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-s13608" xml:space="preserve">
              <pb o="197" file="0203" n="203" rhead="OPTICAE LIBER VI."/>
            40 n 5 nulla fieret à pũcto m reflexio:</s>
            <s xml:id="echoid-s13609" xml:space="preserve"> multò igitur minus tangẽs à pũcto z, tanget citra punctũ m] ſi
              <lb/>
            uerò caderet in punctũ 3, ſecaret peripheriã, nõ tangeret:</s>
            <s xml:id="echoid-s13610" xml:space="preserve"> cadit igitur in peripheriá m 3.</s>
            <s xml:id="echoid-s13611" xml:space="preserve"> & contingẽs
              <lb/>
            illa cadet ſupra q:</s>
            <s xml:id="echoid-s13612" xml:space="preserve"> quoniá punctũ, in quod cadit, erit finis contingentiæ, & finis imaginũ:</s>
            <s xml:id="echoid-s13613" xml:space="preserve"> [per 17 n 5]
              <lb/>
            & puncta ſub puncto illo, quod eſt finis cõtingentię, nõ poterũt reflecti:</s>
            <s xml:id="echoid-s13614" xml:space="preserve"> ſuperiora uerò poterũt.</s>
            <s xml:id="echoid-s13615" xml:space="preserve"> Igi-
              <lb/>
            tur perpendicularis ducta à puncto i ſuper n q, ſi ceciderit ſupra punctũ, quod eſt finis cõtingentiæ:</s>
            <s xml:id="echoid-s13616" xml:space="preserve">
              <lb/>
            reflectetur punctũ, in quod cadit:</s>
            <s xml:id="echoid-s13617" xml:space="preserve"> & erit imago perpendicularis maior perpendiculari.</s>
            <s xml:id="echoid-s13618" xml:space="preserve"> Siuerò per-
              <lb/>
            pendicularis cadat in punctũ contingentiæ, aut infra:</s>
            <s xml:id="echoid-s13619" xml:space="preserve"> non reflectetur punctũ, in quod cadit.</s>
            <s xml:id="echoid-s13620" xml:space="preserve"> Quare
              <lb/>
            nulla erit imago perpendicularis.</s>
            <s xml:id="echoid-s13621" xml:space="preserve"> Veruntamen quoniá finis cõtingentiæ eſt infra n:</s>
            <s xml:id="echoid-s13622" xml:space="preserve"> erunt inter finẽ
              <lb/>
            cõtingentiæ & n infinita pũcta:</s>
            <s xml:id="echoid-s13623" xml:space="preserve"> quorũ quodlibet reflectetur:</s>
            <s xml:id="echoid-s13624" xml:space="preserve"> & erit imago cuiuslibet ſuper n q:</s>
            <s xml:id="echoid-s13625" xml:space="preserve"> & cu
              <lb/>
            iuslibet lineę ductę à puncto i ad quodlibet illorũ punctorũ, erit imago maior linea, cuius fuerit ima
              <lb/>
            go.</s>
            <s xml:id="echoid-s13626" xml:space="preserve"> Igitur accidit in his ſpeculis imaginem aliquando æqualem rei uiſæ:</s>
            <s xml:id="echoid-s13627" xml:space="preserve"> aliquando maiorem eſſe.</s>
            <s xml:id="echoid-s13628" xml:space="preserve">
              <lb/>
            Quod erat explanandum.</s>
            <s xml:id="echoid-s13629" xml:space="preserve"> Huius autem rei explanationem nec ſcriptam legimus, nec aliquem, qui
              <lb/>
            dixiſſet, aut intellexiſſet, audiuimus.</s>
            <s xml:id="echoid-s13630" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div463" type="section" level="0" n="0">
          <head xml:id="echoid-head420" xml:space="preserve" style="it">7. Si duo uiſibilis pũcta à centro ſpeculi ſphærici cõuexi æquabiliter, à uiſu uerò inæquabiliter
            <lb/>
          diſtẽt: imago & finis cõtingẽtiæ pũcti lõginquioris à uiſu, erũt lõginquiores à cẽtro ſpeculi. 4 p 6.</head>
