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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[131.] 4. Duærectæ lineæ ab utro uiſu ductæad concurſum duorum axium, factum in recta linea ad utrun axem obliqua, ſunt ferè inæquales. 41 p 3.
[132.] 5. E plurib. uiſibilib. ordinatim intraopticos axes diſpoſitis: remotiora incertè uidẽtur. 50 p 3.
[133.] 6. Si duæ rectæ lineæ à medio nerui cõmunis ſint contermi-nærectæ cõnectenti centra for aminum gyrineruorum cauo-rum: conſtituent triangulum æquicrurum. 30 p 3.
[134.] 7. Si recta linea ſit à medio nerui communis admedium rectæ lineæ connectentis centra fo-raminum gyrineruorum cauorum: erit ad ipſam perpendicularis. 33 p 3.
[135.] 8. Si axes, communis & duo optici, in uno uiſibilis puncto concurrant: erunt in eodem plano cum rectis, connectente centra foraminum gyrineruorum cauorum, & duab{us} à medio nerui communis connectenti conterminis. 34 p 3.
[136.] 9. Vtro uiſu uiſibile unum plerun uidetur. 28 p 3. Idem 27 n 1.
[137.] 10. Concurſiis axium opticorum in axe communifacit uiſionem certißimam: extrà, tantò certiorem, quantò axi propinquior fuerit. 44 p 3.
[138.] 11. Viſibile intra axes opticos ſitum: ueluni uiſui rectè, reliquo obliquè oppoſitum: uidetur geminum. 104.103 p 4.
[139.] 12. Viſibile aliàs unum: aliàs geminum uideri organo ostenditur. 108 p 4.
[140.] 13. Viſibile medio unius uiſus rectè, reliquo obliquè oppoſitum, uidetur geminum. 103 p 4. Idem II n.
[141.] 14. Viſibile, in quo concurrunt axes optici, aut radij his propinqui: uidetur unum. 46 p 3.
[142.] 15. Viſibile in axium opticorum concurſu certißimè uidetur: extratantò certius, quantò concurſui fuerit propinquius. 45 p 3.
[143.] 16. Viſibile magnum ſimul totum æquabiliter non uidetur. 48 p 3.
[144.] 17. Viſibile uiſui directũ, certißimè uidetur: obliquũ tantò minus, quantò obliquius. 33 p 4.
[145.] DE CAVSSIS, QVIBVS VISVI ACCIDIT DE-ceptio. Cap. III. 18. Ad uiſionem perficiendam octo neceſſaria ſunt: quorum quodlibet ad uitandum allu-cinationes, uiſibili ſymmetrum eſſe oportet. 1. 2. 13. 14. 15. 16. 19. 56 p 3. 1 p 4. Vide 36 n 1.
[146.] DE DISTINGVENDIS ERRORIBVS VI-ſus. Cap. IIII. 19. In uiſione erratur aut ſolo uiſu: aut anticipata notione: aut ſyllogiſmo.
[147.] DE QVALITATIBVS DECEPTIONVM VISVS, QVAE fiunt ſolo ſenſu. Cap. v. 20. Erratur ſolo uiſu in luce & colore, propter ſingulorum uiſionem perficientium aſymme-triam. 156 p 4.
[148.] DE QVALITATIBVS DECEPTIONVM VISVS, QVAE fiuntin ſcientia & cognitione. Cap. VI. 21. Erratur anticipata nõtione: cum forma anticipata, obiecto uiſibili perperam aßimila-tur, propter ſingulorum uiſionem perficientium aſymmetriam. 155 p 4.
[149.] DE QVALITATIBVS DECEPTIONVM VISVS, QVAE AC-cidunt in ſyllogiſmo & ratione. Cap. VII. 22. Erratur ſyllogiſmo propter ſingulorum uiſionem perficientium aſymmetriam.
[150.] 23. Diſtantia immoder ata cre at errores in ſingulis uiſibilibus ſpeciebus. In remotione. 16 p 4.
