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-s5065" xml:space="preserve">
              <pb o="93" file="0099" n="99" rhead="OPTICAE LIBER III."/>
            ipſam collata.</s>
            <s xml:id="echoid-s5066" xml:space="preserve"> Fines enim rebus uiſis inſenſibiles eligit in longitudine tẽperata exiſtimatio uiden-
              <lb/>
            tis:</s>
            <s xml:id="echoid-s5067" xml:space="preserve"> unde non abſconduntur partes toti proportionales.</s>
            <s xml:id="echoid-s5068" xml:space="preserve"> Quare corpus nõ apparet minus, quàm ha-
              <lb/>
            beat ueritas eius.</s>
            <s xml:id="echoid-s5069" xml:space="preserve"> Amplius, ſicut dictũ eſt in ſuperioribus, [38 n 2] magnitudo nõ acquiritur in cor
              <lb/>
            pore, niſi ex lõgitudinis & anguli collatione:</s>
            <s xml:id="echoid-s5070" xml:space="preserve"> & iã dictũ eſt, quòd eximmoderata lõgitudine apparet
              <lb/>
            minor angulus:</s>
            <s xml:id="echoid-s5071" xml:space="preserve"> quia minor eſt in ueritate.</s>
            <s xml:id="echoid-s5072" xml:space="preserve"> Sed remotionis nõ fit diſcretio.</s>
            <s xml:id="echoid-s5073" xml:space="preserve"> Iã enim ſuprà patuit [39 n
              <lb/>
            2] quòd remotio moderata cõprehenditur per corpora interpoſita:</s>
            <s xml:id="echoid-s5074" xml:space="preserve"> immoderata uerò minimè.</s>
            <s xml:id="echoid-s5075" xml:space="preserve"> Cũ
              <lb/>
            ergo remotio rei uiſæ ſit ignota:</s>
            <s xml:id="echoid-s5076" xml:space="preserve"> fiet fortaſsis collatio ipſius ad longitudinẽ notã, & æſtimabit eã mi
              <lb/>
            norem.</s>
            <s xml:id="echoid-s5077" xml:space="preserve"> Quare putabitur minor & in angulo minoritas, & in longitudine, quã ſit in ueritate:</s>
            <s xml:id="echoid-s5078" xml:space="preserve"> unde er
              <lb/>
            ror in corporis quãtitate.</s>
            <s xml:id="echoid-s5079" xml:space="preserve"> Et quãtò augmẽtabitur longitudo, tantò inualeſcet error.</s>
            <s xml:id="echoid-s5080" xml:space="preserve"> Et adeò poterit
              <lb/>
            augmentari lõgitudo, ut æſtimetur quãtitas corporis quaſi punctualis.</s>
            <s xml:id="echoid-s5081" xml:space="preserve"> Et ſi ultrà creuerit lõgitudo,
              <lb/>
            occultabitur uiſui corpus illud.</s>
            <s xml:id="echoid-s5082" xml:space="preserve"> Simili modo accidit corporis occultatio in lõgitudine tẽperata, nõ
              <lb/>
            ex ipſa remotione, ſed ex coloris corporis debilitate.</s>
            <s xml:id="echoid-s5083" xml:space="preserve"> Et patet occultationem fieri ex debili colore.</s>
            <s xml:id="echoid-s5084" xml:space="preserve">
              <lb/>
            Quoniã ſi loco huius corporis in eadem longitudine ſtatuatur corpus eiuſdẽ quantitatis, in quo ſit
              <lb/>
            fortitudo coloris, nõ latebit uiſum, ſicut corpus, in quo fuerat coloris debilitas.</s>
            <s xml:id="echoid-s5085" xml:space="preserve"> Quare aliquãdo oc-
              <lb/>
            cultat corpus uiſui, non elongatio, nõ diminuta quãtitas, ſed ſola coloris debilitas.</s>
            <s xml:id="echoid-s5086" xml:space="preserve"> Amplius, aliquã-
              <lb/>
            do euenit corporis occultatio ex coloris eius ſimilitudine, cũ interpoſitorum ipſi & uiſui corporũ
              <lb/>
            colore:</s>
            <s xml:id="echoid-s5087" xml:space="preserve"> & hoc in tẽperata longitudine.</s>
            <s xml:id="echoid-s5088" xml:space="preserve"> Vnde corpus albũ à longè poſitũ, effuſa niue ſuper ſupficiem
              <lb/>
            interiacẽtis terrę, non diſcernitur:</s>
            <s xml:id="echoid-s5089" xml:space="preserve"> niue uerò remota percipitur.</s>
            <s xml:id="echoid-s5090" xml:space="preserve"> Et palã, quòd erat occultatio ex hac
              <lb/>
            colorũ identitate.</s>
            <s xml:id="echoid-s5091" xml:space="preserve"> Quoniã ſi loco illius corporis opponatur uiſui ab eadem remotione corpus ęqua
              <lb/>
            le alterius coloris, non occultabitur.</s>
            <s xml:id="echoid-s5092" xml:space="preserve"> Cũigitur aliqua res oppoſita uiſui nõ քcipitur, poterit eſſe cau
              <lb/>
