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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[361.] 5. In ſpeculo ſphærico conuexo, imago uiſibilis, cuius uera magnitudo uiſione directa percipi poteſt, minor eſt uiſibili. 39 p 6.
[362.] 6. In ſpeculo ſphærico conuexo, imagouiſibilis, cuius uera magnitudo uiſione directa propter immoder at am diſtantiam percipi non poteſt: aliâs eſt æquabilis uiſibili: aliâs maior. 38 p 6.
[363.] 7. Si duo uiſibilis pũcta à centro ſpeculi ſphærici cõuexi æquabiliter, à uiſu uerò inæquabiliter diſtẽt: imago & finis cõtingẽtiæ pũcti lõginquioris à uiſu, erũt lõginquiores à cẽtro ſpeculi. 4 p 6.
[364.] 8. Si data recta in duob{us} punctis ſecta, ſit ad alterũ extremorũ ſegmentorũ, ut reliquũ ex-tremum ad intermediũ: & ab altero ipſi{us} termino, ſectionum́ punctis tres rectæ in eodẽ pun cto cõcurrant: recta à reliquo termino ſecãs cõcurrentes, ſecabitur proportionaliter datæ. 123 p 1.
[365.] 9. Si duæ rectæ facientes angulum, ſimiliter́ in duob{us} punctis ita ſectæ (ut tota ſit ad alterũ extremorũ ſegmentorũ, ſicut reliquum extremum ad intermedium) baſi infinita cõnect antur: rectæ per pũcta ſectionũ utriuſ, cũ baſi & inter ſe cõcurrẽtes, in eodẽ puncto cõcurrẽt. 124 p 1.
[366.] 10. Si data recta in duob{us} punctis ſecta, ſit ad alterum extremorum ſegmẽtorum, ſicut re-liquum extremum ad intermedium: & ab altero ipſi{us} termino, ſectionum́ punctis tres rectæ li- neæ ſint parallelæ: recta à reliquo termino ſecan s parallel{as}, ſecabitur proportionaliter datæ. 122 p 1.
[367.] 11. Sirecta linea à uiſu ſit perpendicularis ſu-perficiei incidentiæ: imago perιpheriæ concentricæ peripheriæ circuli (qui eſt communis ſectio ſuperficierum reflexionis & ſpeculi ſphærici cõuexi) uidebitur curua, & par allela ipſi peripheriæ concentricæ. 46 p 6.
[368.] 12. Si recta linea à uiſu ſit obliqua ſuperficiei incidentiæ: ima-go peripheriæ concentricæ peripheriæ circuli (qui eſt communis ſe-ctio ſuperficierum, reflexionis & ſpeculi ſphærici conucxi) uidebi-tur curua, non parallela peripheriæ concentricæ. 47 p 6.
[369.] 13. Si uiſ{us} ſit extra ſuperficiem incidentiæ: imago peripheriæ eccentricæ peripheriæ circuli (qui eſt communis ſectio ſuperficierum, reflex ionis & ſpeculi ſphærici conuexi) uidebitur magis curua, quàm imago peripheriæ concentricæ. 48 p 6.
[370.] 14. Si uiſ{us} ſit extra ſuperficiem incidentiæ: imago lineæ rectæ, parallelæ rectæ tangẽti peri-pheriam circuli (qui eſt communis ſectio ſuperficierum, reflexionis & ſpeculi ſphærici conuexi) uidebitur curua. 49 p 6.
[371.] 15. Si uiſ{us} ſit extra ſuperficiem incidẽtiæ: imago lineæ rectæ infinitæ, nec parallelæ, nec tan-gentis, nec ſecantis peripheriam cir culi (qui eſt communis ſectio ſuper- ficierum, reflexionis & ſpeculi ſphæ- rici cõuexi) uidebitur curua. 50 p 6.
[372.] 16. Si uiſ{us} ſit extra ſuperficiem incidentiæ: imago lineæ rectæ infinitæ, tangentis periphe-riam circuli (qui eſt communis ſectio ſuperficierum, reflexionis & ſpeculi ſphærici conuexi) uidebitur curua. 51 p 6.
