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-s7385" xml:space="preserve">
              <pb o="126" file="0132" n="132" rhead="ALHAZEN"/>
            uel ſuperficiei ſpeculo continuæ, & ſuperficiei reflexionis.</s>
            <s xml:id="echoid-s7386" xml:space="preserve"> Et nos hæc declarabímus.</s>
            <s xml:id="echoid-s7387" xml:space="preserve"> Sumatur ſpe-
              <lb/>
            culum planum, & ſtatuatur æquidiſtans horizonti:</s>
            <s xml:id="echoid-s7388" xml:space="preserve"> & lignum directũ & politum erigatur ſuper ſpe
              <lb/>
            culum:</s>
            <s xml:id="echoid-s7389" xml:space="preserve"> & ſit ſpeculi quantitas, ut totũ poſsit uideri lignum:</s>
            <s xml:id="echoid-s7390" xml:space="preserve"> niſi enim totum appareat, error inerit:</s>
            <s xml:id="echoid-s7391" xml:space="preserve">
              <lb/>
            & ſignetur in ligno punctum aliquod nigrum:</s>
            <s xml:id="echoid-s7392" xml:space="preserve"> apparebit quidem uiſui lignũ æquale huic ultra ſpe-
              <lb/>
            culum, huic ligno continuum, & orthogonale ſupra ſpeculum, & in ligno apparẽte apparebit pun-
              <lb/>
            ctum ſignatum, tantùm diſtans à ſuperficie ſpeculi, quantùm ab eadem diſtat in ligno ſuperiore.</s>
            <s xml:id="echoid-s7393" xml:space="preserve"> Et
              <lb/>
            ſi declinetur lignum ſupra ſpeculum:</s>
            <s xml:id="echoid-s7394" xml:space="preserve"> apparebit apparens eadem declinatione declinatum:</s>
            <s xml:id="echoid-s7395" xml:space="preserve"> & pun-
              <lb/>
            ctum ſignatum in apparente apparebit æquè remotum à ſuperficie ſpeculi.</s>
            <s xml:id="echoid-s7396" xml:space="preserve"> Et ſi à puncto ſignato
              <lb/>
            lignum aliquod erigatur orthogonaliter ſupra ſpeculum:</s>
            <s xml:id="echoid-s7397" xml:space="preserve"> uidebitur etiam hoc lignum à puncto ap-
              <lb/>
            parente orthogonaliter ſupra ſpeculum, & huic orthogonali continuum.</s>
            <s xml:id="echoid-s7398" xml:space="preserve"> Idem accidet pluribus
              <lb/>
            punctis in ligno ſignatis.</s>
            <s xml:id="echoid-s7399" xml:space="preserve"> Idemq́ue penitus accidet eleuato aut depreſſo ſpeculo.</s>
            <s xml:id="echoid-s7400" xml:space="preserve"> Planum ergo per
              <lb/>
            hoc, quòd imago puncti uiſi apparet in perpendiculari, ducta à puncto uiſo ad ſuperficiem ſpeculi.</s>
            <s xml:id="echoid-s7401" xml:space="preserve">
              <lb/>
            Et in hoc ſpeculo, quæ perpendicularis eſt ſuper ſuperficiem ſpeculi, eſt perpendicularis ſuper li-
              <lb/>
            neam communem ſuperficiei ſpeculi & ſuperficiei reflexionis.</s>
            <s xml:id="echoid-s7402" xml:space="preserve"> Idem patére poteſt in pyramide ſu-
              <lb/>
            per baſim orthogonali, cuius baſis plana ſpeculo plano ſit orthogonaliter adhibita:</s>
            <s xml:id="echoid-s7403" xml:space="preserve"> apparebit enim
              <lb/>
            huic pyramis alia continua, & harum pyramidum baſis eadem, & acumina ipſarum æqualiter à ſpe
              <lb/>
            culo diſtantia.</s>
            <s xml:id="echoid-s7404" xml:space="preserve"> Et planum, quòd ſi ab acumine ad acumen ducatur linea recta, erit perpendicularis
              <lb/>
            ſuper baſim:</s>
            <s xml:id="echoid-s7405" xml:space="preserve"> & ita ſuper ſpeculum, cum eadem ſit ſuperficies ſpeculi & baſis.</s>
            <s xml:id="echoid-s7406" xml:space="preserve"> Quare uertex pyra-
              <lb/>
            midis in perpendiculari uidebitur ab eo ad ſpeculum ducta.</s>
            <s xml:id="echoid-s7407" xml:space="preserve"> Similiter à quocunq;</s>
            <s xml:id="echoid-s7408" xml:space="preserve"> puncto pyrami-
              <lb/>
            dis ducatur linea æquidiſtans axi, cadet ad punctum reſpiciens ipſum in apparente pyramide:</s>
            <s xml:id="echoid-s7409" xml:space="preserve"> &