[151.] 24. In ſitu. 44. 59. 61. 62. 97 p 4.
[152.] 25. In ſoliditate & figura. 98. 97. 95. 50. 65 p 4.
[153.] 26. In magnitudine. 28 p 4.
[154.] 27. In diuiſione, & continuatione & numero 109 p 4.
[155.] 28. In motu & quiete. 138 p 4.
[156.] 29. In aſperitate & lenitate. 141 p 4.
[157.] 30. In raritate & denſitate. 144 p 4.
[158.] 31. In umbra & tenebris. 147 p 4.
[159.] 32. In pulchritudine & deformitate. 150 p 4.
[160.] 33. In ſimilitudine & dißimilitudine. 153 p 4.
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          <p>
            <s xml:id="echoid-s4985" xml:space="preserve">
              <pb o="92" file="0098" n="98" rhead="ALHAZEN"/>
            Et hæc erit enumeratio ſecundum unam quam que octo cauſſarum prius dictarum, & primò ſecun-
              <lb/>
            dum longitudinem.</s>
            <s xml:id="echoid-s4986" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div161" type="section" level="0" n="0">
          <head xml:id="echoid-head190" xml:space="preserve" style="it">23. Diſtantia immoder ata cre at errores in ſingulis uiſibilibus ſpeciebus. In remotione. 16 p 4.</head>
          <p>
            <s xml:id="echoid-s4987" xml:space="preserve">DIco ergo, quòd longitudo egreſſa à temperamento errare facit uidentem in longitudine:</s>
            <s xml:id="echoid-s4988" xml:space="preserve"> ſi-
              <lb/>
            cut accidit, cum quis arbores ualde remotas inſpexerit, licet plurimùm diſtent inter ſe, uide-
              <lb/>
            buntur tamen quaſi coniunctæ, aut ſaltem æſtimabuntur ſibi propinquæ.</s>
            <s xml:id="echoid-s4989" xml:space="preserve"> Ob eandem cauſ-
              <lb/>
            ſam euenit, ut ſtellæ aliquando reputentur quaſi coniunctæ, licet plurimùm diſtent in ueritate.</s>
            <s xml:id="echoid-s4990" xml:space="preserve"> Ob
              <lb/>
            hoc ſtellæ erraticæ æſtimantur ab hominib.</s>
            <s xml:id="echoid-s4991" xml:space="preserve"> in eadem ſuperficie cum fixis, licet plurimùm elongatę
              <lb/>
            ſint ab eis.</s>
            <s xml:id="echoid-s4992" xml:space="preserve"> Eſt ergo error in longitudine propter egreſſum longitudinis à temperantia.</s>
            <s xml:id="echoid-s4993" xml:space="preserve"> Et eſt error
              <lb/>
            iſte in ſyllogiſmo, cum longitudin is tantùm per ſyllogiſmum fiat comprehenſio.</s>
            <s xml:id="echoid-s4994" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div162" type="section" level="0" n="0">
          <head xml:id="echoid-head191" xml:space="preserve" style="it">24. In ſitu. 44. 59. 61. 62. 97 p 4.</head>
          <p>
            <s xml:id="echoid-s4995" xml:space="preserve">LOngitudo extra temperantiam, ſitus errorem inducit:</s>
            <s xml:id="echoid-s4996" xml:space="preserve"> quoniam à tali longitudine corpus de-
              <lb/>
            clinatum apparebit rectum:</s>
            <s xml:id="echoid-s4997" xml:space="preserve"> & ob hoc corpus quadratũ in hac lõgitudine declinatũ, uidebitur
              <lb/>
            oblongum.</s>
            <s xml:id="echoid-s4998" xml:space="preserve"> Eodẽ modo oblõga apparebit circularis forma in hac longitudine declinata.</s>
            <s xml:id="echoid-s4999" xml:space="preserve"> Nec
              <lb/>
            accidit error iſte, niſi ex declinationis occultatione, quę latet in tanta lõgitudine.</s>