[373.] 17. Si uiſ{us} ſit extra ſuperficem incidentiæ: imago lineæ rectæ infinitæ, ſecantis inæquabili-ter peripheriam circuli (qui eſt communis ſectio ſuperficierum, reflexionis & ſpeculi ſphærici con- uexi) uidebitur curua. 52 p 6.
[374.] 18. Si uiſ{us} ſit in ſuperficie incidentiæ, extra rectam lineam infinitam per centrum circuli (qui eſt communis ſectio ſuperficierum, reflexionis & ſpeculi ſphæ- riciconuexi) trãſeuntis: imago illi{us} lineæ uidebitur recta. 53 p 6.
[375.] 19. Si uiſ{us} ſit in ſuperficie incidẽtiæ: imago lineæ rectæ, infini-tæ peripheriam circuli (qui eſt communis ſectio ſuperficierum, re-flexionis & ſpeculi ſphærici conuexi) tangentis, & ad partem ui-ſui oppoſitam obliquatæ, uidebitur punctum. 54 p 6.
[376.] 20. Si uiſ{us} ſit in ſuperficie inci-dentiæ: imago lineæ rectæ infinitæ, peripheriam circuli (qui eſt commu-nis ſectio ſuperficierũ reflexionis & ſpeculi ſphærici conuexi) ſiue tangen tis, ſiue non, & ad uiſ{us} partemobli-quatæ, nulla uidebitur. 55 p 6.
[377.] 21. Si uiſ{us} ſit in ſuperficie incidentiæ: ιmago lιneæ rectæ infinitæ; peripheriam circuli (qui eſt communis ſectio ſuperficierum, reflexionis & ſpeculi ſphærici conuexi) nec tangentis nec per centrum ſecantis, & ad partem uιſuι oppoſitam obliquatæ, uidebitur curua. 56 p 6.
[378.] 22. Si uiſ{us} ſit in ſuperficie incidentiæ: imago lineæ rectæ infinitæ, quæ uel non concurrens
[379.] 23. Imago peripheriæ cum uiſu in eodem planoſitæ, intra ſpeculum ſphæricum conuexum ſen ſiliter uiſa, curua uidetur. 58. 62 p 6.
[380.] DE ERRORIBVS, QVI ACCIDVNT IN SPECVLIS CO-lumnaribus conuexis. Cap. V. 24. Si à duob{us} ellipſis cylindraceæ punctis ſint duæ perpendiculares: prima axi, continens cum recta à ſecundo puncto, ad idem axis punctum ducta acutum angulum: ſecunda rectæ el-lipſin in ſecundo puncto tangenti: ultra axem & dictum acutum angulum concurrent. 114 p 1. 44 p 7.
[381.] 25. Si uiſ{us}, & linea recta, axi ſpeculi cylindracei conuexi parallela, fuerint in eodem plana: à toto cylindri latere ad uiſum reflecti poteſt: & imago uidetur linea recta, æqualis par alle-læ. 50 p 7.
[382.] 26. Si uiſ{us} ſit extra planum lineæ rectæ, axi ſpeculi cylindracei conuexi parallelæ: à latere cy lindri fit reflexio. 30 p 7.
[383.] 27. Si uiſ{us} ſit extra planum lineæ rectæ, axi ſpeculi cylindracei conuexi parallelæ: imago ui-debitur parum curua, & minor ipſaparallela. 51 p 7.
[384.] 28. Si uiſ{us} ſit in communi ſectione planorum, lineæ rectæ & axis ſpeculi cylindracei conuexi, inter ſeperpendicularium: fiet reflexio à peripheria circuli, qui eſt communis ſectio plani lineæ & ſuperficiei ſpeculi: & imago uidebi- tur curua. 52 p 7.
[385.] 29. Si uiſ{us} æquabiliter diſtans à terminis lineæ rectæ, ſit extra eiuſdem planum, perpendiculare plano axis ſpeculi cylindracei cõ-uexi: imago maximè curua uidebitur. 53 p 7.
