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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        <div xml:id="echoid-div738" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s21378" xml:space="preserve">
              <pb o="21" file="0323" n="323" rhead="LIBER PRIMVS."/>
            per 1 p 3.</s>
            <s xml:id="echoid-s21379" xml:space="preserve"> Et quoniam punctum h cadit in diametrum a b:</s>
            <s xml:id="echoid-s21380" xml:space="preserve"> palàm, quia ipſum punctum h eſt centrum
              <lb/>
            circuli.</s>
            <s xml:id="echoid-s21381" xml:space="preserve"> Eſt ergo linea a d, pars diametri a b, maior quàm linea d b:</s>
            <s xml:id="echoid-s21382" xml:space="preserve"> & hoc eſt propoſitum.</s>
            <s xml:id="echoid-s21383" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div739" type="section" level="0" n="0">
          <head xml:id="echoid-head623" xml:space="preserve" style="it">49. Si ab angulis duorum trigonorum ad medietates ſuarũ baſiũ æqualiũ una perpendicula
            <lb/>
          riter, alia obliquè æquales lineæ duc antur, ſit́ quælibet duct arum maior medietate ſuæ baſis:
            <lb/>
          erit angulus trigoni, à quo ducitur perpendicularis, maior angulo alterius trigoni, à quo linea
            <lb/>
          ducitur obliqua.</head>
          <p>
            <s xml:id="echoid-s21384" xml:space="preserve">Sint duo trigona a b c & d e f, quorum baſes b c, & e f, ſint æquales:</s>
            <s xml:id="echoid-s21385" xml:space="preserve"> quæ ſecentur per 10 p 1 in par-
              <lb/>
            tes æquales, b c in puncto g, & e f in puncto h:</s>
            <s xml:id="echoid-s21386" xml:space="preserve"> & ducantur ab angulis ad baſes lineæ a g & d h, quæ
              <lb/>
            ſint ęquales:</s>
            <s xml:id="echoid-s21387" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s21388" xml:space="preserve"> linea a g ք-
              <lb/>
              <figure xlink:label="fig-0323-01" xlink:href="fig-0323-01a" number="314">
                <variables xml:id="echoid-variables298" xml:space="preserve">a b ſ m g c k</variables>
              </figure>
              <figure xlink:label="fig-0323-02" xlink:href="fig-0323-02a" number="315">
                <variables xml:id="echoid-variables299" xml:space="preserve">d e h f</variables>
              </figure>
            pẽdicularis ſuper lineã b c, li-
              <lb/>
            nea uerò d h nõ ſit perpẽdicu
              <lb/>
            laris ſuք lineã e f.</s>
            <s xml:id="echoid-s21389" xml:space="preserve"> Sitq́;</s>
            <s xml:id="echoid-s21390" xml:space="preserve"> linea
              <lb/>
            perpendicularis a g maior li-
              <lb/>
            nea b g parte baſis:</s>
            <s xml:id="echoid-s21391" xml:space="preserve"> item obli-
              <lb/>
            qua d h maior linea e h parte
              <lb/>
            baſis.</s>
            <s xml:id="echoid-s21392" xml:space="preserve"> Dico, quod angulus b a
              <lb/>
            c eſt maior angulo e d f.</s>
            <s xml:id="echoid-s21393" xml:space="preserve"> Cir-
              <lb/>
            cũſcribatur enim trigono a b
              <lb/>
            c circulus per 5 p 4, & produ-
              <lb/>
            catur linea a g ad circũferen-
              <lb/>
            tiã in punctũ k:</s>
            <s xml:id="echoid-s21394" xml:space="preserve"> hoc aũt poſsi-
              <lb/>
            bile.</s>
            <s xml:id="echoid-s21395" xml:space="preserve"> Quoniã uerò ſuppoſitũ
