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

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          <p>
            <s xml:id="echoid-s47246" xml:space="preserve">
              <pb o="407" file="0709" n="709" rhead="LIBER DECIMVS."/>
            dente) quoniam ille non refringitur, ut in 47 th.</s>
            <s xml:id="echoid-s47247" xml:space="preserve"> 2 huius oſtenſum eſt.</s>
            <s xml:id="echoid-s47248" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s47249" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1799" type="section" level="0" n="0">
          <head xml:id="echoid-head1332" xml:space="preserve" style="it">4. Omnis formæ per refractionem uiſæ ſi fiat refractio à medio ſecundi diaphani denſioris pri
            <lb/>
          mo ad uiſum, uidetur fieri ad partem perpendicularis, ductæ à puncto refractionis ſuper ſuperfi
            <lb/>
          ciem, à qua fit refractio. Si uerò fiat à diaphano rariori, uidetur fieri ad partem contrariam il-
            <lb/>
          lius perpendicularis. Alhazen 14 n 7.</head>
          <p>
            <s xml:id="echoid-s47250" xml:space="preserve">Quod hic proponitur, poteſt inſtrumentaliter demonſtrari, ita ut demonſtratio auxilio inſtru-
              <lb/>
            menti ſenſibiliter exprimatur.</s>
            <s xml:id="echoid-s47251" xml:space="preserve"> Accipiatur itaq;</s>
            <s xml:id="echoid-s47252" xml:space="preserve"> prædictum inſtrumentum, quo in præcedentib.</s>
            <s xml:id="echoid-s47253" xml:space="preserve"> uſi
              <lb/>
            ſumus:</s>
            <s xml:id="echoid-s47254" xml:space="preserve"> cuius diametrũ, quã ibi ſignauimus per literas f, g, nunc dicimus b q g, ita ut punctũ q ſit cẽ-
              <lb/>
            trum laminæ baſis inſtrumenti.</s>
            <s xml:id="echoid-s47255" xml:space="preserve"> Hoc itaque inſtrumentum ponatur in uaſe æquidiſtáter ſuperficiei
              <lb/>
            horizontis ſituato, & infundatur aqua uſque ad centrum laminæ, quod eſt q:</s>
            <s xml:id="echoid-s47256" xml:space="preserve"> oppilentur quoq;</s>
            <s xml:id="echoid-s47257" xml:space="preserve"> fora
              <lb/>
            mina inſtrumenti cum cera uel alio modo, ita quòd modicùm remaneat de foraminibus circa me-
              <lb/>
            dium ipſorum, quod in ambobus foraminibus ſit æquale:</s>
            <s xml:id="echoid-s47258" xml:space="preserve"> & hoc poteſt æquali colum na illis forami
              <lb/>
            nibus immiſſa menſurari.</s>
            <s xml:id="echoid-s47259" xml:space="preserve"> Dein de moueatur inſtrumentum, donec diameter b q g ſit perpendicula
              <lb/>
            ris ſuper ſuperficiem aquæ.</s>
            <s xml:id="echoid-s47260" xml:space="preserve"> Immittatur quoque ſtilus albus ſubtilis in ipſum uas, ita quòd eius ex-
              <lb/>
            tremitas cadat in punctum z, quod eſt extremitas diametri circuli medij, quæ ſit k f z:</s>
            <s xml:id="echoid-s47261" xml:space="preserve"> ponaturq́;</s>
            <s xml:id="echoid-s47262" xml:space="preserve"> u-
              <lb/>
            nus uiſuum ſuper ſuperius foramen in punctum k, & claudatur reliquus:</s>
            <s xml:id="echoid-s47263" xml:space="preserve"> tunc enim uidebitur extre
              <lb/>
            mitas ſtili ſecundum rectitudinem perpendicularis exeuntis ab extremitate ſtili ſuper ſuperficiem
              <lb/>
            aquæ:</s>
            <s xml:id="echoid-s47264" xml:space="preserve"> nam centrum uiſus & extremitas ſtili tunc ſunt in linea k f z perpendiculari ſuper ſuperficiẽ
              <lb/>
            aquę, ſecundum quam fit uiſio.</s>
            <s xml:id="echoid-s47265" xml:space="preserve"> Eſt enim linea k f z perpendicularis ſuper ſuperficiẽ aquæ per 8 p 11:</s>
