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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          <head xml:id="echoid-head435" xml:space="preserve" style="it">
            <pb o="204" file="0210" n="210" rhead="ALHAZEN"/>
          cum ſuperficie ſpeculi ſphærici cõuexi, parallela eſt rectæ connectenti centra ſpeculi & uiſ{us}, uel
            <lb/>
          quæ cum eadem connectente extra ſpeculum, uerſ{us} uiſum concurrit: uidebitur curua. 57 p 6.</head>
          <p>
            <s xml:id="echoid-s14150" xml:space="preserve">QVòd autẽ imago rei uiſæ ſit curua, uiſu exi-
              <lb/>
              <figure xlink:label="fig-0210-01" xlink:href="fig-0210-01a" number="177">
                <variables xml:id="echoid-variables167" xml:space="preserve">h e m c u t s k o b z ſ q r f g a d</variables>
              </figure>
            ſtente in ſuperficie cẽtri ſpeculi & rei uiſæ,
              <lb/>
            probabitur.</s>
            <s xml:id="echoid-s14151" xml:space="preserve"> Sit d centrũ uiſus:</s>
            <s xml:id="echoid-s14152" xml:space="preserve"> g centrũ ſpe-
              <lb/>
            culi:</s>
            <s xml:id="echoid-s14153" xml:space="preserve"> h e ſit linea uiſa:</s>
            <s xml:id="echoid-s14154" xml:space="preserve"> quæ quidẽ h e non cõcurrat cũ
              <lb/>
            circulo ſpeculi, ſed ſit æquidiſtãs lineę d g:</s>
            <s xml:id="echoid-s14155" xml:space="preserve"> uel ſecet
              <lb/>
            eã ex parte d.</s>
            <s xml:id="echoid-s14156" xml:space="preserve"> Superficies incidentiæ ſit, in qua ſint
              <lb/>
            lineæ d g, h e.</s>
            <s xml:id="echoid-s14157" xml:space="preserve"> Circulus cõmunis huic ſuperficiei &
              <lb/>
            ſpeculo ſit a b.</s>
            <s xml:id="echoid-s14158" xml:space="preserve"> Producatur linea h g, & punctum in
              <lb/>
            ipſa z ſit imago h:</s>
            <s xml:id="echoid-s14159" xml:space="preserve"> punctũ circuli à quo reflectitur h
              <lb/>
            ad d, ſit b.</s>
            <s xml:id="echoid-s14160" xml:space="preserve"> Et [per 17 p 3] à pũcto b ducatur linea cõ-
              <lb/>
            tingẽs, quæ ſecet lineã h g ſuper punctũ t:</s>
            <s xml:id="echoid-s14161" xml:space="preserve"> erit t finis
              <lb/>
            contingẽtiæ [ք 17 n 5.</s>
            <s xml:id="echoid-s14162" xml:space="preserve">] Ducatur linea b g:</s>
            <s xml:id="echoid-s14163" xml:space="preserve"> quę pro-
              <lb/>
            ducta neceſſario concurret cũ h e.</s>
            <s xml:id="echoid-s14164" xml:space="preserve"> Si enim h e fuerit
              <lb/>
            æquidiſtãs d g:</s>
            <s xml:id="echoid-s14165" xml:space="preserve"> cõcurret quidẽ:</s>
            <s xml:id="echoid-s14166" xml:space="preserve"> [ք lemma Procli ad
              <lb/>
            29 p 1] ſi uerò d g cõcurrat cũ h e:</s>
            <s xml:id="echoid-s14167" xml:space="preserve"> multò fortius g b
              <lb/>
            cũ eadẽ cõcurret.</s>
            <s xml:id="echoid-s14168" xml:space="preserve"> Cõcurſus ille aut erit in linea h e:</s>
            <s xml:id="echoid-s14169" xml:space="preserve">
              <lb/>
            aut ultra hãc lineã.</s>
            <s xml:id="echoid-s14170" xml:space="preserve"> Sit ultra:</s>
            <s xml:id="echoid-s14171" xml:space="preserve"> cõcurrat in puncto m:</s>
            <s xml:id="echoid-s14172" xml:space="preserve">
              <lb/>
            imago pũcti m ſit q:</s>
            <s xml:id="echoid-s14173" xml:space="preserve"> finis contingẽtiæ ſit s:</s>
            <s xml:id="echoid-s14174" xml:space="preserve"> & duca-
              <lb/>
            tur linea z q, & ſimiliter linea t s:</s>
            <s xml:id="echoid-s14175" xml:space="preserve"> & d g ſecet circulũ in a:</s>