[386.] DE ERRORIBVS, QVI ACCIDVNT IN SPECVLIS pyramidalibus conuexis. Cap. VI. 30. Si duæ rectæ à duob{us} punctis ellipſis conicæ, inæquabiliter à uertice diſtantib{us}, ſint per-pendiculares duab{us} rectis, ellipſin in dictis punctis tangentib{us}: ultra axem concurrent. Opor tet autem ut perpendicularis à puncto propinquiore, & recta à longinquiore ad axem ductæ, acutum angulum comprehendant. 113 p 1. 45 p 7.
[387.] 31. Linea recta tota ab uno ſpeculi conici conuexi latere ad uiſum reflecti po-teſt. 41 p 7.
[388.] 32. Si linea recta obliquè inciderit uertici ſpeculi conici conuexi: reflectetur à latere coni-co ad uiſum inter dictam lineam & ſpeculi ſuperficiem ſitum: eius́ imago parum curua ui-debitur. 55 p 7.
[389.] 33. Si recta linea ſit parallela latitudini ſpeculi conici conuexi: & uiſ{us} ſit extra planum di-ctæ lineæ baſi parallelum: reflectetur ab ellipſi: & imago uidebitur maximè curua. 56 p 7.
[390.] 34. Si recta linea nec uertici ſpeculi conici conuexi obliquè incidat, nec latitudini ei{us} ſit paral lela: imaginem uariæ obliquitatis prouario ſit u uiſui offeret. 57 p 7.
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        <div xml:id="echoid-div879" type="section" level="0" n="0">
          <head xml:id="echoid-head712" xml:space="preserve">VITELLONIS FI-
            <lb/>
          LII THVRINGORVM ET PO-
            <lb/>
          LONORVM OPTICAE LIBER SECVNDVS.</head>
          <p style="it">
            <s xml:id="echoid-s23988" xml:space="preserve">VNiuerſalib{us} hui{us} ſcientiæ axiomatib{us} mathematicis præmißis:</s>
            <s xml:id="echoid-s23989" xml:space="preserve"> in hoc
              <lb/>
            ſecundo libro (ut promiſim{us}) uniuerſali actioni ſenſibilium formarum
              <lb/>
            quædã præambula naturalia præmittentes, de modo proiectionis luminis
              <lb/>
            per mediũ uni{us} diaphani, uel pluriũ ſuper diuerſas figuras corporum, &
              <lb/>
            de proiectione umbrarũ, & de figuratione lucis cadentis per fenestras aggredimur tra-
              <lb/>
            ctatum, ut de ijs, ſine quibus ſermonẽ uiſibilium formarũ aggredi conueniens non fuit,
              <lb/>
            prout in proceſſu postmodum patebit:</s>
            <s xml:id="echoid-s23990" xml:space="preserve"> quæ uerò præmittim{us}, ut nota ſenſui, ſunt iſta.</s>
            <s xml:id="echoid-s23991" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div880" type="section" level="0" n="0">
          <head xml:id="echoid-head713" xml:space="preserve">DEFINITIONES.</head>
          <p>
            <s xml:id="echoid-s23992" xml:space="preserve">1.</s>
            <s xml:id="echoid-s23993" xml:space="preserve"> Corpus luminoſum, dicitur omne corpus, quod eſt ſui luminis diffuſiuũ.</s>
            <s xml:id="echoid-s23994" xml:space="preserve"> 2.</s>
            <s xml:id="echoid-s23995" xml:space="preserve"> Cor
              <lb/>
            pus diaphanum dιcitur omne corpus, per quod lumini patet tranſitus.</s>
            <s xml:id="echoid-s23996" xml:space="preserve"> 3.</s>
            <s xml:id="echoid-s23997" xml:space="preserve"> Corpus
              <lb/>
            umbroſum dicitur corpus, per quod lumini non patet tranſitus.</s>
            <s xml:id="echoid-s23998" xml:space="preserve"> 4.</s>
            <s xml:id="echoid-s23999" xml:space="preserve"> Lux prima dici-
              <lb/>