            <s xml:id="echoid-s47266" xml:space="preserve">
              <lb/>
            ideo quòd ipſa æquidiſtat lineæ b q g, quæ ex hypothe
              <lb/>
            ſi eſt perpendicularis ſuper eandem ſuperficiem aquę.</s>
            <s xml:id="echoid-s47267" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0709-01" xlink:href="fig-0709-01a" number="842">
                <variables xml:id="echoid-variables819" xml:space="preserve">k b d o f q u g z r e a</variables>
              </figure>
            Deinde declinetur inſtrum entum, donec linea b q g
              <lb/>
            obliquetur ſuper ſuperficiem aquæ:</s>
            <s xml:id="echoid-s47268" xml:space="preserve"> ponaturq́ue
              <lb/>
            uiſus ſuper ſuperius foramen:</s>
            <s xml:id="echoid-s47269" xml:space="preserve"> & non uidebitur ex-
              <lb/>
            tremitas ſtili.</s>
            <s xml:id="echoid-s47270" xml:space="preserve"> Moueatur itaque extremitas ſtili in
              <lb/>
            circumferentia medij circuli paulatim ad partem op-
              <lb/>
            poſitam uiſui, donec uideatur illa extremitas, & figa-
              <lb/>
            tur in illo pũcto circuli medij, in quo apparet.</s>
            <s xml:id="echoid-s47271" xml:space="preserve"> Si itaq;</s>
            <s xml:id="echoid-s47272" xml:space="preserve">
              <lb/>
            tunc ponatur aliquod corpuſculum denſum in ſuper-
              <lb/>
            ficie aquæ in centro medij circuli, quod eſt f:</s>
            <s xml:id="echoid-s47273" xml:space="preserve"> tunc nó
              <lb/>
            uidebitur illa extremitas ſtili:</s>
            <s xml:id="echoid-s47274" xml:space="preserve"> ablato uerò illo corpu-
              <lb/>
            ſculo, uidebitur illa extremitas ſtili.</s>
            <s xml:id="echoid-s47275" xml:space="preserve"> Quòd ſi cóſidere-
              <lb/>
            tur in numero graduũ medij circuli diſtátia extremita
              <lb/>
            tis ſtili à pũcto z:</s>
            <s xml:id="echoid-s47276" xml:space="preserve"> inuenietur diſtantia ſenſibilis.</s>
            <s xml:id="echoid-s47277" xml:space="preserve"> Poteſt
              <lb/>
            aũt punctus z, qui eſt extremitas diametri medij cir-
              <lb/>
            culi, tranſeuntis per centrum duorum foraminum ſic
              <lb/>
            inueniri:</s>
            <s xml:id="echoid-s47278" xml:space="preserve"> ſcilicet ut regulæ ſubtilis latior extremitas ponatur ſuper centrum laminæ, & media linea
              <lb/>
            ipſius protendatur ſecundum diametrum laminæ:</s>
            <s xml:id="echoid-s47279" xml:space="preserve"> tunc enim acumen regulæ cadit ſuper punctũ z,
              <lb/>
            ut præmiſſum eſt prius in propoſitionibus 2 huius.</s>
            <s xml:id="echoid-s47280" xml:space="preserve"> Quòd ſi aſſumpto uitro, quod ſit pars alicuius
              <lb/>
            ſphæræ, ut in illis propoſitionibus aliquib.</s>
            <s xml:id="echoid-s47281" xml:space="preserve"> aſſumptũ eſt, cuius uitri ſuperficies aliqua ſit plana & ali
              <lb/>
            qua cõuexa ſphęrica:</s>
            <s xml:id="echoid-s47282" xml:space="preserve"> & illud uitrũ applicetur laminę, ita ut eius plana ſuperficies ſit ex parte ſorami
              <lb/>
            num, lineaq́;</s>
            <s xml:id="echoid-s47283" xml:space="preserve"> (quę eſt ſuarũ ſuperficierum planarũ cõmunis differentia) ſit ſuper lineam o d, ſecantẽ
              <lb/>
            b q ſemidiametrum laminæ perpendiculariter:</s>
            <s xml:id="echoid-s47284" xml:space="preserve"> ſic ergo erit diameter k f z perpẽdicularis ſuper pla-
              <lb/>
            ná ſuperficiem uitri & ſuper conuexá.</s>
