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-s8219" xml:space="preserve">
              <pb o="139" file="0145" n="145" rhead="OPTICAE LIBER V."/>
            ræ:</s>
            <s xml:id="echoid-s8220" xml:space="preserve"> a d b z diameteruiſualis:</s>
            <s xml:id="echoid-s8221" xml:space="preserve"> z c g circulus ſphæræ in ſuperficie linearũ contingẽtiæ:</s>
            <s xml:id="echoid-s8222" xml:space="preserve"> & protrahatur
              <lb/>
            à centro ad punctũ contingentiæ diameter b g.</s>
            <s xml:id="echoid-s8223" xml:space="preserve"> Palàm, quòd angulus z b g eſt maior recto.</s>
            <s xml:id="echoid-s8224" xml:space="preserve"> Cũ enim
              <lb/>
            in triãgulo b a g angulus b g a [per 18 p 3]
              <lb/>
              <figure xlink:label="fig-0145-01" xlink:href="fig-0145-01a" number="55">
                <variables xml:id="echoid-variables45" xml:space="preserve">a d q c m x b g p o k t f z h</variables>
              </figure>
            ſit rectus, erit [per 17 p 1] angulus g b a mi
              <lb/>
            nor recto:</s>
            <s xml:id="echoid-s8225" xml:space="preserve"> quare [per 13 p 1] z b g maior.</s>
            <s xml:id="echoid-s8226" xml:space="preserve">
              <lb/>
            Sit ergo [per 23 p 1] h b g rectus:</s>
            <s xml:id="echoid-s8227" xml:space="preserve"> erit ergo
              <lb/>
            [per 28 p 1] h b æquidiſtans lineę cõtingẽ
              <lb/>
            tię a g:</s>
            <s xml:id="echoid-s8228" xml:space="preserve"> Igitur [per 35 d 1] productæ nunꝗ̃
              <lb/>
            concurrent:</s>
            <s xml:id="echoid-s8229" xml:space="preserve"> & quęlibet diameter inter h
              <lb/>
            & g concurret cũ linea a g [per lẽma Pro-
              <lb/>
            cli ad 29 p 1.</s>
            <s xml:id="echoid-s8230" xml:space="preserve">] Ducatur à pũcto a linea ſe-
              <lb/>
            cans ſphęrã:</s>
            <s xml:id="echoid-s8231" xml:space="preserve"> quæ ſit a m o:</s>
            <s xml:id="echoid-s8232" xml:space="preserve"> ita quod chor-
              <lb/>
            da, quę eſt m o, ſit ęqualis ſemidiametro
              <lb/>
            o b:</s>
            <s xml:id="echoid-s8233" xml:space="preserve"> & cõcurrat ſemidiameter b o cum li-
              <lb/>
            nea a g, in puncto t.</s>
            <s xml:id="echoid-s8234" xml:space="preserve"> Dico, quòd in quoli-
              <lb/>
            bet pũcto t o eſt locus imaginis:</s>
            <s xml:id="echoid-s8235" xml:space="preserve"> & in nul
              <lb/>
            lo alio puncto diametri t b eſt locus ima-
              <lb/>
            ginis:</s>
            <s xml:id="echoid-s8236" xml:space="preserve"> & ſunt o, t termini locorũ imaginũ
              <lb/>
            [per 23 n.</s>
            <s xml:id="echoid-s8237" xml:space="preserve">] Sumatur enim punctũ:</s>
            <s xml:id="echoid-s8238" xml:space="preserve"> & ſit k:</s>
            <s xml:id="echoid-s8239" xml:space="preserve">
              <lb/>
            & a n k ducatur ſecans ſphærã in puncto
              <lb/>
            n:</s>
            <s xml:id="echoid-s8240" xml:space="preserve"> & ducatur perpendicularis b n x:</s>
            <s xml:id="echoid-s8241" xml:space="preserve"> & [ք
              <lb/>
            23 p 1] angulo x n a fiat angulus ęqualis per lineam f n.</s>
            <s xml:id="echoid-s8242" xml:space="preserve"> Palàm, quò d n f nõ cadet inter b, g.</s>
            <s xml:id="echoid-s8243" xml:space="preserve"> Quoniã ſic
              <lb/>
            aut ſecaret ſphæram, aut ſecaret contingentẽ a g in duobus punctis [& ſic duę lineę rectę ſpatiũ cõ-
              <lb/>
            prehenderent contra 12 ax.</s>
            <s xml:id="echoid-s8244" xml:space="preserve">] Igitur forma puncti f mouebitur per f n ad punctum n, & reflectetur ad
              <lb/>
            a per lineam a n:</s>
            <s xml:id="echoid-s8245" xml:space="preserve"> & apparebit imago eius in puncto k [per 3 n.</s>
            <s xml:id="echoid-s8246" xml:space="preserve">] Et eadem probatio eſt, ſumpto
              <lb/>
            quocunque alio puncto.</s>
            <s xml:id="echoid-s8247" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div320" type="section" level="0" n="0">
          <head xml:id="echoid-head329" xml:space="preserve" style="it">26. Si linea reflexionis æquans ſua parte inſcripta ſemidiametrum circuli (qui est communis
            <lb/>
          ſectio ſuperficierum reflexionis & ſpeculi ſphærici conuexi) terminetur in peripheria non appa
            <lb/>
          rente: perpẽdicularis incidẽtiæ, ſecãs peripheriã inter lineã reflexionis, & rectã à uiſu ſpeculũ
            <lb/>
          tangentẽ: habebit quaſdam imagines intra, quaſdam extra ſpeculũ: unam in ſuperficie. 31 p 6.</head>
          <p>
            <s xml:id="echoid-s8248" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s8249" xml:space="preserve"> dico, quòd in arcu o g, quęcunque
              <lb/>