            <s xml:id="echoid-s5000" xml:space="preserve"> Si enim appareret
              <lb/>
            declinatio, nõ eſſet aſsignare, quare occultaretur ueritas corporalis formę.</s>
            <s xml:id="echoid-s5001" xml:space="preserve"> Eſt igitur error in ſolo ſi-
              <lb/>
            tu ex lõgitudinis immoderatione.</s>
            <s xml:id="echoid-s5002" xml:space="preserve"> Et quare ignoretur ſitus, eſt hęc ratio.</s>
            <s xml:id="echoid-s5003" xml:space="preserve"> Exceſſus unius radiorũ in
              <lb/>
            latus quadrati cadentium ſuper longitudinem alterius, nõ eſt proportionalis, reſpectu totalis remo
              <lb/>
            tionis corporis à uiſu:</s>
            <s xml:id="echoid-s5004" xml:space="preserve"> proportione dico ſenſibili:</s>
            <s xml:id="echoid-s5005" xml:space="preserve"> unde propter inſenſibilitatẽ exceſſus nõ ęſtimatur
              <lb/>
            maior aliquo aliquis radius.</s>
            <s xml:id="echoid-s5006" xml:space="preserve"> Reputatur uerò oblõga quadrati forma, qñ unũ eius latus nõ declina-
              <lb/>
            tũ, reſpectu uiſus, cadit in partem oculi, & in minorem incidit forma lateris declinati, quoniã ſub mi
              <lb/>
            nore angulo.</s>
            <s xml:id="echoid-s5007" xml:space="preserve"> Et erit huiuſmodi minoritatis perceptio, ſecundum quod fuerit quadrati declinatio.</s>
            <s xml:id="echoid-s5008" xml:space="preserve">
              <lb/>
            Et quoniã non attenditur declinatio, æſtimabitur unũ latus maius alio:</s>
            <s xml:id="echoid-s5009" xml:space="preserve"> quoniã ſub maiore angulo.</s>
            <s xml:id="echoid-s5010" xml:space="preserve">
              <lb/>
            Proinde forma apparebit oblonga.</s>
            <s xml:id="echoid-s5011" xml:space="preserve"> Pari ratione in circulari forma, una diameter maior apparet alia:</s>
            <s xml:id="echoid-s5012" xml:space="preserve">
              <lb/>
            unde reputatur oblõga.</s>
            <s xml:id="echoid-s5013" xml:space="preserve"> Et eſt error iſte exintẽperantia longitudinis:</s>
            <s xml:id="echoid-s5014" xml:space="preserve"> quod nõ accideret, ſi tẽperata
              <lb/>
            eſſet.</s>
            <s xml:id="echoid-s5015" xml:space="preserve"> Si uerò lõgitudo, licet intẽperata, non fuerit multũ magna, ſed ualida ſit illius corporis declina
              <lb/>
            tio:</s>
            <s xml:id="echoid-s5016" xml:space="preserve"> perpendet fortaſſe uidens declinationem, ſed non declinationis ueritatẽ:</s>
            <s xml:id="echoid-s5017" xml:space="preserve"> imò minorem æſtima
              <lb/>
            bit quàm ſit, & conferet declinationẽ lateris cum angulo, ſub quo cõprehenditur:</s>
            <s xml:id="echoid-s5018" xml:space="preserve"> unde minor appa
              <lb/>
            rebit quantitas talis quã ſit:</s>
            <s xml:id="echoid-s5019" xml:space="preserve"> unde & ſic reputabitur quadrati forma oblõga, ſed minus quàm prius.</s>
            <s xml:id="echoid-s5020" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div163" type="section" level="0" n="0">
          <head xml:id="echoid-head192" xml:space="preserve" style="it">25. In ſoliditate & figura. 98. 97. 95. 50. 65 p 4.</head>
          <p>
            <s xml:id="echoid-s5021" xml:space="preserve">SVperfluitas longitudinis errorem generat corporeitatis.</s>