          <p>
            <s xml:id="echoid-s13631" xml:space="preserve">AMplius:</s>
            <s xml:id="echoid-s13632" xml:space="preserve"> in his ſpeculis lineæ rectæ uidentur curuæ, & in pluribus curuitate quidẽ ſpeculũ nõ
              <lb/>
            reſpiciente, ſed ei aduerſa.</s>
            <s xml:id="echoid-s13633" xml:space="preserve"> Similiter curuæ apparebũt in his ſpeculis curuæ:</s>
            <s xml:id="echoid-s13634" xml:space="preserve"> & ſi curuitas ſpe-
              <lb/>
            culum reſpexerit, cõtrario ſitu apparebit.</s>
            <s xml:id="echoid-s13635" xml:space="preserve"> Et hoc quidẽ intelligendũ nõ in omnibus, ſed in pluribus.</s>
            <s xml:id="echoid-s13636" xml:space="preserve">
              <lb/>
            Ad cuius rei explanationẽ neceſſe eſt quędam antecedentia præmittere:</s>
            <s xml:id="echoid-s13637" xml:space="preserve"> quorũ unum eſt.</s>
            <s xml:id="echoid-s13638" xml:space="preserve"> Si fuerint
              <lb/>
            duo puncta eiuſdẽ longitudinis à centro ſpeculi, & inæqualis lõgitudinis à centro uiſus:</s>
            <s xml:id="echoid-s13639" xml:space="preserve"> imago pun
              <lb/>
            cti remotioris à centro uiſus erit remotior à centro ſpeculi, ꝗ̃ propinquioris:</s>
            <s xml:id="echoid-s13640" xml:space="preserve"> & finis cõtingentię re-
              <lb/>
            motioris erit remotior à centro ſpeculi, ꝗ̃ finis cõtingentię propinquioris:</s>
            <s xml:id="echoid-s13641" xml:space="preserve"> ſiue puncta illa ſint in ea-
              <lb/>
            dem ſuperficie cum centro uiſus, ſiue in diuerſis.</s>
            <s xml:id="echoid-s13642" xml:space="preserve"> Sintt, d duo puncta æqualiter à g cẽtro ſpeculi re-
              <lb/>
            mota:</s>
            <s xml:id="echoid-s13643" xml:space="preserve"> e centrũ uiſus:</s>
            <s xml:id="echoid-s13644" xml:space="preserve"> & d propinquius uiſui ꝗ̃ t.</s>
            <s xml:id="echoid-s13645" xml:space="preserve"> Superficies cõmunis ſectionis d t g ſecabit ſpeculũ
              <lb/>
            ſuper circulũ [per 1 th.</s>
            <s xml:id="echoid-s13646" xml:space="preserve"> 1 ſphæ.</s>
            <s xml:id="echoid-s13647" xml:space="preserve">] qui ſit a b:</s>
            <s xml:id="echoid-s13648" xml:space="preserve"> & ſit angulus e g d æqualis angulo t g z:</s>
            <s xml:id="echoid-s13649" xml:space="preserve"> angulus e g t æqua-
              <lb/>
            lis angulo t g h:</s>
            <s xml:id="echoid-s13650" xml:space="preserve"> & ſumatur in circulo punctũ, à quo t reflectatur ad z:</s>
            <s xml:id="echoid-s13651" xml:space="preserve"> [per 31.</s>
            <s xml:id="echoid-s13652" xml:space="preserve"> uel 39 n 5] quod ſit q.</s>
            <s xml:id="echoid-s13653" xml:space="preserve"> Di
              <lb/>
            co, quòd t non reflectitur ad h ab aliquo puncto b q.</s>
            <s xml:id="echoid-s13654" xml:space="preserve"> Palàm, quòd non à puncto b [quia cũ ea ſit per-
              <lb/>
            pendicularis ſpeculo, reflectetur in ſeipſam, nõ ad h per 11 n 4.</s>
            <s xml:id="echoid-s13655" xml:space="preserve">] Si aũt ſumatur punctũ quodcunq;</s>
            <s xml:id="echoid-s13656" xml:space="preserve"> in
              <lb/>
            b q:</s>
            <s xml:id="echoid-s13657" xml:space="preserve"> linea ducta à puncto h ad illud punctũ, ſecabit lineá q z.</s>
