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-s4282" xml:space="preserve">
              <pb o="82" file="0088" n="88" rhead="ALHAZEN"/>
            ta:</s>
            <s xml:id="echoid-s4283" xml:space="preserve"> & intingantur diuerſis coloribus, & erigatur unum indiuiduorum in medio tabulæ in puncto q,
              <lb/>
            & applicetur tabulæ adeò, ut non poſsit auferri à ſuo loco:</s>
            <s xml:id="echoid-s4284" xml:space="preserve"> & ſit ſtans ſuper tabulam ſtatu æquali:</s>
            <s xml:id="echoid-s4285" xml:space="preserve">
              <lb/>
            duo aũt indiuidua reliqua erigantur ſuper extrema lineæ latę in duobus punctis k, t:</s>
            <s xml:id="echoid-s4286" xml:space="preserve"> & ſic tria indi-
              <lb/>
            uidua erunt in una uerticatione.</s>
            <s xml:id="echoid-s4287" xml:space="preserve"> Et hoc quidem facto:</s>
            <s xml:id="echoid-s4288" xml:space="preserve"> eleuet experimentator hanc tabulam, & ſu-
              <lb/>
            perponat concauitatẽ, quæ eſt in medio longitudinis, cornu naſi, & inter oculos adeò, ut cornu naſi
              <lb/>
            intret concauitatẽ, & applicetur cum tabula, & fientduo anguli tabulę apud duo media ſuperficierũ
              <lb/>
            duorum uiſuum, & propinqui, ut tangãt ipſa ferè.</s>
            <s xml:id="echoid-s4289" xml:space="preserve"> Deinde experimentator debet inſpicere indiui-
              <lb/>
            duum poſitum in medio tabulę, & pupillam ſuper ipſum tenere fortiter.</s>
            <s xml:id="echoid-s4290" xml:space="preserve"> Cum igitur experimẽtator
              <lb/>
            inſpexerit indiuiduum poſitum in medio hoc modo:</s>
            <s xml:id="echoid-s4291" xml:space="preserve"> axes duorum uiſuum concurrent in hoc indi-
              <lb/>
            uiduo, & ſuperponentur duabus diametris, aut erũt æquidiſtantes illis:</s>
            <s xml:id="echoid-s4292" xml:space="preserve"> & erit axis cõmunis, quem
              <lb/>
            prius determinauimus, ſuperpoſitus lineæ extẽſę in medio lõgitudinis tabulę, quę eſt linea h z.</s>
            <s xml:id="echoid-s4293" xml:space="preserve"> De-
              <lb/>
            inde experimẽtator in hac diſpoſitione debet intueri omnia, quę ſunt in ſuperficie tabulę:</s>
            <s xml:id="echoid-s4294" xml:space="preserve"> tunc aũt
              <lb/>
            inueniet unum quodq;</s>
            <s xml:id="echoid-s4295" xml:space="preserve"> triũ indiuiduorũ, quę ſunt in punctis k, q, t unum:</s>
            <s xml:id="echoid-s4296" xml:space="preserve"> & inueniet lineã k q t etiã
              <lb/>
            unam:</s>
            <s xml:id="echoid-s4297" xml:space="preserve"> linea aũt h z extenſa in longitudine tabulę, inuenientur duę, ſe ſecantes apud indiuiduũ poſi
              <lb/>
            tum in medio.</s>
            <s xml:id="echoid-s4298" xml:space="preserve"> Et ſimiliter duæ diametri etiã, cum experimentator intuetur eas in hoc ſtatu, appare
              <lb/>
            bunt quatuor:</s>
            <s xml:id="echoid-s4299" xml:space="preserve"> utraq;</s>
            <s xml:id="echoid-s4300" xml:space="preserve"> earũ ſcilicet duplex.</s>
            <s xml:id="echoid-s4301" xml:space="preserve"> Deinde experimentator debet ponere pupillã circa alte-
              <lb/>
            rum indiuiduorũ, quæ ſunt in duobus punctis k, t, ut duo axes concurrãt in indiuiduo poſito in ex-
              <lb/>
            tremo:</s>
            <s xml:id="echoid-s4302" xml:space="preserve"> deinde intueatur etiã in hac diſpoſitione:</s>
            <s xml:id="echoid-s4303" xml:space="preserve"> & inueniet triũ indiuiduorũ unumquodq;</s>