              <lb/>
            eſt lineã a g eſſe maiorẽ linea
              <lb/>
            g b, erit per 47 huius linea a g
              <lb/>
            maior ꝗ̃ linea g k:</s>
            <s xml:id="echoid-s21396" xml:space="preserve"> ergo per 1 p 3 centrũ circuli eſt in linea a g inter pũcta a & g:</s>
            <s xml:id="echoid-s21397" xml:space="preserve"> & erit a k diameter, &
              <lb/>
            per 7 p 3 linea g a eſt lõgiſsima omnium linearũ à puncto g ad circũferentiã productarũ:</s>
            <s xml:id="echoid-s21398" xml:space="preserve"> & linea g k
              <lb/>
            erit omniũ linearũ illarum minima:</s>
            <s xml:id="echoid-s21399" xml:space="preserve"> & quęlibet propinquior lineę g a eſt maior remotiore.</s>
            <s xml:id="echoid-s21400" xml:space="preserve"> Fiat itaq;</s>
            <s xml:id="echoid-s21401" xml:space="preserve">
              <lb/>
            per 23 p 1 ſuper punctũ g termini lineę, c g angulus ęqualis angulo f h d minori angulo d h e, qui ſit l
              <lb/>
            g c, producta linea g l uſq;</s>
            <s xml:id="echoid-s21402" xml:space="preserve"> ad peripheriã circuli.</s>
            <s xml:id="echoid-s21403" xml:space="preserve"> Palã itaq;</s>
            <s xml:id="echoid-s21404" xml:space="preserve"> ex 7 p 3, quoniã linea g a eſt maior ꝗ̃ linea
              <lb/>
            g l:</s>
            <s xml:id="echoid-s21405" xml:space="preserve"> ergo & linea d h, quę ex hypotheſi eſt ęqualis lineę a g, eſt maior ꝗ̃ linea g l.</s>
            <s xml:id="echoid-s21406" xml:space="preserve"> Producatur itaq;</s>
            <s xml:id="echoid-s21407" xml:space="preserve"> li-
              <lb/>
            nea g l, quouſq;</s>
            <s xml:id="echoid-s21408" xml:space="preserve"> ſit ęqualis lineę d h per 3 p 1, & ſit linea g m ęqualis lineę d h:</s>
            <s xml:id="echoid-s21409" xml:space="preserve"> & ducantur lineę m b
              <lb/>
            & m c:</s>
            <s xml:id="echoid-s21410" xml:space="preserve"> angulus itaq;</s>
            <s xml:id="echoid-s21411" xml:space="preserve"> b m c eſt ęqualis angulo e d f ex hypotheſi per 4.</s>
            <s xml:id="echoid-s21412" xml:space="preserve"> 13 p 1.</s>
            <s xml:id="echoid-s21413" xml:space="preserve"> Sed angulus b a c eſt ma
              <lb/>
            ior angulo b m c.</s>
            <s xml:id="echoid-s21414" xml:space="preserve"> Producantur enim lineę b l & c l:</s>
            <s xml:id="echoid-s21415" xml:space="preserve"> palã, quia angulus b l c eſt maior angulo b m c per
              <lb/>
            21 p 1:</s>
            <s xml:id="echoid-s21416" xml:space="preserve"> ſed angulus b a c eſt æqualis angulo b l c per 21 p 3.</s>
            <s xml:id="echoid-s21417" xml:space="preserve"> Erit ergo angulus b a c maior angulo b m c:</s>
            <s xml:id="echoid-s21418" xml:space="preserve">
              <lb/>
            ergo & angulo e d f:</s>
            <s xml:id="echoid-s21419" xml:space="preserve"> & hoc proponebatur.</s>
            <s xml:id="echoid-s21420" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div741" type="section" level="0" n="0">
          <head xml:id="echoid-head624" xml:space="preserve" style="it">50. Si ab angulis duorum trigonorum ad medietates ſuarum baſium æqualium una perpẽdi-
            <lb/>
          culariter, alia obliquè, æquales lineæ ducantur, ſit́ quælibet ductarum minor medietate baſis
            <lb/>
          ſuæ: erit angulus trigoni, à quo ducitur perpendicularis, minor angulo alterius trigoni, à quo
            <lb/>
