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-s12226" xml:space="preserve">
              <pb o="182" file="0188" n="188" rhead="ALHAZEN"/>
            uno uiſu, quantum ab alio, uel modica ſit differentia:</s>
            <s xml:id="echoid-s12227" xml:space="preserve"> erit locus imaginis reſpectu utríuſque uiſus
              <lb/>
            idem, aut diuerſus, ſed modicùm diſtans.</s>
            <s xml:id="echoid-s12228" xml:space="preserve"> Vnde aut una apparebit imago, aut ferè una:</s>
            <s xml:id="echoid-s12229" xml:space="preserve"> ſicut proba-
              <lb/>
            tum eſt in ſpeculis ſphæricis exterioribus.</s>
            <s xml:id="echoid-s12230" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div431" type="section" level="0" n="0">
          <head xml:id="echoid-head392" xml:space="preserve" style="it">89. Communis ſectio ſuperficierum, reflexionis & ſpeculi cylindracei caui aliâs eſt latus cy-
            <lb/>
          lindri: aliâs circulus: aliâs ellipſis. 1 p 9.</head>
          <p>
            <s xml:id="echoid-s12231" xml:space="preserve">IN ſpeculis columnaribus concauis aliquando linea communis eſt linea recta:</s>
            <s xml:id="echoid-s12232" xml:space="preserve"> cum ſuperficies
              <lb/>
            reflexionis tranſit per axem:</s>
            <s xml:id="echoid-s12233" xml:space="preserve"> [per 21 d 11] aliquando linea communis erit circulus, cum ſuperfi-
              <lb/>
            cies illa eſt æquidiſtans baſibus:</s>
            <s xml:id="echoid-s12234" xml:space="preserve"> [per 5 th.</s>
            <s xml:id="echoid-s12235" xml:space="preserve"> Sereni de ſectione cylindri] aliquando linea commu-
              <lb/>
            nis eſt ſectio columnaris.</s>
            <s xml:id="echoid-s12236" xml:space="preserve"> Quando fuerit linea recta:</s>
            <s xml:id="echoid-s12237" xml:space="preserve"> erit locus imaginis & modus reflexionis, ſicut
              <lb/>
            in ſpeculis planis.</s>
            <s xml:id="echoid-s12238" xml:space="preserve"> Quando fuerit circulus:</s>
            <s xml:id="echoid-s12239" xml:space="preserve"> erit idem modus, qui in ſphæricis concauis.</s>
            <s xml:id="echoid-s12240" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div432" type="section" level="0" n="0">
          <head xml:id="echoid-head393" xml:space="preserve" style="it">90. Sicommunis ſectio ſuperficierum, reflexionis & ſpeculi cylindracei caui fuerit ellipſis:
            <lb/>
          image uidebitur, aliâs ultra ſpeculum: aliâs in ſuperficie: aliâs citra uiſum: aliâs in uiſu: aliâs
            <lb/>
          inter uiſum & ſpeculum. 10 p 9.</head>
          <p>
            <s xml:id="echoid-s12241" xml:space="preserve">CVm uerò linea communis fuerit columnaris ſectio:</s>
            <s xml:id="echoid-s12242" xml:space="preserve"> aut erit locus imaginis ultra ſpeculum:</s>
            <s xml:id="echoid-s12243" xml:space="preserve">
              <lb/>
            aut citra uiſum:</s>
            <s xml:id="echoid-s12244" xml:space="preserve"> aut in centro uiſus:</s>
            <s xml:id="echoid-s12245" xml:space="preserve"> aut inter ſpeculum & uiſum:</s>
            <s xml:id="echoid-s12246" xml:space="preserve"> aut in ipſo ſpeculo:</s>
            <s xml:id="echoid-s12247" xml:space="preserve"> quod ſic
              <lb/>
            patebit.</s>
            <s xml:id="echoid-s12248" xml:space="preserve"> Sit a b g ſectio:</s>
            <s xml:id="echoid-s12249" xml:space="preserve"> ducatur perpendicularis in hac ſectione:</s>
            <s xml:id="echoid-s12250" xml:space="preserve"> [ſuper planum tangens ſpe
              <lb/>
            culum in reflexionis puncto] quæ ſit d g:</s>
            <s xml:id="echoid-s12251" xml:space="preserve"> quam ſecundum prædicta patet eſſe diametrum circuli.</s>
            <s xml:id="echoid-s12252" xml:space="preserve">
              <lb/>
            [Quia enim planum tangens cylindrum, tangit in latere per 26 n 4:</s>
