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-s19439" xml:space="preserve">
              <pb o="280" file="0286" n="286" rhead="ALHAZEN"/>
            centrum mundi & duorum circulorum b d, b e.</s>
            <s xml:id="echoid-s19440" xml:space="preserve"> Duæ ergo lineæ a t, a k ſunt æquales duabus lineis
              <gap/>
              <lb/>
            d, a e, & baſis t k eſt minor quàm baſis d e:</s>
            <s xml:id="echoid-s19441" xml:space="preserve"> ergo [per 25 p 1] angulus t a k eſt minor angulo d a e:</s>
            <s xml:id="echoid-s19442" xml:space="preserve"> & an-
              <lb/>
            gulus t a k eſt ille, quo d e cõprehenditur refractè:</s>
            <s xml:id="echoid-s19443" xml:space="preserve"> & angulus d a e eſt ille, quo d e cõprehenditur re-
              <lb/>
            ctè.</s>
            <s xml:id="echoid-s19444" xml:space="preserve"> Si ergo ſtella fuerit in horizonte, aut inter horizonta & circulũ meridiei:</s>
            <s xml:id="echoid-s19445" xml:space="preserve"> & fuerit diameter eius
              <lb/>
            æquidiſtans horizonti:</s>
            <s xml:id="echoid-s19446" xml:space="preserve"> uidebitur minor, quàm ſi uideretur rectè.</s>
            <s xml:id="echoid-s19447" xml:space="preserve"> Et hocidem eſt de diſtantia inter
              <lb/>
            duas ſtellas, ſi diſtantia fuerit æquidiſtans horizonti.</s>
            <s xml:id="echoid-s19448" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div631" type="section" level="0" n="0">
          <head xml:id="echoid-head539" xml:space="preserve" style="it">54. Diameter ſtellæ, uel duarum ſtellarum dιſtantia in circulo altitudinis refractè uiſa, mi-
            <lb/>
          nor: rectè, maior uidetur. 53 p 10.</head>
          <p>
            <s xml:id="echoid-s19449" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s19450" xml:space="preserve"> iteremus figuram:</s>
            <s xml:id="echoid-s19451" xml:space="preserve"> & ſit diameter aut diſtantia erecta ſcilicet in eodem circulo uerticali:</s>
            <s xml:id="echoid-s19452" xml:space="preserve"> &
              <lb/>
            ſit illa diameter aut diſtantia linea d e in circulo uerticali b d e:</s>
            <s xml:id="echoid-s19453" xml:space="preserve"> & ſit differentia communis inter
              <lb/>
            hunc circulum & inter concauitatem orbis, circulus g h z:</s>
            <s xml:id="echoid-s19454" xml:space="preserve"> & continuemus a d, a e:</s>
            <s xml:id="echoid-s19455" xml:space="preserve"> & refringatur
              <lb/>
            d ad a ex h, & e ad a ex z.</s>
            <s xml:id="echoid-s19456" xml:space="preserve"> Patet ergo, ut in præcedente figura, quòd h eſt altius quàm a d, & quòd z eſt
              <lb/>
            al
              <gap/>
            ius quàm a e:</s>
            <s xml:id="echoid-s19457" xml:space="preserve"> & continuemus lineas a h, h d, a z, z
              <lb/>
              <figure xlink:label="fig-0286-01" xlink:href="fig-0286-01a" number="248">
                <variables xml:id="echoid-variables235" xml:space="preserve">b
                  <gap/>
                d g q h n k z o a p e m</variables>
              </figure>
            e, m h, m z:</s>
            <s xml:id="echoid-s19458" xml:space="preserve"> & extrahamus m h a d t, & m z a d k.</s>
            <s xml:id="echoid-s19459" xml:space="preserve"> Erit
              <lb/>
            ergo angulus a z m ualde paruus.</s>
            <s xml:id="echoid-s19460" xml:space="preserve"> [Nam ſemidiame
              <lb/>
            ter terræ ad ſemidiametrũ cœli, rationem ſenſilem
              <lb/>
            nullam habet, ut docetur in aſtrologia] & angulus
              <lb/>
            refractionis erit pars illius Erit ergo [per 12 n] angu
              <lb/>
            lus e z k acutus:</s>
            <s xml:id="echoid-s19461" xml:space="preserve"> & ſimiliter d h t acutus:</s>
            <s xml:id="echoid-s19462" xml:space="preserve"> & [ք 13 p 1]
              <lb/>
            uterq;</s>
            <s xml:id="echoid-s19463" xml:space="preserve"> angulus a h d, a z e obtuſus.</s>
            <s xml:id="echoid-s19464" xml:space="preserve"> z autem aut erit
              <lb/>
            in horizonte, aut altius:</s>