            ſa abſconſionis ſuperfluitas elõgationis, ad partem uiſus inſenſibilẽ formã dirigentis, uel quaſi pun
              <lb/>
            ctualẽ.</s>
            <s xml:id="echoid-s5093" xml:space="preserve"> Quòd ſi in partẽ uiſus ſenſibilẽ forma inciderit:</s>
            <s xml:id="echoid-s5094" xml:space="preserve"> poterit iterũ pręterire uiſum, uel propter co-
              <lb/>
            loris remiſsionẽ, uel colorũ rei uiſę & corporũ interiacentiũ conformitatẽ.</s>
            <s xml:id="echoid-s5095" xml:space="preserve"> A mplius accidit error in
              <lb/>
            rei uiſę quantitate, etiã in longitudine tẽperata.</s>
            <s xml:id="echoid-s5096" xml:space="preserve"> Quoniã corpore aliquo ſecondũ moderationẽ elon
              <lb/>
            gato & uiſo:</s>
            <s xml:id="echoid-s5097" xml:space="preserve"> occultabuntur uiſui partes eius minutę:</s>
            <s xml:id="echoid-s5098" xml:space="preserve"> quę quidẽ in minore elongatione apparent, li-
              <lb/>
            cet fortaſsis non plenè:</s>
            <s xml:id="echoid-s5099" xml:space="preserve"> & paululũ amplius elongatæ iterum, minus plenè.</s>
            <s xml:id="echoid-s5100" xml:space="preserve"> Et minuetur cõprehẽſio
              <lb/>
            nis plenitudo, inualeſcente remotionis augmento:</s>
            <s xml:id="echoid-s5101" xml:space="preserve"> donec occurrat partiũ occultatio:</s>
            <s xml:id="echoid-s5102" xml:space="preserve"> licet nõ egre-
              <lb/>
            diatur tẽperantiam illa elongatio.</s>
            <s xml:id="echoid-s5103" xml:space="preserve"> Iterũ immoderata remotione pars aliqua plenè cõprehenditur,
              <lb/>
            aliqua minimarum eius partium occultatur.</s>
            <s xml:id="echoid-s5104" xml:space="preserve"> Quoniã elongatio rei egreſſa eſt à temperamento pro-
              <lb/>
            portionato ad partes illas, licet non reſpectu totius corporis, aut cõprehenſę partis.</s>
            <s xml:id="echoid-s5105" xml:space="preserve"> Et licet nota ſit
              <lb/>
            hominihęclongitudo:</s>
            <s xml:id="echoid-s5106" xml:space="preserve"> tñ accidit error in cõprehenſione quãtitatis partium:</s>
            <s xml:id="echoid-s5107" xml:space="preserve"> & hoc propter angulũ,
              <lb/>
            ſub quo pars cõprehenditur, cuius capacitas minor æſtimatur, ꝗ̃ habeat ueritas.</s>
            <s xml:id="echoid-s5108" xml:space="preserve"> Et cauſſa apparen-
              <lb/>
            tiæ minoritatis eius, eſt ex punctis terminalib.</s>
            <s xml:id="echoid-s5109" xml:space="preserve"> ſectę partis, in uiſu partẽ occultantib.</s>
            <s xml:id="echoid-s5110" xml:space="preserve"> & anguli capa-
              <lb/>
            citatem conſtringentib.</s>
            <s xml:id="echoid-s5111" xml:space="preserve"> Igitur cũ immoderata ſuerit rei uiſæ ab aliquo diſtantia:</s>
            <s xml:id="echoid-s5112" xml:space="preserve"> proueniet error in
              <lb/>
            eius quantitate dupliciter:</s>
            <s xml:id="echoid-s5113" xml:space="preserve"> & ex anguli minoritate:</s>
            <s xml:id="echoid-s5114" xml:space="preserve"> & exlõgitudinis incertitudine.</s>
            <s xml:id="echoid-s5115" xml:space="preserve"> In moderata ue-
              <lb/>
            rò longitudine erit error in quantitate minutarũ partium ex errore anguli tantùm.</s>
            <s xml:id="echoid-s5116" xml:space="preserve"> Et hæ ſunt cauſ-
              <lb/>
            ſæ, quare corpus æſtimetur minus, quàm ſit in longitudine temperata.</s>
            <s xml:id="echoid-s5117" xml:space="preserve"> Immoderatio longitudinis
              <lb/>
            aliquando errorem inducit maioritatis.</s>
            <s xml:id="echoid-s5118" xml:space="preserve"> Vnde in longitudine immoderata, minima ſcilicet, qñ cor-
              <lb/>
            pus uiſum fuerit multùm uicinum uiſui, uidebitur corpus maioris quantitatis, quàm in longitudi-
              <lb/>
            ne temperata, uel quàm ſit reuera:</s>
            <s xml:id="echoid-s5119" xml:space="preserve"> & hoc duplici de cauſſa.</s>
            <s xml:id="echoid-s5120" xml:space="preserve"> Quoniã, ut dictũ eſt [38 n 2] intellectus
              <lb/>
            longitudinem & angulum conſiderat, & inde quantitatem corporis ſyllogizat.</s>
            <s xml:id="echoid-s5121" xml:space="preserve"> Et in hac elongatio-