            <s xml:id="echoid-s5022" xml:space="preserve"> Corporeitas aũt eſt ex diſpoſitione
              <lb/>
            ſpeciei, & cõprehenditur notitia corporeitatis ex notitia huiuſmodi diſpoſitionis.</s>
            <s xml:id="echoid-s5023" xml:space="preserve"> Cum ergo
              <lb/>
            error acciditin corporeitate, erit in ſpeciei uel ſpecierum diſp oſitione:</s>
            <s xml:id="echoid-s5024" xml:space="preserve">uelut ſi ſpecies corporis
              <lb/>
            incuruata ex aliqua lõgitudine uideatur plana, aut plana æſtimetur curua.</s>
            <s xml:id="echoid-s5025" xml:space="preserve"> Et hęc apparentia erit in
              <lb/>
            figura.</s>
            <s xml:id="echoid-s5026" xml:space="preserve"> Eſt igitur figura ſpecierũ corporis diſpoſitio.</s>
            <s xml:id="echoid-s5027" xml:space="preserve"> Recipit etiã ſitũ ſpecierũ diſpoſitio:</s>
            <s xml:id="echoid-s5028" xml:space="preserve"> unde corpo
              <lb/>
            reitas includitur ſub figura & ſitu:</s>
            <s xml:id="echoid-s5029" xml:space="preserve"> unde errorem corporeitatis gerit in ſe error ſitus & figuræ.</s>
            <s xml:id="echoid-s5030" xml:space="preserve"> Acci-
              <lb/>
            dit aũt error figuræ abſque ſitus errore ex longitudinis immoderatione.</s>
            <s xml:id="echoid-s5031" xml:space="preserve"> Verbi gratia, figura multo
              <lb/>
            rum laterum ęqualium, directè oppoſita uiſui in longitudine intemperata, circularis apparet:</s>
            <s xml:id="echoid-s5032" xml:space="preserve"> nõ ob
              <lb/>
            aliud quidẽ, niſi quia anguli figuræ ſunt imperceptibiles uiſui.</s>
            <s xml:id="echoid-s5033" xml:space="preserve"> Longitudo enim illa abſcondit uiſui
              <lb/>
            etiam proportionalia toti, quamuis nõ totum.</s>
            <s xml:id="echoid-s5034" xml:space="preserve"> Eodem erroris tenore ab hac longitudine linea cur-
              <lb/>
            ua æſtimatur recta.</s>
            <s xml:id="echoid-s5035" xml:space="preserve"> Non enim perceptibilis eſt maioritas acceſſus unius lineæ partis incuruatæ ad
              <lb/>
            uiſum, ſuper partis eiuſdem remotioris acceſſum:</s>
            <s xml:id="echoid-s5036" xml:space="preserve"> quia occultatur incuruatio partiũ, licet error non
              <lb/>
            accidit in ſitu lineę illius.</s>
            <s xml:id="echoid-s5037" xml:space="preserve"> Similiter uiſa ſphæra ab hac longitudine æſtimabitur ſpecies plana.</s>
            <s xml:id="echoid-s5038" xml:space="preserve"> Quo-
              <lb/>
            niam propin quitas tumoris eius imperceptibiliter propinquitatẽ extremitatũ ab hac longitudine
              <lb/>
            excedit:</s>
            <s xml:id="echoid-s5039" xml:space="preserve"> unde ęſtimatur æqualis partium propinquitas:</s>
            <s xml:id="echoid-s5040" xml:space="preserve"> unde ſpeciei planitudo.</s>
            <s xml:id="echoid-s5041" xml:space="preserve"> Inde eſt, quòd ſol &
              <lb/>
            luna ſuperficiales uidentibus reputantur;</s>
            <s xml:id="echoid-s5042" xml:space="preserve"> quę erronea excluderetur figuræ reputatio, ſi temperata
              <lb/>
            eſſet longitudo.</s>
            <s xml:id="echoid-s5043" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div164" type="section" level="0" n="0">
