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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[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)
[221.] DE MODO COMPREHENSIONIS FORMARVM È COR-poribus politis. Cap. V. 21. Imago uiſibilis percipitur è reflexione formæ uiſibilis à ſpeculo ad uiſum facta. 24 p 5.
Page: 120 (114)
[222.] 22. Si uiſibile & ſpeculum figuræ ſit{us}́ ſimilitudine conueniant: uera & distincta imago uidetur. 35 p 5.
Page: 120 (114)
[223.] 23. Superficies reflexionis quatuor habet puncta: uiſibilis: reflexionis: uiſ{us}: & terminũ per-pendicularis ductæ à puncto reflexionis ſuper planum in eodem puncto ſpeculum tangens. Ita perpendicularis hæc cõmunis eſt omnib{us} reflexionis ſuperficieb{us}. 27 p 5.6 p 6.24 p 7.3 p 8.3 p 9.
Page: 121 (115)
[224.] 24. Si uiſ{us} ſit extra ſuperficiem ſpeculi ſphærici conuexi, uelipſi continuam: communis ſe-ctio baſis pyramidis opticæ & ſuperficiei ſpeculi, erit peripheria minimi in ſphæra circuli. 3 p 6.
Page: 121 (115)
[225.] 25. Si duarum rectarum linearum à uiſu, alter a ſpeculum ſphæricum conuexum tangat, re-liqua per centrum ſecet: tangens circa ſecantem fixam cõuerſa, definiet ſegmentum ſuperficiei ſpeculι: à cui{us} puncto quolibet poteſt ad uiſum fieri reflexio. Et centra uiſ{us} & ſpeculi, puncta reflexionis & uiſibilis ſunt in reflexionis ſuperficie. 2.5.6 p 6.
Page: 122 (116)
[226.] 26. Siduo plana à cẽtro uiſiis, ducãtur ք later a cõſpicuam ſpeculi cylindracei cõuexi ſuperficiẽ terminãtia: tangẽt ſpeculũ: & facient in uiſu cõmunem ſectionẽ par allelã axiſpeculi. 2.3 p 7.
Page: 122 (116)
[227.] 27. Si linea recta à cẽtro uiſ{us}, ducta ad punctũ cõſpicuæ ſuper-ficiei ſpeculi cylindr acei cõuexi, cõtinuetur: ſecabit ſpeculũ. 4.5 p 7.
Page: 123 (117)
[228.] 28. In ſpeculo cylindraceo conuexo, à quolibet conſpicuæ ſuperficiei puncto poteſt ad uiſum reflexio fieri. 25 p 7.
Page: 123 (117)
[229.] 29. Si uiſ{us} ſit extra ſuperficiem ſpeculi cylindr acei conuexi, in plano uiſibilis per axem du-cto: cõm unis ſectio ſuperficier um reflexionis & ſpeculi, erit lat{us} cylindri: & unicum tantùm eſt in eadem conſpicua ſuperficie planum, à quo ad eundem uiſum reflexio fieri poteſt. 7.16 p 7.
Page: 123 (117)
[230.] 30. Si uiſ{us} ſit extrá ſuperficiem ſpeculi cylindracei cõuexi, in planò uiſibilis ad axem recto: communis ſectio ſuperficierum reflexionis & ſpeculi, erit circul{us}: & unic{us} tantùm eſt in ea-dem conſpicuà ſuperficie, à quo ad uiſum reflexio fieri poteſt. 9.17 p 7.
