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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            <s xml:id="echoid-s19369" xml:space="preserve">
              <pb o="279" file="0285" n="285" rhead="OPTICAE LIBER VII."/>
            & g m eſt perpendicularis, exiens ex m (quod eſt punctum refractionis) ſuper ſuperficiem corpo-
              <lb/>
            ris, quod eſt in parte t [ut oſtenſum eſt 25 n 4.</s>
            <s xml:id="echoid-s19370" xml:space="preserve">] Et quia corpus z m eſt ſubtilius corpore g t [per 16
              <lb/>
            n] erit refractio m t ad partem perpendicularis m g:</s>
            <s xml:id="echoid-s19371" xml:space="preserve"> [per 14 n] m ergo erit inter duas lineas t b, t k.</s>
            <s xml:id="echoid-s19372" xml:space="preserve">
              <lb/>
            Nam ſim eſſet ultra t k:</s>
            <s xml:id="echoid-s19373" xml:space="preserve"> tunc perpendicularis, quæ exit ex g, eſſet ultra t:</s>
            <s xml:id="echoid-s19374" xml:space="preserve"> & forma k cum extendere-
              <lb/>
            tur ad illud punctum:</s>
            <s xml:id="echoid-s19375" xml:space="preserve"> refringeretur ad partem perpendicularis g m, & non perueniret ad perpendi
              <lb/>
            cularem g e:</s>
            <s xml:id="echoid-s19376" xml:space="preserve"> & ſic non perueniret ad t.</s>
            <s xml:id="echoid-s19377" xml:space="preserve"> M ergo eſt inter duas lineas t b, t k.</s>
            <s xml:id="echoid-s19378" xml:space="preserve"> Et ſimiliter declarabitur
              <lb/>
            quòd z eſt inter duas lineas t b, t l.</s>
            <s xml:id="echoid-s19379" xml:space="preserve"> Et extrahamus t m ad
              <lb/>
              <figure xlink:label="fig-0285-01" xlink:href="fig-0285-01a" number="246">
                <variables xml:id="echoid-variables233" xml:space="preserve">k q f b o r c l m e z f g</variables>
              </figure>
            q, & t z ad r:</s>
            <s xml:id="echoid-s19380" xml:space="preserve"> erit ergo arcus q k æqualis arcui l r:</s>
            <s xml:id="echoid-s19381" xml:space="preserve"> [Quia
              <lb/>
            enim puncta k & l æquabiliter à uiſu diſtant per theſin:</s>
            <s xml:id="echoid-s19382" xml:space="preserve">
              <lb/>
            puncta refractionis m & z in refractiuo m e z æquabili-
              <lb/>
            ter à puncto e diſtabunt:</s>
            <s xml:id="echoid-s19383" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s19384" xml:space="preserve"> peripheria m e æquabi-
              <lb/>
            tur peripheriæ z e:</s>
            <s xml:id="echoid-s19385" xml:space="preserve"> & per 33 p 6 angulus b t q angulo b t
              <lb/>
            r, & peripheria b q peripheriæ b r (eſt enim uiſus t, ut in
              <lb/>
            aſtrologia demonſtratur, tanquam centrum mundi) at
              <lb/>
            tota peripheria b k æqualis concluſa eſt peripheriæ b l:</s>
            <s xml:id="echoid-s19386" xml:space="preserve">
              <lb/>
            reliqua igitur q k æquatur reliquæ r l] & angulus q t r
              <lb/>
            eſt ille, per quem t comprehendit k l refractè:</s>
            <s xml:id="echoid-s19387" xml:space="preserve"> & angu-
              <lb/>
            lus k t l eſt ille, per quem t comprehenderet k l, ſi rectè
              <lb/>
            cõprehenderet.</s>
            <s xml:id="echoid-s19388" xml:space="preserve"> Sed remotio k l à uiſu eſt maxima:</s>
            <s xml:id="echoid-s19389" xml:space="preserve"> qua-
              <lb/>
            propter quantitas eius non certificatur.</s>
            <s xml:id="echoid-s19390" xml:space="preserve"> Quare t exiſti-
              <lb/>
            mat remotionem k l, ſicut in ſecundo libro diximus [24.</s>
            <s xml:id="echoid-s19391" xml:space="preserve">