            turilla, quæ efficit ſecundã, ſicut lux intrans domũ per feneſtrã, & illuminãs domũ
              <lb/>
            reſiduã in loco, cui incidit, dicitur prima:</s>
            <s xml:id="echoid-s24000" xml:space="preserve"> in angulis uerò domus dicitur lux ſecun-
              <lb/>
            da.</s>
            <s xml:id="echoid-s24001" xml:space="preserve"> 5.</s>
            <s xml:id="echoid-s24002" xml:space="preserve"> Lux minima dicitur, quæ ſi diuidi intelligatur, nõ habebit amplius actũ lucis.</s>
            <s xml:id="echoid-s24003" xml:space="preserve">
              <lb/>
            6.</s>
            <s xml:id="echoid-s24004" xml:space="preserve"> Radius dicitur linea luminoſa.</s>
            <s xml:id="echoid-s24005" xml:space="preserve"> 7.</s>
            <s xml:id="echoid-s24006" xml:space="preserve"> Linea radialis dicitur linea, per quam fit diffuſio
              <lb/>
            formarũ.</s>
            <s xml:id="echoid-s24007" xml:space="preserve"> 8.</s>
            <s xml:id="echoid-s24008" xml:space="preserve"> Linea refracta dicitur linea, cuius partes angulũ continẽt.</s>
            <s xml:id="echoid-s24009" xml:space="preserve"> 9.</s>
            <s xml:id="echoid-s24010" xml:space="preserve"> Pyramis ra-
              <lb/>
            dialis dicitur pyramis, cuius baſis eſt in ſuperficie corporis ſuã formã diffundentis,
              <lb/>
            & uertex in puncto alterius corporis cuiuſcunq;</s>
            <s xml:id="echoid-s24011" xml:space="preserve">. 10.</s>
            <s xml:id="echoid-s24012" xml:space="preserve"> Pyramis illuminatiõis dicitur
              <lb/>
            illa, cuius uertex eſt in pũcto corporis luminoſi, & baſis in ſuperficie rei illuminatę.</s>
            <s xml:id="echoid-s24013" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div881" type="section" level="0" n="0">
          <head xml:id="echoid-head714" xml:space="preserve">PETITIONES.</head>
          <p>
            <s xml:id="echoid-s24014" xml:space="preserve">Petimus autẽ hæc, ut per ſe ſenſui nota:</s>
            <s xml:id="echoid-s24015" xml:space="preserve"> 1.</s>
            <s xml:id="echoid-s24016" xml:space="preserve"> Lucẽ cõpreſſam fortiorẽ eſſe luce diſ-
              <lb/>
            gregata.</s>
            <s xml:id="echoid-s24017" xml:space="preserve"> 2.</s>
            <s xml:id="echoid-s24018" xml:space="preserve"> Item lucem fortiorem uehementius illuminare, & lõgius ſe diffundere.</s>
            <s xml:id="echoid-s24019" xml:space="preserve">
              <lb/>
            3.</s>
            <s xml:id="echoid-s24020" xml:space="preserve"> Item in abſentia luminis umbram fieri.</s>
            <s xml:id="echoid-s24021" xml:space="preserve"> 4.</s>
            <s xml:id="echoid-s24022" xml:space="preserve"> Item in allatione luminis umbram defi
              <lb/>
            cere.</s>
            <s xml:id="echoid-s24023" xml:space="preserve"> 5.</s>
            <s xml:id="echoid-s24024" xml:space="preserve"> Item aliquam umbram in ſui termino acui, & ad punctum terminari.</s>
            <s xml:id="echoid-s24025" xml:space="preserve"> 6.</s>
            <s xml:id="echoid-s24026" xml:space="preserve"> Item
              <lb/>
            lucẽ ad omnẽ poſitionis differentiam ęqualiter diffundi.</s>
            <s xml:id="echoid-s24027" xml:space="preserve"> 7.</s>
            <s xml:id="echoid-s24028" xml:space="preserve"> Item lucẽ res coloratas
              <lb/>