Page: 124 (118)
< >
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          <p>
            <s xml:id="echoid-s17032" xml:space="preserve">
              <pb o="241" file="0247" n="247" rhead="OPTICAE LIBER VII."/>
            neceſſe eſt, ut ſit aliqua groſsities:</s>
            <s xml:id="echoid-s17033" xml:space="preserve"> nam corpus paruæ diaphanitatis nõ habet finem in imaginatio-
              <lb/>
            ne, quæ eſt imaginatio lucidæ diaphanitatis:</s>
            <s xml:id="echoid-s17034" xml:space="preserve"> & omnia corpora naturalia perueniũt ad finem, quem
              <lb/>
            non poſſunt tranſire.</s>
            <s xml:id="echoid-s17035" xml:space="preserve"> Corporà ergo naturalia diaphana non poſſunt euadere aliquam groſsitiem.</s>
            <s xml:id="echoid-s17036" xml:space="preserve">
              <lb/>
            Luces ergo cum tranſeunt per corpora diaphana, tranſeunt ſecundũ diaphanitatem, quæ eſt in eis,
              <lb/>
            & ſic impediunt lucem ſecundum groſsitiem, quæ eſt in eis.</s>
            <s xml:id="echoid-s17037" xml:space="preserve"> Cum ergo lux tranſiuerit per corpus
              <lb/>
            diaphanum, & occurrit alij corpori groſsiori primo:</s>
            <s xml:id="echoid-s17038" xml:space="preserve"> tunc corpus groſsius reſiſtit luci uehemẽtιus,
              <lb/>
            quàm primum reſiſtebat:</s>
            <s xml:id="echoid-s17039" xml:space="preserve"> & omne motum cum mouetur ad aliquam partem eſſentialiter aut acci-
              <lb/>
            dentaliter, ſi occurrerit reſiſtenti, neceſſe eſt, ut motus eius tranſmutetur:</s>
            <s xml:id="echoid-s17040" xml:space="preserve"> & ſi reſiſtentia fuerit for-
              <lb/>
            tis:</s>
            <s xml:id="echoid-s17041" xml:space="preserve"> tunc motus ille refringetur ad contrariam partem:</s>
            <s xml:id="echoid-s17042" xml:space="preserve"> ſi uerò debilis, nõ refringetur ad contrariam
              <lb/>
            partem, nec poterit per illã procedere, per quam incœperat:</s>
            <s xml:id="echoid-s17043" xml:space="preserve"> ſed motus eius mutabitur.</s>
            <s xml:id="echoid-s17044" xml:space="preserve"> Omnium
              <lb/>
            autem motorum naturaliter, quæ rectè mouentur per aliquod corpus paſsibile:</s>
            <s xml:id="echoid-s17045" xml:space="preserve"> trãſitus ſuper per-
              <lb/>
            pendicularem, quæ eſt in ſuperficie corporis, in quo eſt trãſitus, erιt facilior.</s>
            <s xml:id="echoid-s17046" xml:space="preserve"> Et hoc uidetur in cor-
              <lb/>
            poribus naturalibus.</s>
            <s xml:id="echoid-s17047" xml:space="preserve"> Si enim aliquis acceperit tabulã ſubtilem, & paxιllauerit illam ſuper aliquod
              <lb/>
            foramen amplum, & ſteterit in oppoſitione tabulæ, & acceperit pilam ferream, & eiecerit eã ſuper
              <lb/>
            tabulam fortiter, & obſeruauerit, ut motus pilæ ſit ſuper perpendicularem ſuper ſuperficiem tabu-
              <lb/>
            læ:</s>
            <s xml:id="echoid-s17048" xml:space="preserve"> tunc tabula cedet pilæ aut frangetur, ſi tabula ſubtilis fuerit, & uis, qua ſphæra mouetur, fuerit
              <lb/>
            fortis.</s>
            <s xml:id="echoid-s17049" xml:space="preserve"> Et ſi ſteterit in parte obliqua ab oppoſitione tabulę, & in illa eadẽ diſtantia, in qua prius erat,
              <lb/>
            & eiecerit pilam ſuper tabulam illam eandem, in quam prius eiecerat:</s>
            <s xml:id="echoid-s17050" xml:space="preserve"> tunc ſphæra labetur de tabu-