            <s xml:id="echoid-s4304" xml:space="preserve"> unum:</s>
            <s xml:id="echoid-s4305" xml:space="preserve">
              <lb/>
            & lineam poſitã in latitudine etiã unam:</s>
            <s xml:id="echoid-s4306" xml:space="preserve"> & inueniet lineã mediam extenſam in longitudine tabulæ
              <lb/>
            duas:</s>
            <s xml:id="echoid-s4307" xml:space="preserve"> & utrãq;</s>
            <s xml:id="echoid-s4308" xml:space="preserve"> diametrorũ duas.</s>
            <s xml:id="echoid-s4309" xml:space="preserve"> Cum igitur experimentator cõprehenderit has lineas & indiuidua
              <lb/>
            poſita ſuper tabulã:</s>
            <s xml:id="echoid-s4310" xml:space="preserve"> auferat duo indiuidua, quę ſunt in duob.</s>
            <s xml:id="echoid-s4311" xml:space="preserve"> punctis k, t:</s>
            <s xml:id="echoid-s4312" xml:space="preserve"> & ponat ea ſuper lineã h z,
              <lb/>
            extẽſam in lõgitudine, unũ ſcilicet in puncto l, quod ſequitur uiſum, & reliquũ in puncto s, quod eſt
              <lb/>
            ultra indiuiduũ poſitum in medio:</s>
            <s xml:id="echoid-s4313" xml:space="preserve"> deinde uertat tabulam ad ſuam primã poſitionem, & dirigat pu
              <lb/>
            pillam ad indiuiduũ poſitũ in medio:</s>
            <s xml:id="echoid-s4314" xml:space="preserve"> tunc aũt inueniet duo indiuidua, quatuor, & obliqua à medio,
              <lb/>
            duo ſcilicet in dextro, & duo in ſiniſtro:</s>
            <s xml:id="echoid-s4315" xml:space="preserve"> & inueniet ea ſuper duas lineas, quæ in rei ueritate ſunt una
              <lb/>
            linea in medio, ſed apparent duę:</s>
            <s xml:id="echoid-s4316" xml:space="preserve"> & inueniet quælibet duo horũ quatuor ſuper alterã duarũ linearũ.</s>
            <s xml:id="echoid-s4317" xml:space="preserve">
              <lb/>
            Et ſimiliter ſi abſtulerit duo indiuidua ab hac linea, & poſuerit ea ſuper alterã diametrorũ duarũ, u-
              <lb/>
            num in parte uiſus, & reliquũ ultra indiuiduũ poſitũ in medio inueniet illa quatuor:</s>
            <s xml:id="echoid-s4318" xml:space="preserve"> nam utraq;</s>
            <s xml:id="echoid-s4319" xml:space="preserve"> dia
              <lb/>
            metrorũ apparebit duplex.</s>
            <s xml:id="echoid-s4320" xml:space="preserve"> Quaproter apparebunt ſuper utrãq;</s>
            <s xml:id="echoid-s4321" xml:space="preserve"> linearũ, quæ ſunt unius diametri, in
              <lb/>
            rei ueritate duo indiuidua, unum in parte uiſus, & aliud ultra indiuiduũ poſitum in medio.</s>
            <s xml:id="echoid-s4322" xml:space="preserve"> Et ſimi-
              <lb/>
            liter ſi poſuerit duo indiuidua ſuper ambas diametros, utrumq;</s>
            <s xml:id="echoid-s4323" xml:space="preserve"> ſuper alterã diametrum, & poſuerit
              <lb/>
            in ea parte uiſus:</s>
            <s xml:id="echoid-s4324" xml:space="preserve"> inueniet illa quatuor:</s>
            <s xml:id="echoid-s4325" xml:space="preserve"> duo propinqua, & duo remota.</s>
            <s xml:id="echoid-s4326" xml:space="preserve"> Deinde experimentator de-
              <lb/>
            bet auferre duo indiuidua à tabula, & ponere alterum eorum ſuper marginẽ tabulæ, ultra punctum
              <lb/>
            k, & prope ipſum ualde, utſuper punctum r, & reuertatur tabula ad ſuam primam poſitionem, & di-
              <lb/>
            rigat pupillam ad indiuiduũ poſitũ in medio:</s>
            <s xml:id="echoid-s4327" xml:space="preserve"> tunc inueniet indiuiduũ poſitum in puncto r, unum.</s>
            <s xml:id="echoid-s4328" xml:space="preserve">
              <lb/>