            <s xml:id="echoid-s13658" xml:space="preserve"> Igitur ad illud punctũ ſectionis reflecti-
              <lb/>
            tur t ab aliquo puncto, ſumpto in b q:</s>
            <s xml:id="echoid-s13659" xml:space="preserve"> & ad idẽ ſectionis punctũ reflectitur à puncto q.</s>
            <s xml:id="echoid-s13660" xml:space="preserve"> Igitur t refle-
              <lb/>
            ctitur ad idem punctum à duobus punctis illius circuli:</s>
            <s xml:id="echoid-s13661" xml:space="preserve"> quod impoſsibile in his ſpeculis, ut in libro
              <lb/>
            quinto [29 n] patuit.</s>
            <s xml:id="echoid-s13662" xml:space="preserve"> Reſtat ergo, ut t reflectatur ad h ab aliquo puncto q a:</s>
            <s xml:id="echoid-s13663" xml:space="preserve"> ſit illud m:</s>
            <s xml:id="echoid-s13664" xml:space="preserve"> & [per 17 p 3]
              <gap/>
              <lb/>
            puncto m ducatur contingens circulum uſq;</s>
            <s xml:id="echoid-s13665" xml:space="preserve"> ad li
              <lb/>
              <figure xlink:label="fig-0203-01" xlink:href="fig-0203-01a" number="162">
                <variables xml:id="echoid-variables152" xml:space="preserve">d t e
                  <gap/>
                h s n q b l q m f p a g</variables>
              </figure>
            neam g t:</s>
            <s xml:id="echoid-s13666" xml:space="preserve"> quæ ſit m n.</s>
            <s xml:id="echoid-s13667" xml:space="preserve"> Erit n finis contingentiæ t,
              <lb/>
            reſpectu h:</s>
            <s xml:id="echoid-s13668" xml:space="preserve"> [per 17 n 5] & à puncto q ducatur cõtin
              <lb/>
            gens:</s>
            <s xml:id="echoid-s13669" xml:space="preserve"> quę ſit q o:</s>
            <s xml:id="echoid-s13670" xml:space="preserve"> quę quidẽ neceſſariò cadet ſub m
              <lb/>
            n:</s>
            <s xml:id="echoid-s13671" xml:space="preserve"> [quòd enim non cadar in punctũ n, inde perſpi
              <lb/>
            cuum eſt:</s>
            <s xml:id="echoid-s13672" xml:space="preserve"> quia ductis ſemidiametrιs g q, g m:</s>
            <s xml:id="echoid-s13673" xml:space="preserve"> angu
              <lb/>
            li n q g, n m g per 18 p 3 recti, eſſent inęquales per 21
              <lb/>
            p 1 contra 10 ax:</s>
            <s xml:id="echoid-s13674" xml:space="preserve"> Si uerò cadat ultra n:</s>
            <s xml:id="echoid-s13675" xml:space="preserve"> erit per 21 p 1
              <lb/>
            angulus rectus obtuſo maior cótra 11 p 1] & produ
              <lb/>
            catur z q uſq;</s>
            <s xml:id="echoid-s13676" xml:space="preserve"> dum cadat ſuper g t in puncto p.</s>
            <s xml:id="echoid-s13677" xml:space="preserve"> [ca
              <lb/>
            det aũt per 3 uel 16 n 5.</s>
            <s xml:id="echoid-s13678" xml:space="preserve">] Erit p locus imaginis z.</s>
            <s xml:id="echoid-s13679" xml:space="preserve"> E-
              <lb/>
            rit ergo [per 18 n 5] proportio g t ad p g, ſicut t o ad
              <lb/>
            o p:</s>
            <s xml:id="echoid-s13680" xml:space="preserve"> igitur maior erit proportio g t ad t n, quàm g t
              <lb/>
            ad t o [per 8 p 5:</s>
            <s xml:id="echoid-s13681" xml:space="preserve"> quia t o màior eſt t n.</s>
            <s xml:id="echoid-s13682" xml:space="preserve">] Ergo multò
              <lb/>
            maior g t ad t n, quàm g p ad p n.</s>