            <s xml:id="echoid-s14176" xml:space="preserve"> & [per 17 p 3] ducatur à puncto a cõtingen
              <gap/>
              <lb/>
            a u.</s>
            <s xml:id="echoid-s14177" xml:space="preserve"> Palàm [è 24 n 4] quòd a b eſt minor quarta circuli:</s>
            <s xml:id="echoid-s14178" xml:space="preserve"> cum d uideat ex circulo minus medietate.</s>
            <s xml:id="echoid-s14179" xml:space="preserve">
              <lb/>
            Quare angulus a g b eſt acutus:</s>
            <s xml:id="echoid-s14180" xml:space="preserve"> [ք 33 p 6] & [per 18
              <lb/>
              <figure xlink:label="fig-0210-02" xlink:href="fig-0210-02a" number="178">
                <variables xml:id="echoid-variables168" xml:space="preserve">h e m c u s t b o q z r f g a d</variables>
              </figure>
            p 3] angulus u a g eſt rectus.</s>
            <s xml:id="echoid-s14181" xml:space="preserve"> Igitur a u cõcurret cum
              <lb/>
            b g [per 11 ax.</s>
            <s xml:id="echoid-s14182" xml:space="preserve">] cõcurrat in puncto u.</s>
            <s xml:id="echoid-s14183" xml:space="preserve"> Dico, quòd pun
              <lb/>
            ctum u cadet ſupra punctũ s.</s>
            <s xml:id="echoid-s14184" xml:space="preserve"> Cũ enim m reflectatur
              <lb/>
            à puncto aliquo arcus a b [per 29 n 5] & a ſit demiſ-
              <lb/>
            ſius illo puncto:</s>
            <s xml:id="echoid-s14185" xml:space="preserve"> erit finis contingentiæ a, altior fine
              <lb/>
            contingentiæ illius puncti:</s>
            <s xml:id="echoid-s14186" xml:space="preserve"> & ita s demiſsius pũcto
              <lb/>
            u.</s>
            <s xml:id="echoid-s14187" xml:space="preserve"> Procedat ergo t s, donec concurrat cum linea a u:</s>
            <s xml:id="echoid-s14188" xml:space="preserve">
              <lb/>
            [cõcurret aũt per 11 ax] & ſit cõcurſus in pũcto k:</s>
            <s xml:id="echoid-s14189" xml:space="preserve"> &
              <lb/>
            ducatur linea g k:</s>
            <s xml:id="echoid-s14190" xml:space="preserve"> quę producta concurrat cũ h m in
              <lb/>
            pũcto c:</s>
            <s xml:id="echoid-s14191" xml:space="preserve"> [cõcurret autẽ per lemma Procli ad 29 p 1]
              <lb/>
            Punctũ c reflectitur ad d ab aliquo puncto arcus a b
              <lb/>
            [per 29 n 5.</s>
            <s xml:id="echoid-s14192" xml:space="preserve">] Sit illud punctũ f:</s>
            <s xml:id="echoid-s14193" xml:space="preserve"> à quo ducatur linea
              <lb/>
            contingẽs uſq;</s>
            <s xml:id="echoid-s14194" xml:space="preserve"> ad g c, quę quidẽ erit demiſsior linea
              <lb/>
            a k:</s>
            <s xml:id="echoid-s14195" xml:space="preserve"> & erit punctũ o demiſsius pũcto k.</s>
            <s xml:id="echoid-s14196" xml:space="preserve"> Sit o finis cõ-
              <lb/>
            tingẽtiæ.</s>
            <s xml:id="echoid-s14197" xml:space="preserve"> Ducatur linea d f, quouſq;</s>
            <s xml:id="echoid-s14198" xml:space="preserve"> cadat ſuper g c:</s>
            <s xml:id="echoid-s14199" xml:space="preserve">
              <lb/>
            cadat in punctũ r:</s>
            <s xml:id="echoid-s14200" xml:space="preserve"> & producatur z q uſq;</s>
            <s xml:id="echoid-s14201" xml:space="preserve"> ad lineã g c:</s>
            <s xml:id="echoid-s14202" xml:space="preserve">
              <lb/>
            & cadat in punctum l.</s>
            <s xml:id="echoid-s14203" xml:space="preserve"> Dico quòd l eſt ſupra r.</s>
            <s xml:id="echoid-s14204" xml:space="preserve"> Lineæ
              <lb/>
            enim h c, t k, z l autſunt æquidiſtantes:</s>
            <s xml:id="echoid-s14205" xml:space="preserve"> aut cõcurrunt.</s>