            Deinde auferat indiuiduũ à puncto r, & ponat ipſum in margine tabulæ etiam ultra punctum k, ſu-
              <lb/>
            per punctum remotum à puncto k, ut ſuper punctũ f, & dirigat pupillam ad indiuiduum poſitum in
              <lb/>
            medio:</s>
            <s xml:id="echoid-s4329" xml:space="preserve"> quoniã tunc inueniet indiuiduum poſitum in puncto f, duo.</s>
            <s xml:id="echoid-s4330" xml:space="preserve"> Experimentator aũt inueniet
              <lb/>
            omnia, quæ diximus, cum direxerit pupillam ad indiuiduũ poſitũ in medio, aut ad indiuiduũ poſitũ
              <lb/>
              <figure xlink:label="fig-0088-01" xlink:href="fig-0088-01a" number="18">
                <variables xml:id="echoid-variables11" xml:space="preserve">d z c s f r t q k l h b n m a</variables>
              </figure>
            in linea recta in latitudine, aut ad punctũ unius li-
              <lb/>
            neę, quodcunq;</s>
            <s xml:id="echoid-s4331" xml:space="preserve"> ſit, & dum duo axes cõcurrunt in
              <lb/>
            indiuiduo poſito in medio, aut in aliquo puncto li
              <lb/>
            neæ poſitæ in latitudine.</s>
            <s xml:id="echoid-s4332" xml:space="preserve"> Si ergo experimentator
              <lb/>
            direxerit pupillã in illo ſitu ad indiuiduũ, poſitũ
              <lb/>
            extra lineam poſitam in latitudine, aut ad pun-
              <lb/>
            ctum poſitum extra lineam illam, & concurrerint
              <lb/>
            duo axes in aliquo puncto extra lineam poſitam
              <lb/>
            in latitudine:</s>
            <s xml:id="echoid-s4333" xml:space="preserve"> tunc indiuiduum poſitum in medio
              <lb/>
            uidebitur duo:</s>
            <s xml:id="echoid-s4334" xml:space="preserve"> & ſi reliqua indiuidua fuerint in
              <lb/>
            duobus punctis k, t:</s>
            <s xml:id="echoid-s4335" xml:space="preserve"> tũc utrumq;</s>
            <s xml:id="echoid-s4336" xml:space="preserve"> eorum etiã uide
              <lb/>
            bitur duo.</s>
            <s xml:id="echoid-s4337" xml:space="preserve"> Deinde cũ experimẽtator direxerit pu
              <lb/>
            pillam ad mediũ indiuiduum, aut ad aliquẽ locũ
              <lb/>
            lineæ poſitæ in latitudine:</s>
            <s xml:id="echoid-s4338" xml:space="preserve"> ſtatim diſpoſitio reuer-
              <lb/>
            tetur ut in prima figura.</s>
            <s xml:id="echoid-s4339" xml:space="preserve"> Igitur à puncto b extra-
              <lb/>
            hantur lineæ b k, b r, b f, linea igitur k b eſt maior
              <lb/>
            linea b t, [per theſin & 19 p 1] & linea k q eſt æ-
              <lb/>
            qualis q t[ex theſi.</s>
            <s xml:id="echoid-s4340" xml:space="preserve">] Sic igitur angulus t b q, eſt ma
              <lb/>
            ior angulo q b k [per 4 p geometriæ Iordani.</s>
            <s xml:id="echoid-s4341" xml:space="preserve"> In
              <lb/>
            triangulo enim b t k ab angulo t b k, inæqualibus
              <lb/>
            lateribus b t, b k comprehenſo, recta b q eſt in me-
              <lb/>
            diũ baſis t k:</s>
            <s xml:id="echoid-s4342" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s4343" xml:space="preserve"> angulus q b k ab ipſa b q & ma-
              <lb/>
            iore latere b k coprehẽſus, minor eſt angulo t b q,
              <lb/>
            ab eadẽ b q & minore latere b t comprehenſo] &
              <lb/>
            angulus t b q eſt æqualis angulo k a q [per 8 p 1]
              <lb/>
            </s>
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