoid-s10764" xml:space="preserve"> ք 32 p 1 reliquus angu
              <lb/>
            lus ad b, reliquo ad h:</s>
            <s xml:id="echoid-s10765" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s10766" xml:space="preserve"> ք 4 p.</s>
            <s xml:id="echoid-s10767" xml:space="preserve"> 1 d 6 triãgu-
              <lb/>
            la b g e, h g e erunt ſimilia.</s>
            <s xml:id="echoid-s10768" xml:space="preserve">] lgitur proportio b
              <lb/>
            e ad h e, ſicut b g ad g h.</s>
            <s xml:id="echoid-s10769" xml:space="preserve"> Qđ eſt propoſitum.</s>
            <s xml:id="echoid-s10770" xml:space="preserve">
              <lb/>
            Quare in hoc caſu non põt ſumi aliud punctũ
              <lb/>
            cõtingẽtię, ꝗ̃punctũ g, eo modo, quo punctũ
              <lb/>
            contingentię ſuprà [17 n] appellauimus.</s>
            <s xml:id="echoid-s10771" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div386" type="section" level="0" n="0">
          <head xml:id="echoid-head368" xml:space="preserve" style="it">65. Viſu & uiſibili in diametro ſpeculi ſphærici caui æquabiliter à cẽtro diſtantib{us}: poteſt fie-
            <lb/>
          rireflexio à tota peripheria circuli, quẽ ſemidiameter perpẽdicularis ad dictã diametrum, cõ-
            <lb/>
          uerſa deſcribit. 14 p 8.</head>
          <p>
            <s xml:id="echoid-s10772" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s10773" xml:space="preserve"> ſit circulus a b g d:</s>
            <s xml:id="echoid-s10774" xml:space="preserve"> & h centrum ui-
              <lb/>
              <figure xlink:label="fig-0170-05" xlink:href="fig-0170-05a" number="104">
                <variables xml:id="echoid-variables94" xml:space="preserve">b z a c g h d</variables>
              </figure>
            ſus intra ſpeculum:</s>
            <s xml:id="echoid-s10775" xml:space="preserve"> e centrum ſpeculi:</s>
            <s xml:id="echoid-s10776" xml:space="preserve"> z pun
              <lb/>
            ctum uiſum:</s>
            <s xml:id="echoid-s10777" xml:space="preserve"> & ducatur diameter b e d.</s>
            <s xml:id="echoid-s10778" xml:space="preserve"> Si fue
              <lb/>
            rit z in ſemidiametro b e:</s>
            <s xml:id="echoid-s10779" xml:space="preserve"> poterit eſſe reflexio ab ali
              <lb/>
            quo puncto ſemicirculi b a d, & ab aliquo pũcto ſe-
              <lb/>
            micirculi ei oppoſiti.</s>
            <s xml:id="echoid-s10780" xml:space="preserve"> Quoniam quocunq;</s>
            <s xml:id="echoid-s10781" xml:space="preserve"> puncto
              <lb/>
            ſemidiametri b e ſumpto:</s>
            <s xml:id="echoid-s10782" xml:space="preserve"> ſi ab eo ducatur linea ad
              <lb/>
            aliquod punctum ſemicirculi, & à puncto h ad idẽ
              <lb/>
            punctum ducatur alia linea:</s>
            <s xml:id="echoid-s10783" xml:space="preserve"> illæ duę lineæ efficient
              <lb/>
            angulum, quem diuidet per æqualia ſemidiameter
              <lb/>
            ducta à puncto e ad illud punctum [quia enim ſe-
              <lb/>
            midiameter illa extheſi eſt perpendicularis diame-
              <lb/>
            tro, in qua uiſus & uiſibile ęquabiliter à centro ſpe-
              <lb/>
            culi diſtantia collocantur:</s>
            <s xml:id="echoid-s10784" xml:space="preserve"> ita que ſi à uiſu & uiſibi-
              <lb/>
            li duę rectæ lineæ cum dicta ſemidiametro in peri-
              <lb/>
            pheria cõcurrant:</s>
            <s xml:id="echoid-s10785" xml:space="preserve"> erunt anguli ad cõcurſus punctũ
              <lb/>
            ęquales per 4 p 1.</s>
            <s xml:id="echoid-s10786" xml:space="preserve"> Quare per 12 n 4 ipſum eſt reflexionis punctũ.</s>
            <s xml:id="echoid-s10787" xml:space="preserve">] Similiter in ſemicirculo oppoſito.</s>
            <s xml:id="echoid-s10788" xml:space="preserve"/>
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