            <s xml:id="echoid-s47285" xml:space="preserve"> Deinde ponatur inſtrumentũ in aqua, ponaturq́;</s>
            <s xml:id="echoid-s47286" xml:space="preserve"> extremitas
              <lb/>
            ſtili ſuper punctum z, & centrũ uiſus ſuper ſuperius foramen:</s>
            <s xml:id="echoid-s47287" xml:space="preserve"> uidebiturq́;</s>
            <s xml:id="echoid-s47288" xml:space="preserve"> extremitas ſtili, quæ in a-
              <lb/>
            lio puncto circuli medij non poterat uideri.</s>
            <s xml:id="echoid-s47289" xml:space="preserve"> Ex quo patet quoniam extremitas ſtili, quando eſt in li
              <lb/>
            nea perpendiculari ſuper ſuperficiem corporis, à qua fit refractio, (ut nunc eſt linea k f z perpẽdicu-
              <lb/>
            laris ſuper ſuperficiem uitri) forma ipſius uidetur non per refractionẽ, ſed rectè.</s>
            <s xml:id="echoid-s47290" xml:space="preserve"> Ex quo patet quò d
              <lb/>
            forma perpendiculariter incidens non refringitur.</s>
            <s xml:id="echoid-s47291" xml:space="preserve"> Quòd ſi conuexum uitri ponatur ex parte ſecũ-
              <lb/>
            da foraminum, & differentia communis duarum ſuperficierum planarum uitri ponatur ſuper pri-
              <lb/>
            mum locum, ſcilicet lineę o d:</s>
            <s xml:id="echoid-s47292" xml:space="preserve"> quoniam & tunc linea k f z eſt perpendicularis ſuper utraſque ſuperfi
              <lb/>
            cies uitri:</s>
            <s xml:id="echoid-s47293" xml:space="preserve"> uidebitur ergo tunc, ut prius, extremitas ſtili in puncto z.</s>
            <s xml:id="echoid-s47294" xml:space="preserve"> Quòd ſi à ſuperficie laminę in-
              <lb/>
            ſtrumenti euulſo uitro à centro laminæ, quod eſt q, in ſuperficie laminę ducatur ſemidiameter q r,
              <lb/>
            continens cum ſemidiametro b q angulum obtuſum:</s>
            <s xml:id="echoid-s47295" xml:space="preserve"> deinde ducatur ſemidiameter q u, continens
              <lb/>
            cũ linea q r angulũ rectum:</s>
            <s xml:id="echoid-s47296" xml:space="preserve"> & protrahatur ad aliã oram inſtrumenti:</s>
            <s xml:id="echoid-s47297" xml:space="preserve"> erit ergo angulus b q u acutus,
              <lb/>
            & erit ſemidiameter b q obliqua ſuք lineã q u.</s>
            <s xml:id="echoid-s47298" xml:space="preserve"> Deinde linea, quę eſt cómunis differẽtia ſuperficierũ
              <lb/>
            planarum uitri, ponatur ſuper lineá q u, & ſit plana uitri ſuperficies ex parte foraminum, & ſit me-
              <lb/>
            dium differentiæ communis planarũ ſuperficierum ipſius uitri ſuper centrum q.</s>
            <s xml:id="echoid-s47299" xml:space="preserve"> Erit itaq;</s>
            <s xml:id="echoid-s47300" xml:space="preserve"> tunc cen
              <lb/>
            trum uitri ſuper centrum medij circuli, ut pręoſtenſum eſt in alijs, & linea k f tranſit per centrũ uitri
              <lb/>
            & eſt obliqua ſuք ſuperficiem ipſius planá:</s>
            <s xml:id="echoid-s47301" xml:space="preserve"> quoniã diameter b q ęquidiſtans illi lineę, quę eſt k f, ob-
              <lb/>
            liquè cadit ſuper lineam q u:</s>
            <s xml:id="echoid-s47302" xml:space="preserve"> & quoniã linea k f tranſit per centrũ uitri:</s>
            <s xml:id="echoid-s47303" xml:space="preserve"> palàm quoniam ipſa eſt per-
              <lb/>
            pendicularis ſuper conuexam ſuperficiem uitri.</s>
            <s xml:id="echoid-s47304" xml:space="preserve"> Deinde à puncto r ſuper lineam q r ducatur per-
              <lb/>
            </s>
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    </echo>
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