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

Page concordance

< >
Scan Original
141 135
142 136
143 137
144 138
145 139
146 140
147 141
148 142
149 143
150 144
151 145
152 146
153 147
154 148
155 149
156 150
157 151
158 152
159 153
160 154
161 155
162 156
163 157
164 158
165 159
166 160
167 161
168 162
169 163
170 164
< >
page |< < (204) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div487" type="section" level="0" n="0">
          <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>
Impressum