              <lb/>
            erit linea illa perpendicularis ſuper baſim & ſuper ſpeculi ſuperficiem [per 8 p 11.</s>
            <s xml:id="echoid-s7410" xml:space="preserve">] Quare imago
              <lb/>
            cuiuſq;</s>
            <s xml:id="echoid-s7411" xml:space="preserve"> puncti pyramidis cadit in perpẽdicularem, intellectam à puncto illo in ſpeculi ſuperficiem.</s>
            <s xml:id="echoid-s7412" xml:space="preserve">
              <lb/>
            Sed quodcunq;</s>
            <s xml:id="echoid-s7413" xml:space="preserve"> punctum opponatur ſpeculo plano, eſt intelligere pyramidem, cuius punctum il-
              <lb/>
            lud uertex:</s>
            <s xml:id="echoid-s7414" xml:space="preserve"> [per 14 n 4] quæ quidem pyramis ſuper baſim orthogonalis eſt, & etiam ſuper ſpeculi
              <lb/>
            ſuperficiem, aut ei continuam:</s>
            <s xml:id="echoid-s7415" xml:space="preserve"> & eſt intelligere aliam huic pyramidi oppoſitam, quarum baſis ea-
              <lb/>
            dem, & perpendicularis à uertice ad uerticẽ orthogonalis erit ſuper ſpeculum.</s>
            <s xml:id="echoid-s7416" xml:space="preserve"> Quare imago cuiuſ-
              <lb/>
            cunq;</s>
            <s xml:id="echoid-s7417" xml:space="preserve"> puncti ſpeculo oppoſiti, cadit in perpendicularem ductam à puncto ad ſpeculi ſuperficiem,
              <lb/>
            aut ei continuam.</s>
            <s xml:id="echoid-s7418" xml:space="preserve"> Sed [per 21 n 4] planum eſt, quòd in ſpeculis non accidit comprehenſio forma-
              <lb/>
            rum, niſi per lineas reflexionum.</s>
            <s xml:id="echoid-s7419" xml:space="preserve"> Quare imago puncti uiſi cadit in lineam reflexionis:</s>
            <s xml:id="echoid-s7420" xml:space="preserve"> & quælibet
              <lb/>
            talis linea eſt recta.</s>
            <s xml:id="echoid-s7421" xml:space="preserve"> Quare imago cuiuſcunq;</s>
            <s xml:id="echoid-s7422" xml:space="preserve"> puncti cadit in punctum ſectionis perpẽdicularis, du-
              <lb/>
            ctæ ab illo puncto ad ſuperficiem ſpeculi, & lineæ reflexionis.</s>
            <s xml:id="echoid-s7423" xml:space="preserve"> Et in ſpeculis planis linea communis
              <lb/>
            ſuperficiei ſpeculι & ſuperficiei reflexionis eſt una linea cum linea contingente locum reflexionis.</s>
            <s xml:id="echoid-s7424" xml:space="preserve">
              <lb/>
            Quare planum, quòd in ſpeculis planis imaginis locus, eſt punctũ ſectionis perpendicularis à pun-
              <lb/>
            cto uiſo ſuper lineam, contingentem communem lineam ſuperficiei ſpeculi & ſuperficiei reflexio-
              <lb/>
            nis, & lineæ reflexionis.</s>
            <s xml:id="echoid-s7425" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div281" type="section" level="0" n="0">
          <head xml:id="echoid-head306" xml:space="preserve" style="it">3. In ſpeculo ſphærico conuexo, imago uidetur in concurſu perpendicularis incidentiæ & li-
            <lb/>
          neæ reflexionis. 11 p 6.</head>
          <p>
            <s xml:id="echoid-s7426" xml:space="preserve">IN ſpeculis ſphæricis extrà politis patebit quod diximus.</s>
            <s xml:id="echoid-s7427" xml:space="preserve"> Quęratur ſuperficies ſpeculi talis ma-
              <lb/>
            gna, in qua appareat forma baculi gracilis, perpendiculariter erecti ſuper ipſum:</s>
            <s xml:id="echoid-s7428" xml:space="preserve"> apparebit qui-
              <lb/>
            dem forma baculi baculo continua:</s>
            <s xml:id="echoid-s7429" xml:space="preserve"> & apparebit in forma baculi punctum ſignatum, diſtans à
              <lb/>
            ſuperficie ſpeculi ſecundum diſtantiam eius ab eodem, in baculo:</s>
            <s xml:id="echoid-s7430" xml:space="preserve"> & ſi fuerit baculus gracilior ex
              <lb/>
            parte unius capitis, quàm ex parte alterius:</s>
            <s xml:id="echoid-s7431" xml:space="preserve"> apparebit quidem in hoc ſpeculo forma eius pyrami-
              <lb/>