          <head xml:id="echoid-head193" xml:space="preserve" style="it">26. In magnitudine. 28 p 4.</head>
          <p>
            <s xml:id="echoid-s5044" xml:space="preserve">IN magnitudine corporis erit error ex intemperata lõgitudine:</s>
            <s xml:id="echoid-s5045" xml:space="preserve"> quoniã uidebitur multò minus,
              <lb/>
            quàm ſit in ueritate.</s>
            <s xml:id="echoid-s5046" xml:space="preserve"> Ethuius rei ratio eſt.</s>
            <s xml:id="echoid-s5047" xml:space="preserve"> Quoniã, ut diximus, longitudo intẽperata eſt, quæ par
              <lb/>
            tes proportionales toti proportione etiam ſenſibili abſcondit uiſui.</s>
            <s xml:id="echoid-s5048" xml:space="preserve"> Et cum fuerit occultatio par
              <lb/>
            tium ſenſui perceptibilium:</s>
            <s xml:id="echoid-s5049" xml:space="preserve"> anguli, in quos cadunt, non ſentientur, licet totali angulo proportiona-
              <lb/>
            les ſint.</s>
            <s xml:id="echoid-s5050" xml:space="preserve"> Vnde cum diſcurrit axis rem uiſam, abſconduntur ei lineæ multę ex ea, & partes multæ.</s>
            <s xml:id="echoid-s5051" xml:space="preserve"> Vn
              <lb/>
            de minor efficitur totalis apparentia.</s>
            <s xml:id="echoid-s5052" xml:space="preserve"> Amplius magnitudo partis alicuius corporis non conſidera-
              <lb/>
            tur, niſi ſecundum magnitudinem anguli, in quẽ cadit:</s>
            <s xml:id="echoid-s5053" xml:space="preserve"> & magnitudo anguli attenditur ſecundũ par
              <lb/>
            tem in uiſu ſectam:</s>
            <s xml:id="echoid-s5054" xml:space="preserve"> & partis ſectę quantitas æſtimatur ſecundũ duo puncta illius partis terminalia:</s>
            <s xml:id="echoid-s5055" xml:space="preserve">
              <lb/>
            & puncta illa ſenſibilia ſunt, & parti ſectæ proportionalia.</s>
            <s xml:id="echoid-s5056" xml:space="preserve"> Quoniã à lõgitudine tanta æſtimatur res
              <lb/>
            uiſa ſecundũ fines toti uiſo proportionales:</s>
            <s xml:id="echoid-s5057" xml:space="preserve"> aliter enim non eſſent fines illi ſenſibiles:</s>
            <s xml:id="echoid-s5058" xml:space="preserve"> & fines partis
              <lb/>
            ſectę directè opponuntur finib.</s>
            <s xml:id="echoid-s5059" xml:space="preserve"> partis uiſę proportionalib.</s>
            <s xml:id="echoid-s5060" xml:space="preserve"> Puncta ergo illa partis ſe ctæ terminalia
              <lb/>
            abſcondunt ex re uiſa partes ſenſibiles.</s>
            <s xml:id="echoid-s5061" xml:space="preserve"> Cum ergo incedit axis ſuperſingulas rei partes:</s>
            <s xml:id="echoid-s5062" xml:space="preserve"> ex ſingulis
              <lb/>
            partib.</s>
            <s xml:id="echoid-s5063" xml:space="preserve"> abſconduntur partes ſenſibiles:</s>
            <s xml:id="echoid-s5064" xml:space="preserve"> & ita minor apparet tota rei quantitas.</s>
            <s xml:id="echoid-s5065" xml:space="preserve"> Cum aũt uidetur cor
              <lb/>
            pus à tẽperata long tudine, puncta terminalia partis ſectę ualde ſunt parua, & quaſi inſenſibilia ad
              <lb/>
            </s>
          </p>
        </div>
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