            pertrãſeuntẽ illarũ coloribus colorari, ut patet de luce trãſeunte uitreas feneſtras,
              <lb/>
            quę illorũ uitrorũ colorib.</s>
            <s xml:id="echoid-s24029" xml:space="preserve"> informat̃, ſecũ formas illorũ colorũ ſuper obiecta cor-
              <lb/>
            pora deferendo.</s>
            <s xml:id="echoid-s24030" xml:space="preserve"> 8.</s>
            <s xml:id="echoid-s24031" xml:space="preserve"> Itẽ quòd natura nihil fruſtra agit, ſicut nec deficit in neceſſarijs.</s>
            <s xml:id="echoid-s24032" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div882" type="section" level="0" n="0">
          <head xml:id="echoid-head715" xml:space="preserve">THEOREMATA</head>
          <head xml:id="echoid-head716" xml:space="preserve" style="it">1. Radij quorumcun luminum & multiplic ationes formarum, ſecundum rectas lineas
            <lb/>
          protenduntur. Alhazen 2 n 7.</head>
          <p>
            <s xml:id="echoid-s24033" xml:space="preserve">HOc quod hic proponitur, non demonſtratione, ſed inſtrumentaliter poteſt declarari:</s>
            <s xml:id="echoid-s24034" xml:space="preserve">
              <lb/>
            diuerſitas tamen antiquorũ ad hoc proban dũ pluribus & diuerſis uſa eſt inſtrumentis,
              <lb/>
            nos uerò utimuriſto, quod hic ſubſcribimus, quòd regularius huic ꝓpoſito credimus
              <lb/>
            cõuenire.</s>
            <s xml:id="echoid-s24035" xml:space="preserve"> Aſſumaturitaq;</s>
            <s xml:id="echoid-s24036" xml:space="preserve"> uas æneum rotundũ cõuenienter ſpiſſum, ad modum matris
              <lb/>
            aſtrolabij, cuius fundi latitudo ſit unius cubiti, uel maior, & altitudo oræ eius ſit æqua-
              <lb/>
            lis latitudini duorũ digitorũ perpẽdicularis ſuper baſim uaſis:</s>
            <s xml:id="echoid-s24037" xml:space="preserve"> & in medio dorſi huius uaſis ſit per-
              <lb/>
            pendiculariter erectũ aliquod corpus plurimũ rotundũ columnare, cuius longitudo ſit æqualis la
              <lb/>
            titudini trium digitorũ, latitudo uerò eιus ſit minor uno digito:</s>
            <s xml:id="echoid-s24038" xml:space="preserve"> & ponatur hoc uas ſecũdũ ſui pun-
              <lb/>
            cta media in tornatorio, & tornetur quouſq;</s>
            <s xml:id="echoid-s24039" xml:space="preserve"> peripheria eius ſit intrinſecus & extrinſecus ueræ ro-
              <lb/>
            tunditatis, & adæquentur planæ ſuperficies ipſius, & corpus columnare, quod eſt in medio dorſi,
              <lb/>
            fiat rotundũ.</s>
            <s xml:id="echoid-s24040" xml:space="preserve"> Signentur itaq;</s>
            <s xml:id="echoid-s24041" xml:space="preserve"> in interiori ſuperficie fundi huius uaſis duæ diametri orthogonaliter
              <lb/>
            ſe ſecantes, quæ ſint a b & c d:</s>
            <s xml:id="echoid-s24042" xml:space="preserve"> palàm, quoniam illę diametri tranſeunt per centrum circuli fun-
              <lb/>
            di, quod ſit e:</s>
            <s xml:id="echoid-s24043" xml:space="preserve"> deinde ſignetur in baſi oræ iſtius uaſis, quæ eſt circulus a c b d, in diſtantia extremita-
              <lb/>
            tis alterius diametrorum productarum, ut diametri a b, ſecundum latitudinem unius digiti pun-
              <lb/>
            </s>
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