              <lb/>
            25 n.</s>
            <s xml:id="echoid-s19392" xml:space="preserve">] Sed æſtimatio eius quando comprehendit refra-
              <lb/>
            ctè, nõ differt ab æſtimatione eius quando comprehen-
              <lb/>
            dit rectè, niſi quòd putat ſe rectè comprehendere cum
              <lb/>
            refractè comprehendat.</s>
            <s xml:id="echoid-s19393" xml:space="preserve"> t ergo comprehendit k l refractè ex angulo minore illo, ex quo comprehen
              <lb/>
            dit illam rectè, & ſecundum comparationem ad illam eandem remotionem, ad quam compararet
              <lb/>
            illam, ſi rectè comprehenderet.</s>
            <s xml:id="echoid-s19394" xml:space="preserve"> Sed uiſus comprehendit magnitudinem ex quantitate anguli reſpe
              <lb/>
            ctu remotionis [per 38 n 2.</s>
            <s xml:id="echoid-s19395" xml:space="preserve">] tergo comprehendit quantitatem k l refractè minorem, quàm ſi com-
              <lb/>
            prehenderet illam rectè.</s>
            <s xml:id="echoid-s19396" xml:space="preserve"> Et ſi circumuoluamus figuram k t l circa t b immobilem, faciet circulum:</s>
            <s xml:id="echoid-s19397" xml:space="preserve">
              <lb/>
            & erũt anguli, qui ſunt apud t, quos continent duæ lineæ k t, t l, & ſui compares, æquales:</s>
            <s xml:id="echoid-s19398" xml:space="preserve"> t ergo com
              <lb/>
            prehendit k l refractè in omni ſitu, in reſpectu circuli meridiei, cum fuerit in uertice capitis, minorẽ,
              <lb/>
            quàm ſi cõprehenderet eam rectè.</s>
            <s xml:id="echoid-s19399" xml:space="preserve"> Et ſi t b ſecuerit k l in duo æqualia:</s>
            <s xml:id="echoid-s19400" xml:space="preserve"> tunc duo puncta q, r erunt in-
              <lb/>
            ter duo puncta k, l:</s>
            <s xml:id="echoid-s19401" xml:space="preserve"> & erit angulus q t r minor angulo k t l:</s>
            <s xml:id="echoid-s19402" xml:space="preserve"> & erit omnis angulus eius exiens à pun-
              <lb/>
            cto t, ſecans ſtellam:</s>
            <s xml:id="echoid-s19403" xml:space="preserve"> & linea, quæ exit ex t in ſuperficie illius circuli, ſecabit circulum, & comprehen
              <lb/>
            detur minor, quàm ſit:</s>
            <s xml:id="echoid-s19404" xml:space="preserve"> & ſic tota ſtella uidebitur minor, quàm ſit.</s>
            <s xml:id="echoid-s19405" xml:space="preserve"> Stella ergo in uertice capitis com-
              <lb/>
            prehenditur minor, quàm ſi comprehenderetur rectè.</s>
            <s xml:id="echoid-s19406" xml:space="preserve"> Et ſimiliter diſtantia inter duas ſtellas, cum
              <lb/>
            uertex fuerit inter duas extremitates diſtantiæ, comprehendetur in omnibus poſitionibus minor,
              <lb/>
            quàm ſi rectè comprehenderetur.</s>
            <s xml:id="echoid-s19407" xml:space="preserve"> Et hoc eſt, quod uoluimus.</s>
            <s xml:id="echoid-s19408" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div629" type="section" level="0" n="0">
          <head xml:id="echoid-head538" xml:space="preserve" style="it">53. Diameter ſtellæ, uel duarum ſtellarum diſtantia in horizonte, aut inter horizontem &
            <lb/>
          meridianum, ad horizontem parallela, refractè uiſa, minor: rectè, maior uidetur. 52 p 10.</head>
          <p>
            <s xml:id="echoid-s19409" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s19410" xml:space="preserve"> ſit ſtella ſiue diſtantia in horizonte, aut inter horizonta & uerticem capitis, æquidiſtans ho
              <lb/>
            rizonti:</s>
            <s xml:id="echoid-s19411" xml:space="preserve"> & ſit uiſus a:</s>
            <s xml:id="echoid-s19412" xml:space="preserve"> & uertex capitis b:</s>
            <s xml:id="echoid-s19413" xml:space="preserve"> & continuemus a b:</s>