            <s xml:id="echoid-s19465" xml:space="preserve"> ſi in horizonte:</s>
            <s xml:id="echoid-s19466" xml:space="preserve"> erit ergo in
              <lb/>
            extremitate perpendicularis exeuntis ex a ſuper a
              <lb/>
            b, aut altius illa:</s>
            <s xml:id="echoid-s19467" xml:space="preserve"> & h eſt altius quàm z:</s>
            <s xml:id="echoid-s19468" xml:space="preserve"> ergo angulus
              <lb/>
            a h m erit minor angulo a z m.</s>
            <s xml:id="echoid-s19469" xml:space="preserve"> [Nam conſtitutis ad
              <lb/>
            puncta m & a angulis a m p, g a q ęqualibus angulis
              <lb/>
            z m a, h a g per 23 p 1, connexιsq́;</s>
            <s xml:id="echoid-s19470" xml:space="preserve"> rectis a p, h p:</s>
            <s xml:id="echoid-s19471" xml:space="preserve"> erunt
              <lb/>
            anguli m p h, m h p æquales per 15 d.</s>
            <s xml:id="echoid-s19472" xml:space="preserve"> 5 p 1:</s>
            <s xml:id="echoid-s19473" xml:space="preserve"> & a p ma-
              <lb/>
            ior a h:</s>
            <s xml:id="echoid-s19474" xml:space="preserve"> քa per 7 p 3 maior eſt a q:</s>
            <s xml:id="echoid-s19475" xml:space="preserve"> & per 18 p 1 angulus
              <lb/>
            a h p maior angulo a p h.</s>
            <s xml:id="echoid-s19476" xml:space="preserve"> Quare angulus a h m, mi-
              <lb/>
            nor erit angulo ap m, cui ęqualis eſt angulus a z m ք
              <lb/>
            15 d.</s>
            <s xml:id="echoid-s19477" xml:space="preserve"> 4 p 1.</s>
            <s xml:id="echoid-s19478" xml:space="preserve"> Itaq;</s>
            <s xml:id="echoid-s19479" xml:space="preserve"> angulus a h m minor erit angulo a z m] ergo [per 12 n] angulus d h t eſt minor angulo
              <lb/>
            e z k:</s>
            <s xml:id="echoid-s19480" xml:space="preserve"> ergo angulus a h deſt maior angulo a z e [per 12 n.</s>
            <s xml:id="echoid-s19481" xml:space="preserve"> 13 p 1:</s>
            <s xml:id="echoid-s19482" xml:space="preserve">] & duę lineę m t, m k ſunt ſemidiametri
              <lb/>
            circuli b d e:</s>
            <s xml:id="echoid-s19483" xml:space="preserve"> & duę lineæ m h, m z ſunt ſemidiametri circuli g h z:</s>
            <s xml:id="echoid-s19484" xml:space="preserve"> ergo [per 15 d 1] m t eſt æqualis m k,
              <lb/>
            & m h eſt æqualis m z:</s>
            <s xml:id="echoid-s19485" xml:space="preserve"> ergo [per 3 ax] h t eſt æqualis z k, & angulus d h t eſt minor angulo e z k:</s>
            <s xml:id="echoid-s19486" xml:space="preserve"> ergo
              <lb/>
            linea d h eſt minor quàm e z.</s>
            <s xml:id="echoid-s19487" xml:space="preserve"> [Nam linea æqualis ipſi d h (quę cũ k z continet angulũ æqualẽ angulo
              <lb/>
            d h t) minor eſt linea e z per 7 p 3] & duæ lineæ a d, a e ſunt æquales, ſimiliter duæ a h, a z ſunt æqua-
              <lb/>
            les:</s>
            <s xml:id="echoid-s19488" xml:space="preserve"> quia a eſt quaſi centrum circuli b d e, & circuli g h z.</s>
            <s xml:id="echoid-s19489" xml:space="preserve"> Ergo circulus, qui continet triangulum a
              <lb/>
            h d, maior eſt circulo, qui cõtinet trian gulũ a e z, quia angulus a h d eſt maior angulo a z e, & linea h
              <lb/>
            d eſt minor, ut declaratum eſt, quàm z e.</s>
            <s xml:id="echoid-s19490" xml:space="preserve"> Ergo h d diſtinguit de circulo continente triangulum a h
              <lb/>
            d, arcum minorem arcu, ſimili arcui, quem diuidit z e ex circulo continente a e z:</s>
            <s xml:id="echoid-s19491" xml:space="preserve"> angulus ergo h a d
              <lb/>
            minor eſt angulo z a e:</s>
            <s xml:id="echoid-s19492" xml:space="preserve"> ſit ergo z a d communis:</s>
            <s xml:id="echoid-s19493" xml:space="preserve"> ergo angulus h a z eſt minor angulo d a e:</s>
            <s xml:id="echoid-s19494" xml:space="preserve"> & angu-
              <lb/>
            lus h a z eſt ille, ſub quo a comprehendit refractè d e:</s>