            <s xml:id="echoid-s14206" xml:space="preserve"> Sint æquidiſtantes.</s>
            <s xml:id="echoid-s14207" xml:space="preserve"> Cũ ergo hæ æquidiſtãtes
              <lb/>
            ſecent lineam g c ſuper tria pun-
              <lb/>
              <figure xlink:label="fig-0210-03" xlink:href="fig-0210-03a" number="179">
                <variables xml:id="echoid-variables169" xml:space="preserve">i h e m c t z u s b o k q
                  <gap/>
                r f g a d</variables>
              </figure>
            cta c, k, l, & ſecent utram q;</s>
            <s xml:id="echoid-s14208" xml:space="preserve"> linea-
              <lb/>
            rum m g, h g:</s>
            <s xml:id="echoid-s14209" xml:space="preserve"> & [per 18 n 5.</s>
            <s xml:id="echoid-s14210" xml:space="preserve"> 16 p
              <lb/>
            5] ꝓportio h g ad h t, ſicut g z ad
              <lb/>
            z t:</s>
            <s xml:id="echoid-s14211" xml:space="preserve"> ſimiliter m g ad m s, ſicut g q
              <lb/>
            ad q s:</s>
            <s xml:id="echoid-s14212" xml:space="preserve"> erit [ք 10 n] ꝓportio eadẽ
              <lb/>
            g c ad c k, ſicut l g ad l k.</s>
            <s xml:id="echoid-s14213" xml:space="preserve"> Sed pa-
              <lb/>
            làm [per 3 n 5] quòd r eſt imago
              <lb/>
            c:</s>
            <s xml:id="echoid-s14214" xml:space="preserve"> linea enim d f, linea reflexio-
              <lb/>
            nis, concurrit cum c g in puncto
              <lb/>
            r:</s>
            <s xml:id="echoid-s14215" xml:space="preserve"> & o finis contingentiæ.</s>
            <s xml:id="echoid-s14216" xml:space="preserve"> Quare
              <lb/>
            [per 18 n 5.</s>
            <s xml:id="echoid-s14217" xml:space="preserve"> 16 p 5] proportio g c
              <lb/>
            ad c o, ſicut g r ad r o:</s>
            <s xml:id="echoid-s14218" xml:space="preserve"> ſed [per 8 p
              <lb/>
            5] maior eſt proportio g c ad c k,
              <lb/>
            quàm g c ad c o:</s>
            <s xml:id="echoid-s14219" xml:space="preserve"> & ita maior g l
              <lb/>
            ad l k, quã g r ad r o:</s>
            <s xml:id="echoid-s14220" xml:space="preserve"> ergo maior
              <lb/>
            eſt proportio o r ad r g, quàm l k
              <lb/>
            ad l g:</s>
            <s xml:id="echoid-s14221" xml:space="preserve"> [quia per 26 p Cãpani in
              <lb/>
            quintũ librum elementorum, ratio l k ad g l minor eſt, quã ratio o r ad r g] & ita [per 18 p 5] maior
              <lb/>
            eſt proportio o g ad r g, quàm k g ad l g.</s>
            <s xml:id="echoid-s14222" xml:space="preserve"> Sed [per 9 ax.</s>
            <s xml:id="echoid-s14223" xml:space="preserve"> k g maior eſt o g.</s>
            <s xml:id="echoid-s14224" xml:space="preserve">] Quare [per 14 p 5] l g ma-
              <lb/>
            ior r g.</s>
            <s xml:id="echoid-s14225" xml:space="preserve"> Igitur r demiſsius eſt puncto l.</s>
            <s xml:id="echoid-s14226" xml:space="preserve"> Sed z q l eſt linea recta:</s>
            <s xml:id="echoid-s14227" xml:space="preserve"> igitur z q r eſt linea curua.</s>
            <s xml:id="echoid-s14228" xml:space="preserve"> Et ita imago
              <lb/>
            lineæ h c eſt curua.</s>
            <s xml:id="echoid-s14229" xml:space="preserve"> Poſito ergo aliquo puncto lineæ h e loco puncti m, & puncto e loco puncti c:</s>
            <s xml:id="echoid-s14230" xml:space="preserve"> e-
              <lb/>
            rit probare, quòd imago h e eſt curua.</s>
            <s xml:id="echoid-s14231" xml:space="preserve"> Si uerò lineæ h c, t s, z q concurrant:</s>
            <s xml:id="echoid-s14232" xml:space="preserve"> aut erit concurſus ex par
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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