            <s xml:id="echoid-s12253" xml:space="preserve"> ergo per 3 d 11 linea recta, per-
              <lb/>
            pendicularis plano tangenti, erit perpendicularis lateri, quod eſt parallelum axi per 21 d 11.</s>
            <s xml:id="echoid-s12254" xml:space="preserve"> Quar
              <gap/>
              <lb/>
            per 29 p 1 perpendicularis plano tangenti, perpendicula-
              <lb/>
              <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a" number="144">
                <variables xml:id="echoid-variables134" xml:space="preserve">e b
                  <gap/>
                g q
                  <gap/>
                m d a o
                  <gap/>
                z
                  <gap/>
                h k
                  <gap/>
                </variables>
              </figure>
            ris eſt axi.</s>
            <s xml:id="echoid-s12255" xml:space="preserve"> Planum uerò baſi parallelum & per dictam per-
              <lb/>
            pendicularem ductum eſt circulus, cẽtrum habens in axe
              <lb/>
            per 5th Sereni de ſectione cylindri.</s>
            <s xml:id="echoid-s12256" xml:space="preserve"> Recta igitur linea per
              <lb/>
            pendicularis plano, cylindrum in reflexionis puncto tan-
              <lb/>
            genti, eſt diameter circuli per reflexionis punctum ducti]
              <lb/>
            & unicam poſſe eſſe:</s>
            <s xml:id="echoid-s12257" xml:space="preserve"> cum ab alio puncto ſectionis nõ poſ-
              <lb/>
            ſit duci perpendicularis ſuper ſuperficiem contingentem.</s>
            <s xml:id="echoid-s12258" xml:space="preserve">
              <lb/>
            [Nam cum communis ſectio circuli & ellipſis per reflexio
              <lb/>
            nis punctum ſe ſecantium, ſit perpẽdicularis, tum ad pla-
              <lb/>
            num in eodem reflexionis puncto cylindrum tangẽs, tum
              <lb/>
            ad axem, ut iam patuit:</s>
            <s xml:id="echoid-s12259" xml:space="preserve"> rectæ igitur lineæ ab alijs ſectionis
              <lb/>
            punctis ad axem ductę, ad ipſum obliquæ erunt:</s>
            <s xml:id="echoid-s12260" xml:space="preserve"> ſecus per
              <lb/>
            4 p 11 axis eſſet perpendicularis plano ellipſis:</s>
            <s xml:id="echoid-s12261" xml:space="preserve"> contra 9 th
              <lb/>
            Sereni de ſectione cylindri.</s>
            <s xml:id="echoid-s12262" xml:space="preserve">] Sumatur aliud punctũ, & ſit
              <lb/>
            b:</s>
            <s xml:id="echoid-s12263" xml:space="preserve"> & ducatur ab eo in ſectione linea perpendicularis ſuper
              <lb/>
            lineam, contingẽtem ſectionem in puncto b:</s>
            <s xml:id="echoid-s12264" xml:space="preserve"> quæ quidem
              <lb/>
            linea ſecundũ prędicta neceſſariò concurret cum perpen-
              <lb/>
            diculari g d.</s>
            <s xml:id="echoid-s12265" xml:space="preserve"> Concurrat in puncto d:</s>
            <s xml:id="echoid-s12266" xml:space="preserve"> & ſumptum ſit b circa
              <lb/>
            punctum g, ut angulus b d g ſit acutus.</s>
            <s xml:id="echoid-s12267" xml:space="preserve"> Deinde [per 31 p 1]
              <lb/>
            à puncto g ducatur in ſectione linea æquidiſtans b d:</s>
            <s xml:id="echoid-s12268" xml:space="preserve"> quæ
              <lb/>
            ſit g h:</s>
            <s xml:id="echoid-s12269" xml:space="preserve"> quę quidẽ cadet intra columnarem ſectionem:</s>
            <s xml:id="echoid-s12270" xml:space="preserve"> quia
              <lb/>
            angulus h g d erit acutus, cum ſit æqualis g d b:</s>
            <s xml:id="echoid-s12271" xml:space="preserve"> [per 29 p 1]
              <lb/>
            & à puncto ginter d & h ducatur linea:</s>
            <s xml:id="echoid-s12272" xml:space="preserve"> quæ neceſſariò cõ-
              <lb/>
            curret cum b d:</s>