              <lb/>
            ne angulus pyramidis eſt ualde magnus:</s>
            <s xml:id="echoid-s5122" xml:space="preserve"> & elongatio corporis nõ æſtimatur, niſi à uiſus ſuperficie
              <lb/>
            ad ſuperficiem corporis.</s>
            <s xml:id="echoid-s5123" xml:space="preserve"> Non enim poteſt cadere in uiſus æſtimationẽ lõgitudo, ad interiora uiſus
              <lb/>
            penetrans à corpore uiſo:</s>
            <s xml:id="echoid-s5124" xml:space="preserve"> cũ pars eius interior radijs non ſubiaceat, nec menſurari à uiſu queat.</s>
            <s xml:id="echoid-s5125" xml:space="preserve"> Syl
              <lb/>
            logizat igitur uiſus ex anguli capacitate & tota longitudine.</s>
            <s xml:id="echoid-s5126" xml:space="preserve"> Vera aũt remotio corporis attenditur
              <lb/>
            ſecundum lineam à centro oculi ad corpus procedentem:</s>
            <s xml:id="echoid-s5127" xml:space="preserve"> cum reſpectu centri fiat conſideratio an-
              <lb/>
            guli.</s>
            <s xml:id="echoid-s5128" xml:space="preserve"> Et in temperata corporis diſtantia ſemidiameter oculi, qua uera corporis elongatio excedit
              <lb/>
            apparentem, inſenſibilis eſt, reſpectu totalis diſtantiæ corporis.</s>
            <s xml:id="echoid-s5129" xml:space="preserve"> Vnde non facit errorem in longitu
              <lb/>
            dinis æſtimatione:</s>
            <s xml:id="echoid-s5130" xml:space="preserve"> ſed corpore circa oculum exiſtente, erit magnitudo ſemidiametri proportiona-
              <lb/>
            lis diſtantiæ corporis proportione ſenſibili.</s>
            <s xml:id="echoid-s5131" xml:space="preserve"> Erit enim aliquando maior, aliquando ęqualis, aliquan
              <lb/>
            do minor, ſed proportione modica, uelut ſubdupla, uel huiuſmodi.</s>
            <s xml:id="echoid-s5132" xml:space="preserve"> Vnde in propinquitate rei uiſæ
              <lb/>
            excrementum anguli pyramidalis, & ſenſibilis minoritas longitudinis æſtimatæ, reſpectu ueræ, in-
              <lb/>
            ducunt apparentiam maioritatis in corpore.</s>
            <s xml:id="echoid-s5133" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div165" type="section" level="0" n="0">
          <head xml:id="echoid-head194" xml:space="preserve" style="it">27. In diuiſione, & continuatione & numero 109 p 4.</head>
          <p>
            <s xml:id="echoid-s5134" xml:space="preserve">IMmoderata extenſio remotionis errorẽ inuehit diſtinctionis.</s>
            <s xml:id="echoid-s5135" xml:space="preserve"> Pariete enim aliquo à lõgè uiſo, ſi
              <lb/>
            in parte eius fuerit color tenebroſus:</s>
            <s xml:id="echoid-s5136" xml:space="preserve"> fiet uidenti fides, colorẽ illũ eſſe diſtinctionem partiũ:</s>
            <s xml:id="echoid-s5137" xml:space="preserve"> un-
              <lb/>
            de continuum ex hoc errore reputabitur diſcretum.</s>
            <s xml:id="echoid-s5138" xml:space="preserve"> Similiter ſi prope parietem illum creſcat al
              <lb/>
            titudo herbarum, uidebitur forſan diſtinctio partium, inter quas fuerit pars occulta ab omni oppo
              <lb/>
            ſitione herbarum:</s>
            <s xml:id="echoid-s5139" xml:space="preserve"> Vnde non reputabitur paries aliquid continuum.</s>
            <s xml:id="echoid-s5140" xml:space="preserve"> Pari modo luce ſolis in parie-
              <lb/>
            tem deſcendente non multùm forti:</s>
            <s xml:id="echoid-s5141" xml:space="preserve"> ſi corpus aliquod umbram iaciat, quæ umbra in parietem ca-
              <lb/>
            dat:</s>
            <s xml:id="echoid-s5142" xml:space="preserve"> accidet error idem in partium, ſine intermedio, ſeparatione.</s>
            <s xml:id="echoid-s5143" xml:space="preserve"> Palàm ergo, quòd error diſtinctio
              <lb/>
            nis in ſyllogiſmo eſt ex immoderatione remotionis.</s>
            <s xml:id="echoid-s5144" xml:space="preserve"> Longitudo à moderatione egreſſa erroris con
              <lb/>
            tinuitatis eſt cauſſa.</s>
            <s xml:id="echoid-s5145" xml:space="preserve"> Corpora enim à longè uiſa in colore ſimilia ſibi, propinqua credũtur cõtinua.</s>
            <s xml:id="echoid-s5146" xml:space="preserve">
              <lb/>
            </s>
          </p>
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