            <s xml:id="echoid-s13683" xml:space="preserve"> [Quia enim ra-
              <lb/>
            tio g t ad t n maior eſt, ꝗ̃ ad t o ex concluſo:</s>
            <s xml:id="echoid-s13684" xml:space="preserve"> eſtq́;</s>
            <s xml:id="echoid-s13685" xml:space="preserve">
              <lb/>
            gt ad to, ſicut p g ad p o per 16 p 5.</s>
            <s xml:id="echoid-s13686" xml:space="preserve"> Ratio igitur t
              <lb/>
            g ad tn maior eſt, quàm p g ad p o:</s>
            <s xml:id="echoid-s13687" xml:space="preserve"> ſed ratio p g ad
              <lb/>
            p o maior eſt, quàm ad p n per 8 p 5.</s>
            <s xml:id="echoid-s13688" xml:space="preserve"> Ratio igitur
              <lb/>
            g t ad t n multò maior eſt, quàm p g ad p n.</s>
            <s xml:id="echoid-s13689" xml:space="preserve">] Sit er-
              <lb/>
            go [per 10 p 6] g t ad t n, ſicut g l ad i n.</s>
            <s xml:id="echoid-s13690" xml:space="preserve"> Erit g l ma-
              <lb/>
            ior g p.</s>
            <s xml:id="echoid-s13691" xml:space="preserve"> Et eritl locus imaginis h [per 18 n 5:</s>
            <s xml:id="echoid-s13692" xml:space="preserve"> eſt e-
              <lb/>
            nim per 16 p 5 g t ad g l, ſicut t n ad n l.</s>
            <s xml:id="echoid-s13693" xml:space="preserve">] Sint ergo h
              <lb/>
            g, e g, z g lineę æ quales:</s>
            <s xml:id="echoid-s13694" xml:space="preserve"> g f æqualis g p:</s>
            <s xml:id="echoid-s13695" xml:space="preserve"> g s æqualis g o.</s>
            <s xml:id="echoid-s13696" xml:space="preserve"> Cũ igitur angulus e g d ſit ęqualis angulo t g z
              <lb/>
            [per fabricationẽ] & remotio d à puncto è, ſicut z à puncto t:</s>
            <s xml:id="echoid-s13697" xml:space="preserve"> [Quia enim rectæ e g, d g, z g, t g:</s>
            <s xml:id="echoid-s13698" xml:space="preserve"> itẽ an-
              <lb/>
            guli e g d, z g t æquantur per fabricationẽ:</s>
            <s xml:id="echoid-s13699" xml:space="preserve"> baſes e d, z t ęquabuntur per 4 p 1:</s>
            <s xml:id="echoid-s13700" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s13701" xml:space="preserve"> puncta d, z ęqua
              <lb/>
            biliter diſtabũt à punctis e & t] erit imago d reſpectu e tantùm eleuata in linea g d, quantùm imago t
              <lb/>
            reſpectu z in linea g t:</s>
            <s xml:id="echoid-s13702" xml:space="preserve"> erit igitur imago d in puncto f:</s>
            <s xml:id="echoid-s13703" xml:space="preserve"> & ſimiliter finis cõtingentię d, reſpectu e erit al
              <lb/>
            titudinis eiuſdẽ, cuius eſt finis cõtingẽtię pũcti t, reſpectu z.</s>
            <s xml:id="echoid-s13704" xml:space="preserve"> Quare erit finis cõtingẽtiæ d in pũcto s.</s>
            <s xml:id="echoid-s13705" xml:space="preserve">
              <lb/>
            Verùm quoniá angulus e g t æqualis eſt angulo t g h, & h g æqualis e g:</s>
            <s xml:id="echoid-s13706" xml:space="preserve"> [per fabricationẽ] erit l ima-
              <lb/>
            got, reſpectue, ſicut eſt reſpectu puncti h:</s>
            <s xml:id="echoid-s13707" xml:space="preserve"> & n finis cõtingentiæ reſpectu e, ſicut eſt reſpectu pũcti h.</s>
            <s xml:id="echoid-s13708" xml:space="preserve">
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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