              <lb/>
            la, ſi tabula non fuerit ualde ſubtilis, nec mouebitur ad illam partem, ad quam primò mouebatur,
              <lb/>
            ſed declinabit ad aliquam partem aliam.</s>
            <s xml:id="echoid-s17051" xml:space="preserve"> Et ſimiliter, ſi acceperit enſem, & poſuerit corã ſe lignum,
              <lb/>
            & percuſſeri t cum enſe, ita ut enſis ſit perpendicularis ſuper ſuperficiem ligni:</s>
            <s xml:id="echoid-s17052" xml:space="preserve"> tunc lignum ſecabi-
              <lb/>
            tur magis:</s>
            <s xml:id="echoid-s17053" xml:space="preserve"> & ſi fuerit obliquus, & percuſſerit obliquè lignum:</s>
            <s xml:id="echoid-s17054" xml:space="preserve"> tunc lignum non ſecabitur omnino,
              <lb/>
            ſed fortè ſecabitur in parte, aut fortè enſis errabit deuiando:</s>
            <s xml:id="echoid-s17055" xml:space="preserve"> & quanto magis fuerit enſis obliquus,
              <lb/>
            tantò minus aget in lignum:</s>
            <s xml:id="echoid-s17056" xml:space="preserve"> & alia multa ſunt ſimilia:</s>
            <s xml:id="echoid-s17057" xml:space="preserve"> ex quibus patet, quòd motus ſuper perpen-
              <lb/>
            dicularem eſt fortior & facilior:</s>
            <s xml:id="echoid-s17058" xml:space="preserve"> & quòd de obliquis motibus ille, qui uιcinior eſt perpendiculari,
              <lb/>
            eſt facilior remotiore.</s>
            <s xml:id="echoid-s17059" xml:space="preserve"> Lux ergo, ſi occurrit corpori diaphano groſsiori illo corpore, in quo exiſtit:</s>
            <s xml:id="echoid-s17060" xml:space="preserve">
              <lb/>
            tunc impedietur ab eo, ita quòd non tranſibit in partem, in quam mouebatur, ſed quia non fortiter
              <lb/>
            reſiſtit, non redibit in partem, ad quam mouebatur.</s>
            <s xml:id="echoid-s17061" xml:space="preserve"> Si ergo motus lucis tranſiuerit ſuper perpendi-
              <lb/>
            cularem, tranſibit rectè propter fortitudinem motus ſuper perpendicularem:</s>
            <s xml:id="echoid-s17062" xml:space="preserve"> & ſi motus eius fue-
              <lb/>
            rit ſuper lineam obliquam:</s>
            <s xml:id="echoid-s17063" xml:space="preserve"> tunc nõ poterit tranſire propter debilitatem motus:</s>
            <s xml:id="echoid-s17064" xml:space="preserve"> accidit ergo, ut de-
              <lb/>
            clinetur ad partem motus, in quam facilius mouebitur, quàm in partem, in quam mouebatur:</s>
            <s xml:id="echoid-s17065" xml:space="preserve"> ſed
              <lb/>
            facilior motuum eſt ſuper perpendicularem:</s>
            <s xml:id="echoid-s17066" xml:space="preserve"> & quod uicinius eſt perpendiculari, eſt facilius remo-
              <lb/>
            tiore.</s>
            <s xml:id="echoid-s17067" xml:space="preserve"> Et motus in corpore, in quod tranſit, ſi fuerit obliquus ſuper ſuperficiem illius corporis, com
              <lb/>
            ponitur ex motu in par
              <gap/>
            e perpendicuiaris trãſeuntis in corpus, in quo eſt motus, & ex motu in par-
              <lb/>
            te lineæ, quæ eſt perpendicularis ſuper perpendicularem, quæ tranſit in ipſum.</s>
            <s xml:id="echoid-s17068" xml:space="preserve"> Cum ergo lux fue-
              <lb/>
            rit mota in corpore diaphano groſſo ſuper lineã obliquam:</s>
            <s xml:id="echoid-s17069" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0247-01" xlink:href="fig-0247-01a" number="212">