            dalis:</s>
            <s xml:id="echoid-s7432" xml:space="preserve"> & eſt error uiſus, quem poſtea aſsignabimus.</s>
            <s xml:id="echoid-s7433" xml:space="preserve"> Amplius:</s>
            <s xml:id="echoid-s7434" xml:space="preserve"> fiat pyramis orthogonalis ſuper baſim
              <lb/>
            circularem circulatione perfecta:</s>
            <s xml:id="echoid-s7435" xml:space="preserve"> & applicetur etiam huic ſpeculo:</s>
            <s xml:id="echoid-s7436" xml:space="preserve"> uidebitur quidem pyramis huic
              <lb/>
            cõtinua ſuper eandem baſim erecta, ſed minoriſta.</s>
            <s xml:id="echoid-s7437" xml:space="preserve"> Quòd autem appareat pyramis, planum eſt per
              <lb/>
            hoc, quòd omnes lineæ ab apparehte imagine uerticis ad circulum baſis, uideantur æquales.</s>
            <s xml:id="echoid-s7438" xml:space="preserve"> Et ſi
              <lb/>
            declinetur pyramis modicùm ſupra ſpeculum a ſitu, in quo tota uidetur, ut ſcilicet aliquid ex ea ab-
              <lb/>
            ſcondatur, dum tamen locus reflexionis in ſpeculo uiſui exponatur:</s>
            <s xml:id="echoid-s7439" xml:space="preserve"> apparebit etiam inde imago
              <lb/>
            pyramidis.</s>
            <s xml:id="echoid-s7440" xml:space="preserve"> Et ſi elongetur uiſus à ſpeculo, aut accedat, dum tamẽ ſuper lineam à loco ad ipſum pro-
              <lb/>
            tractam cadat:</s>
            <s xml:id="echoid-s7441" xml:space="preserve"> comprehendetur imago pyramidis.</s>
            <s xml:id="echoid-s7442" xml:space="preserve"> Sed acceſſus uel receſſus ſecundum hanc li-
              <lb/>
            neam erit, ut notetur locus reflexionis, & à nota ad locum uiſus ducatur linea, ſecundum quam
              <lb/>
            fiat proceſſus.</s>
            <s xml:id="echoid-s7443" xml:space="preserve"> Verùm quoniam imago pyramidis orthogonalis eſt ſuper baſim pyramidis, & ba-
              <lb/>
            ſis eſt circulus ex circulis in ſphæra:</s>
            <s xml:id="echoid-s7444" xml:space="preserve"> erit linea à uertice pyramidis ad uerticem imaginis ducta, or-
              <lb/>
            thogonalis ſuper circulum illum, & tranſibit per centrum eius [per 6.</s>
            <s xml:id="echoid-s7445" xml:space="preserve">8 d 1 conicorum] & erit or-
              <lb/>
            thogonalis ſuper ſphæram, & tranſibit per centrum ſphæræ, & erit perpendicularis ſuper ſuperfi-
              <lb/>
            ficiem, ſphæram contingentem in puncto, per quod tranſit hæc linea [per 4 th.</s>
            <s xml:id="echoid-s7446" xml:space="preserve"> 1 ſphær.</s>
            <s xml:id="echoid-s7447" xml:space="preserve"> uel 25
              <lb/>
            n 4] & erit ſimiliter orthogonalis ſuper lineam, contingentem circulum ſphæræ per punctum
              <lb/>
            illud tranſeuntem [per 3 d 11.</s>
            <s xml:id="echoid-s7448" xml:space="preserve">] Et hæc contingens eſt linea, communis ſuperficiei reflexionis &
              <lb/>
            ſuperficiei contingenti ſphæram in puncto illo:</s>
            <s xml:id="echoid-s7449" xml:space="preserve"> & hæc linea contingit circulum ſphæræ, commu-
              <lb/>
            nem ſuperficiei ſphæræ & ſuperficiei reflexionis.</s>
            <s xml:id="echoid-s7450" xml:space="preserve"> Linea ergo à uertice pyramidis ad uerticem
              <lb/>
            imaginis ducta, eſt perpendicularis ſuper lineam contingentem, lineam communem ſuperficiei
              <lb/>
            reflexionis & ſuperficiei ſpeculi:</s>
            <s xml:id="echoid-s7451" xml:space="preserve"> quæ quidem eſt circulus.</s>
            <s xml:id="echoid-s7452" xml:space="preserve"> In hac igitur perpendiculari uide-
              <lb/>
            tur imago uerticis.</s>
            <s xml:id="echoid-s7453" xml:space="preserve"> Et planum [per 21 n 4] quòd imago uerticis eſt in linea reflexionis.</s>
            <s xml:id="echoid-s7454" xml:space="preserve"> Quare
              <lb/>
              <lb/>
            </s>
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