          linea ducitur obliqua.</head>
          <p>
            <s xml:id="echoid-s21421" xml:space="preserve">Remaneat diſpoſitio pręcedentis, niſi quòd perpendicularis a g ſit minor medietate baſis b g.</s>
            <s xml:id="echoid-s21422" xml:space="preserve"> Di
              <lb/>
            co, qđ angulus b a c eſt mi-
              <lb/>
              <figure xlink:label="fig-0323-03" xlink:href="fig-0323-03a" number="316">
                <variables xml:id="echoid-variables300" xml:space="preserve">a l n b g c k</variables>
              </figure>
              <figure xlink:label="fig-0323-04" xlink:href="fig-0323-04a" number="317">
                <variables xml:id="echoid-variables301" xml:space="preserve">d c h f</variables>
              </figure>
            nor angulo e d f.</s>
            <s xml:id="echoid-s21423" xml:space="preserve"> Sit enim,
              <lb/>
            ut prius, angulus c g l ęqua-
              <lb/>
            lis angulo d h f.</s>
            <s xml:id="echoid-s21424" xml:space="preserve"> Et quoniã li
              <lb/>
            nea a g eſt minor quã linea
              <lb/>
            b g, & linea a k eſt diame-
              <lb/>
            ter:</s>
            <s xml:id="echoid-s21425" xml:space="preserve"> palã per 47 huius, quo-
              <lb/>
            niam cẽtrũ circuli eſt inter
              <lb/>
            puncta g & k:</s>
            <s xml:id="echoid-s21426" xml:space="preserve"> ergo per 7 p 3
              <lb/>
            linea g a eſt minima omniũ
              <lb/>
            linearũ à puncto gad peri-
              <lb/>
            pheriã circuli productarũ:</s>
            <s xml:id="echoid-s21427" xml:space="preserve">
              <lb/>
            eſt ergo linea g l maior ꝗ̃ li-
              <lb/>
            nea g a:</s>
            <s xml:id="echoid-s21428" xml:space="preserve"> ergo & maior quã li
              <lb/>
            nea d h.</s>
            <s xml:id="echoid-s21429" xml:space="preserve"> Fiat itaq;</s>
            <s xml:id="echoid-s21430" xml:space="preserve"> per 3 p 1 li
              <lb/>
            nea g n ęqualis lineæ d h:</s>
            <s xml:id="echoid-s21431" xml:space="preserve"> &
              <lb/>
            copulẽtur lineę bn & c n:</s>
            <s xml:id="echoid-s21432" xml:space="preserve"> erit itaq;</s>
            <s xml:id="echoid-s21433" xml:space="preserve">, ut in pręmiſſa, angulus e d f æqualis angulo b n c:</s>
            <s xml:id="echoid-s21434" xml:space="preserve"> ſed angulus b
              <lb/>
            n e maior eſt angulo b l c per 21 p 1, & angulus b l c æqualis angulo b a c per 21 p 3.</s>
            <s xml:id="echoid-s21435" xml:space="preserve"> Erit ergo angulus
              <lb/>
            b a c minor angulo b n c:</s>
            <s xml:id="echoid-s21436" xml:space="preserve"> ergo & eιus æquali, angulo e d f:</s>
            <s xml:id="echoid-s21437" xml:space="preserve"> & hoc eſt propoſitum.</s>
            <s xml:id="echoid-s21438" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div743" type="section" level="0" n="0">
          <head xml:id="echoid-head625" xml:space="preserve" style="it">51. Si ab angulis duorum trigonorum ad medietates ſuarum baſium æqualium duæ lineæ æ-
            <lb/>
          quales, obliquè incidant ad angulos inæquales, & ſi quælibet linearum incidentium maior fue-
            <lb/>
          rit medietate ſuæ baſis: erit angulus ſuperior illius trigoni, cuius incidens linea maiorem angu-
            <lb/>
          </head>
        </div>
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