            <s xml:id="echoid-s19495" xml:space="preserve"> & angulus d a e eſt ille, ſub quo comprehendit
              <lb/>
            d e rectè:</s>
            <s xml:id="echoid-s19496" xml:space="preserve"> ſi comprehenderet:</s>
            <s xml:id="echoid-s19497" xml:space="preserve"> a ergo comprehendit d e refractè minorem, quàm rectè.</s>
            <s xml:id="echoid-s19498" xml:space="preserve"> Et hęc demon
              <lb/>
            ſtratio ſequitur, ſi circulus b d e fuerit circulus meridiei.</s>
            <s xml:id="echoid-s19499" xml:space="preserve"> Diameter ergo ſtellæ cum fuerit directa &
              <lb/>
            recta, & diſtantia inter duas ſtellas recta:</s>
            <s xml:id="echoid-s19500" xml:space="preserve"> comprehenditur refractè minor quàm rectè.</s>
            <s xml:id="echoid-s19501" xml:space="preserve"> Et hoc eſt
              <lb/>
            quod uoluimus.</s>
            <s xml:id="echoid-s19502" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div633" type="section" level="0" n="0">
          <head xml:id="echoid-head540" xml:space="preserve" style="it">55. Stella uidetur circularis: maior in horizonte, quàm in medio cæli: ſimiliter́ duarum ſio
            <lb/>
          ſitarum inter ſe diſtantia. 54 p 10. Idem 51 n.</head>
          <p>
            <s xml:id="echoid-s19503" xml:space="preserve">ET omnis ſtella in cœlo comprehenditur rotunda:</s>
            <s xml:id="echoid-s19504" xml:space="preserve"> quia diametri eius comprehenduntur æ-
              <lb/>
            quales.</s>
            <s xml:id="echoid-s19505" xml:space="preserve"> Et cum ſit manifeſtum, quòd utraq;</s>
            <s xml:id="echoid-s19506" xml:space="preserve"> diameter eius recta & tranſuerſa ſecundum lati-
              <lb/>
            tudinem comprehenditur minor, quàm ſi comprehenderetur rectè:</s>
            <s xml:id="echoid-s19507" xml:space="preserve"> ergo utraq;</s>
            <s xml:id="echoid-s19508" xml:space="preserve"> diameter e-
              <lb/>
            ius decliuis comprehenditur æqualiter minor, quàm ſi comprehenderetur rectè.</s>
            <s xml:id="echoid-s19509" xml:space="preserve"> Et ſimiliter diſtan
              <lb/>
            tiæ inter ſtellas comprehenduntur in omnibus locis & in omnιbus ſitibus minores, quàm ſi com-
              <lb/>
            prehenderentur rectè.</s>
            <s xml:id="echoid-s19510" xml:space="preserve"> Item diximus [51 n] quòd omnis ſtella in uertice capitis comprehenditur
              <lb/>
            minor, quàm in omnibus alijs partibus cœli:</s>
            <s xml:id="echoid-s19511" xml:space="preserve"> & quantò fuerit remotior à uertice capitis, tantò com-
              <lb/>
            prehendetur maior:</s>
            <s xml:id="echoid-s19512" xml:space="preserve"> & quàm maxima comprehenditur, quando comprehenditur in horizonte.</s>
            <s xml:id="echoid-s19513" xml:space="preserve"> Re-
              <lb/>
            ſtat ergo declarare cauſſam, quare hoc ſit.</s>
            <s xml:id="echoid-s19514" xml:space="preserve"> Dico, quòd in ſecundo tractatu huius libri declarauimus,
              <lb/>
            cum tractauimus de magnitudine [38 n:</s>
            <s xml:id="echoid-s19515" xml:space="preserve">] quòd ſi uiſus comprehenderit magnitudines uiſibilium:</s>
            <s xml:id="echoid-s19516" xml:space="preserve">
              <lb/>
            comprehendit illas ex quantitatibus angulorum, quos reſpiciunt uiſibilia apud centrum uiſus, &
              <lb/>
            ex quantitatibus remot onum, & ex comparatione angulorum ad remotiones.</s>
            <s xml:id="echoid-s19517" xml:space="preserve"> Et declarauimus,
              <lb/>
            quòd uiſus nun quam comprehendit uiſibilium quantitates, niſi remotiones eorum ſint in rectitu-
              <lb/>
            dine corporum propinquorum continuorum:</s>
            <s xml:id="echoid-s19518" xml:space="preserve"> &, quòd ſi uiſus non certificarit remotiones uiſibi-
              <lb/>
            lium, non certificabit quantitates uiſibilium.</s>
            <s xml:id="echoid-s19519" xml:space="preserve"> Et declarauimus illic etiam, quòd uiſus, ſi non certifi-
              <lb/>
            </s>
          </p>
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