            <s xml:id="echoid-s12273" xml:space="preserve"> [per lemma Procli ad 29 p 1] concurrat in
              <lb/>
            puncto n:</s>
            <s xml:id="echoid-s12274" xml:space="preserve"> & inter n & g ſumatur punctũ quodcunq;</s>
            <s xml:id="echoid-s12275" xml:space="preserve">: quod
              <lb/>
            ſit o:</s>
            <s xml:id="echoid-s12276" xml:space="preserve"> ultra punctum n ſumatur punctum t.</s>
            <s xml:id="echoid-s12277" xml:space="preserve"> Item à puncto g
              <lb/>
            ducatur ſupra g h, alia linea g z, tamen intra ſectionem:</s>
            <s xml:id="echoid-s12278" xml:space="preserve"> quæ neceſſariò concurret cũ b d ex alia par-
              <lb/>
            re:</s>
            <s xml:id="echoid-s12279" xml:space="preserve"> [per lemma Procli ad 29 p 1] ſit concurſus e.</s>
            <s xml:id="echoid-s12280" xml:space="preserve"> Ducatur g q linea, ut angulus q g d ſit æ qualis z g d
              <lb/>
            [per 23 p 1] & fiat angulus l g d æqualis angulo h g d:</s>
            <s xml:id="echoid-s12281" xml:space="preserve"> & angulus m g d æqualis angulo n g d.</s>
            <s xml:id="echoid-s12282" xml:space="preserve"> Palàm,
              <lb/>
            [per 12 n 4] quòd ſi fuerit uiſus in puncto z:</s>
            <s xml:id="echoid-s12283" xml:space="preserve"> reflectetur punctũ q ad ipſum, à puncto g:</s>
            <s xml:id="echoid-s12284" xml:space="preserve"> & punctum
              <lb/>
            imaginis eſt e:</s>
            <s xml:id="echoid-s12285" xml:space="preserve"> [per 6 n] & ſi uiſus fuerit in puncto h:</s>
            <s xml:id="echoid-s12286" xml:space="preserve"> reflectetur ad ipſum l à puncto g:</s>
            <s xml:id="echoid-s12287" xml:space="preserve"> & erit locus
              <lb/>
            imaginis g:</s>
            <s xml:id="echoid-s12288" xml:space="preserve"> ſi uerò fuerit uiſus in puncto o:</s>
            <s xml:id="echoid-s12289" xml:space="preserve"> reflectetur ad ipſum, punctum m:</s>
            <s xml:id="echoid-s12290" xml:space="preserve"> & locus imaginis erit
              <lb/>
            n:</s>
            <s xml:id="echoid-s12291" xml:space="preserve"> ſi autem fuerit in n:</s>
            <s xml:id="echoid-s12292" xml:space="preserve"> erit locus imaginis puncti m in centro uiſus, id eſt in n:</s>
            <s xml:id="echoid-s12293" xml:space="preserve"> ſi autem fuerit in t:</s>
            <s xml:id="echoid-s12294" xml:space="preserve"> erit
              <lb/>
            locus imaginis tunc inter uiſum & ſpeculum:</s>
            <s xml:id="echoid-s12295" xml:space="preserve"> quia in n.</s>
            <s xml:id="echoid-s12296" xml:space="preserve"> Et ita patet propoſitum.</s>
            <s xml:id="echoid-s12297" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div434" type="section" level="0" n="0">
          <head xml:id="echoid-head394" xml:space="preserve" style="it">91. Si uiſus & uiſibile fuerint in eadẽ recta linea, perpendiculari plano ſpeculum cylindra-
            <lb/>
          ceum cauum tangenti: aliâs ab uno: aliâs à duobus ſpeculi punctis reflexio fiet: & imago uide-
            <lb/>
          bitur in centro uiſus. 11 p 9.</head>
          <p>
            <s xml:id="echoid-s12298" xml:space="preserve">HAec quidem iam dicta intelligenda ſunt, cum punctum uiſum nõ fuerit ſuper perpendicu-
              <lb/>
            larem cum ipſo uiſu.</s>
            <s xml:id="echoid-s12299" xml:space="preserve"> Tunc enim cum infinitæ ſuperficies poſsintintelligi, quarum quælibet
              <lb/>
            orthogonalis ſit ſuper ſuperficiem, contingentem ſpeculum [per 18 p 11:</s>
            <s xml:id="echoid-s12300" xml:space="preserve"> quia ſuperficies illæ
              <lb/>
            ducuntur per rectam plano ſpeculum tangenti perpendicularem] & omnes ſecent ſe ſuper illam
              <lb/>
            </s>
          </p>
        </div>
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