                <variables xml:id="echoid-variables199" xml:space="preserve">a h e d c b k q l g f</variables>
              </figure>
            tunc trãſitus eius in illo corpore diaphano erit per motum
              <lb/>
            compoſitum ex duobus prædictis motibus.</s>
            <s xml:id="echoid-s17070" xml:space="preserve"> Et quia groſsi-
              <lb/>
            ties corporis reſiſtit ei ad uerticationem, quam intẽdebat,
              <lb/>
            & reſiſtentia eius non eſt ualde fortis:</s>
            <s xml:id="echoid-s17071" xml:space="preserve"> ex quo ſequeretur,
              <lb/>
            quòd declinaret ad partẽ, ad quam facilius tranſiret:</s>
            <s xml:id="echoid-s17072" xml:space="preserve"> & mo-
              <lb/>
            tus ſuper perpendicularem eſt facilimus motuum:</s>
            <s xml:id="echoid-s17073" xml:space="preserve"> neceſſe
              <lb/>
            eſt ergo, ut lux quæ extẽditur ſuper lineam obliquam, mo-
              <lb/>
            ueatur ſuper perpendicularem, exeuntem à puncto, in quo
              <lb/>
            lux occurrit ſuperficiei corporis diaphani groſsi.</s>
            <s xml:id="echoid-s17074" xml:space="preserve"> Et quia
              <lb/>
            motus eius eſt compoſitus ex duobus motibus, quorũ al-
              <lb/>
            ter eſt ſuper lineam perpendicularem ſuper ſuperficiẽ cor-
              <lb/>
            poris groſsi, & reliquus ſuper lineam perpendicularem ſu-
              <lb/>
            per perpendicularem hanc:</s>
            <s xml:id="echoid-s17075" xml:space="preserve"> & motus compoſitus, qui eſt in
              <lb/>
            ipſo, nõ omnino dimittitur, ſed ſolummodo impeditur:</s>
            <s xml:id="echoid-s17076" xml:space="preserve"> ne-
              <lb/>
            ceſſe eſt, ut lux declinet ad partẽ faciliorem parte, ad quam
              <lb/>
            prius mouebatur, remanente in ipſo motu compoſito:</s>
            <s xml:id="echoid-s17077" xml:space="preserve"> ſed
              <lb/>
            pars facilior parte, ad quam mouebatur remanente motu
              <lb/>
            in ipſo, eſt illa pars, quę eſt uicinor perpẽdiculari.</s>
            <s xml:id="echoid-s17078" xml:space="preserve"> Vnde lux,
              <lb/>
            quę extẽditur in corpore diaphano, ſi occurrit corpori dia-
              <lb/>
            phano groſsiori corpore, in quo exiſtit:</s>
            <s xml:id="echoid-s17079" xml:space="preserve"> refringetur per li-
              <lb/>
            neam propinquiorem perpendiculari, exeunti à puncto, in
              <lb/>
            quo occurrit corpori groſsiori, quæ extenditur in corpore
              <lb/>
            groſsiore per aliam lineam quàm ſit linea, per quam moue-
              <lb/>
            batur.</s>
            <s xml:id="echoid-s17080" xml:space="preserve"> Hęc ergo cauſſa eſt refractionis ſplendoris in corpo-
              <lb/>
            ribus diaphanis, quæ ſunt groſsiora corporibus diaphanis,
              <lb/>
            in quibus exiſtunt:</s>
            <s xml:id="echoid-s17081" xml:space="preserve"> & ideo refractio propriè eſt inuẽta in lucibus obliquis.</s>
            <s xml:id="echoid-s17082" xml:space="preserve"> Cum ergo lux extendi-
              <lb/>
            tur in corpore diaphano, & occurrerit corpori diaphano diuerſæ diaphanitatis a corpore, in quo
              <lb/>
            exiſtit, & groſsiori, & fuerit obliqua ſuper ſuperficiem corporis diaphani cui occurrit:</s>
            <s xml:id="echoid-s17083" xml:space="preserve"> refringetur
              <lb/>
            </s>
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