            <s xml:id="echoid-s19414" xml:space="preserve"> & ſit diameter ſtellæ aut diſtantia d
              <lb/>
            e æquidiſtans horizonti:</s>
            <s xml:id="echoid-s19415" xml:space="preserve"> & ſit circulus uerticalis, qui tranſit per alteram extremitatem diametri
              <lb/>
            uel diſtantię, circulus b d:</s>
            <s xml:id="echoid-s19416" xml:space="preserve"> & ille, qui tranſit per aliam
              <lb/>
              <figure xlink:label="fig-0285-02" xlink:href="fig-0285-02a" number="247">
                <variables xml:id="echoid-variables234" xml:space="preserve">b g f t n d h k z a m e</variables>
              </figure>
            extremitatem, circulus b e:</s>
            <s xml:id="echoid-s19417" xml:space="preserve"> & ſint duæ differentiæ
              <lb/>
            communes inter duos circulos & inter concauita-
              <lb/>
            tem orbis duo circuli h g, g z.</s>
            <s xml:id="echoid-s19418" xml:space="preserve"> Forma ergo d refringa-
              <lb/>
            tur ad a ex h:</s>
            <s xml:id="echoid-s19419" xml:space="preserve"> & e ad a ex z:</s>
            <s xml:id="echoid-s19420" xml:space="preserve"> & continuemus lineas a h,
              <lb/>
            h d, a z, z e, a d, a e:</s>
            <s xml:id="echoid-s19421" xml:space="preserve"> & ſit centrum mundi m:</s>
            <s xml:id="echoid-s19422" xml:space="preserve"> & conti-
              <lb/>
            nuemus m h, m z, & pertranſeant ad f, n:</s>
            <s xml:id="echoid-s19423" xml:space="preserve"> erit ergo m
              <lb/>
            h perpendicularis, exiens ex h ad ſuperficiem corpo
              <lb/>
            ris diaphani:</s>
            <s xml:id="echoid-s19424" xml:space="preserve"> [ut demonſtratum eſt 25 n 4] & erit h a
              <lb/>
            refracta ad partem h m:</s>
            <s xml:id="echoid-s19425" xml:space="preserve"> erit ergo refracta ad partem
              <lb/>
            contrariam illi, in qua eſt [f h:</s>
            <s xml:id="echoid-s19426" xml:space="preserve"> per 14 n] h ergo eſt al-
              <lb/>
            tius, quàm a d.</s>
            <s xml:id="echoid-s19427" xml:space="preserve"> Et ſimiliter declarabitur, quòd z eſt al
              <lb/>
            tius quã a e:</s>
            <s xml:id="echoid-s19428" xml:space="preserve"> ergo duo puncta f, n ſunt inter duo pun-
              <lb/>
            cta d, e & zenith capitis:</s>
            <s xml:id="echoid-s19429" xml:space="preserve"> & angulus refractionis, qui
              <lb/>
            eſt apud h, eſt æqualis angulo refractionis qui eſt a-
              <lb/>
            pud z:</s>
            <s xml:id="echoid-s19430" xml:space="preserve"> poſitio enim duorum punctorum d, e reſpectu
              <lb/>
            a eſt conſimilis.</s>
            <s xml:id="echoid-s19431" xml:space="preserve"> Tantùm ergo diſtat f à d, quantùm n
              <lb/>
            ab e:</s>
            <s xml:id="echoid-s19432" xml:space="preserve"> & extrahamus a h ad t, & a z ad k.</s>
            <s xml:id="echoid-s19433" xml:space="preserve"> Diſtabit ergo
              <lb/>
            t à d tantùm, quantùm k ab e:</s>
            <s xml:id="echoid-s19434" xml:space="preserve"> & continuemus t k:</s>
            <s xml:id="echoid-s19435" xml:space="preserve"> erit ergo æquidiſtans d e:</s>
            <s xml:id="echoid-s19436" xml:space="preserve"> eſt ergo minor:</s>
            <s xml:id="echoid-s19437" xml:space="preserve"> [quorũ
              <lb/>
            utrumq;</s>
            <s xml:id="echoid-s19438" xml:space="preserve"> demonſtratum eſt à Campano 14 p 12] & lineę a t, a k, a f, a e ſunt æquales:</s>
            <s xml:id="echoid-s19439" xml:space="preserve"> quia a eſt quaſi
              <lb/>
            </s>
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