              <figure xlink:label="fig-0145-02" xlink:href="fig-0145-02a" number="56">
                <variables xml:id="echoid-variables46" xml:space="preserve">a d k u m r h b g i l f e o z t y</variables>
              </figure>
            ſumatur diameter, continebit loca imagi-
              <lb/>
            num:</s>
            <s xml:id="echoid-s8250" xml:space="preserve"> & intra ſpeculum quaſdã:</s>
            <s xml:id="echoid-s8251" xml:space="preserve"> & unã in ſu
              <lb/>
            perficie:</s>
            <s xml:id="echoid-s8252" xml:space="preserve"> & alias extra ſpeculũ.</s>
            <s xml:id="echoid-s8253" xml:space="preserve"> Sumatur ergo pun-
              <lb/>
            ctum l:</s>
            <s xml:id="echoid-s8254" xml:space="preserve"> & protrahatur diameter b l, quouſq;</s>
            <s xml:id="echoid-s8255" xml:space="preserve"> ſecet
              <lb/>
            a t in puncto e:</s>
            <s xml:id="echoid-s8256" xml:space="preserve"> & producatur linea a l, ſecans ſphæ
              <lb/>
            ram in puncto r.</s>
            <s xml:id="echoid-s8257" xml:space="preserve"> Palàm, quòd r l minor eſt t b:</s>
            <s xml:id="echoid-s8258" xml:space="preserve"> quia
              <lb/>
            [per 15 p 3] eſt minor m o:</s>
            <s xml:id="echoid-s8259" xml:space="preserve"> quæ eſt ęqualis ſemidia
              <lb/>
            metro [ex theſi.</s>
            <s xml:id="echoid-s8260" xml:space="preserve">] Si ergo ab a ducatur linea ad dia
              <lb/>
            metrum b l:</s>
            <s xml:id="echoid-s8261" xml:space="preserve"> cuius pars interiacens inter circulũ &
              <lb/>
            diametrum, ſit æqualis parti diametri à puncto, in
              <lb/>
            quod cadit, uſq;</s>
            <s xml:id="echoid-s8262" xml:space="preserve"> ad centrũ:</s>
            <s xml:id="echoid-s8263" xml:space="preserve"> cadet inter l & b.</s>
            <s xml:id="echoid-s8264" xml:space="preserve"> Si e-
              <lb/>
            nim inter l & e ceciderit:</s>
            <s xml:id="echoid-s8265" xml:space="preserve"> erit r l maior l b:</s>
            <s xml:id="echoid-s8266" xml:space="preserve"> oĩs enim
              <lb/>
            linea interiacens inter centrũ, & illam partẽ lineæ
              <lb/>
            reflexionis, illi parti diametri ęqualem:</s>
            <s xml:id="echoid-s8267" xml:space="preserve"> erit maior
              <lb/>
            parte diametri, qua terminatur, ſecundum proba-
              <lb/>
            tionem aſsignatam in explanatione metæ imagi-
              <lb/>
            num [23 & proximo numeris.</s>
            <s xml:id="echoid-s8268" xml:space="preserve">] Sit ergo punctum,
              <lb/>
            in quod linea æqualis cadit:</s>
            <s xml:id="echoid-s8269" xml:space="preserve"> i.</s>
            <s xml:id="echoid-s8270" xml:space="preserve"> Dico, quòd in quo-
              <lb/>
            libet puncto lineę e i eſt locus imaginis:</s>
            <s xml:id="echoid-s8271" xml:space="preserve"> & erit ea-
              <lb/>
            dem demonſtratio, quę fuit in t o [præcedente nu
              <lb/>
            mero.</s>
            <s xml:id="echoid-s8272" xml:space="preserve">] Igitur quędã imagines in diametro e b ſor
              <lb/>
            tiuntur loca intra ſpeculũ:</s>
            <s xml:id="echoid-s8273" xml:space="preserve"> quędam extra ſpeculũ:</s>
            <s xml:id="echoid-s8274" xml:space="preserve">
              <lb/>
            una ſola in ſuperficie:</s>
            <s xml:id="echoid-s8275" xml:space="preserve"> ſcilicet in puncto l.</s>
            <s xml:id="echoid-s8276" xml:space="preserve"> Et ita po
              <lb/>
            teris demonſtrare in qualibet diametro per puncta arcus o g tranſeunte.</s>
            <s xml:id="echoid-s8277" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div322" type="section" level="0" n="0">
          <head xml:id="echoid-head330" xml:space="preserve" style="it">27. Si linea reflexionis, æquans ſua parte in ſcripta ſemidiametrum circuli (qui eſt commu-
            <lb/>
          nis ſectio ſuperficierum reflexionis & ſpeculi ſphærici conuexi) terminetur in peripheria nõ ap-
            <lb/>
          parente: perpendicularis incidentiæ ſecans peripheriam inter terminos lineæ reflexionis &
            <lb/>
          quadr antis peripheriæ, à puncto tact{us}, rectæ à uiſu ſpeculum tangentis, inchoati, habebit i-
            <lb/>
          magines extra ſpeculum. 32 p 6.</head>
          <p>
            <s xml:id="echoid-s8278" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s8279" xml:space="preserve"> ſumpta quacunq;</s>
            <s xml:id="echoid-s8280" xml:space="preserve"> diametro in arcu o h:</s>
            <s xml:id="echoid-s8281" xml:space="preserve"> locus imaginis in eo erit extra ſpeculũ.</s>
            <s xml:id="echoid-s8282" xml:space="preserve"> Suma
              <lb/>
            </s>
          </p>
        </div>
      </text>
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