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

Table of figures

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[251] e d a n b g m q t k z h l
Page: 291
[252] f g k h d c e a b
Page: 292
[253] h d a m e c k z g b
Page: 293
[254] n a d p e q o r f k h g b l c m
Page: 294
[Figure 255]
Page: 295
[256] b a c d
Page: 306
[257] a c b d
Page: 307
[258] c a b d e
Page: 307
[259] a b c d e f
Page: 307
[260] a e b f g
Page: 307
[261] a b c d g c d g f
Page: 307
[262] a b c d
Page: 308
[263] a b e c d
Page: 308
[264] a b c d e f
Page: 308
[265] a b c d
Page: 308
[266] a b c d
Page: 309
[267] a b e c d
Page: 309
[268] a b e c d
Page: 309
[269] a b c e d
Page: 309
[270] a b g d e z
Page: 310
[271] e a b c d f
Page: 310
[272] a d e c b
Page: 310
[273] a c f d b e
Page: 311
[274] g d a h b c f k
Page: 311
[275] g d e a z b f c
Page: 311
[Figure 276]
Page: 311
[277] a b c d e f
Page: 312
[278] e a b k l f g h m c d
Page: 312
[Figure 279]
Page: 312
[280] a b c e f g h d i
Page: 313
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          <p>
            <s xml:id="echoid-s20572" xml:space="preserve">
              <pb o="7" file="0309" n="309" rhead="LIBER I."/>
            Dico, quòd maior eſt proportio a ad b, quàm c ad d.</s>
            <s xml:id="echoid-s20573" xml:space="preserve"> Quoniã enim linea a eſt maior quàm linea c, pa
              <lb/>
            tet per 8 p 5, quoniã maior eſt ꝓportio lineę a ad lineã b quàm lineę c ad lineam b:</s>
            <s xml:id="echoid-s20574" xml:space="preserve"> ſed quia exhypo
              <lb/>
            theſi linea b eſt minor quàm linea d:</s>
            <s xml:id="echoid-s20575" xml:space="preserve"> patet per 8 p 5, quo-
              <lb/>
              <figure xlink:label="fig-0309-01" xlink:href="fig-0309-01a" number="266">
                <variables xml:id="echoid-variables252" xml:space="preserve">a b c d</variables>
              </figure>
            niam maior eſt proportio lineæ c ad lineam b, quàm ad li-
              <lb/>
            neam d.</s>
            <s xml:id="echoid-s20576" xml:space="preserve"> Eſt ergo maior proportio lineæ a primæ ad lineã
              <lb/>
            b ſecũdã, ꝗ̃ lineæ c tertię ad d quartã:</s>
            <s xml:id="echoid-s20577" xml:space="preserve"> & hoc eſt propoſitũ.</s>
            <s xml:id="echoid-s20578" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div671" type="section" level="0" n="0">
          <head xml:id="echoid-head584" xml:space="preserve" style="it">10. Siquatuor quantitatum fuerit maior propor-
            <lb/>
          tio primæ ad ſecundam, quàm tertiæ ad quartam: erit
            <lb/>
          permutatim maior proportio primæ ad tertiam, quàm
            <lb/>
          ſecundæ ad quartam. E' 12 definit. 16 p 5. 27 p 5 elem. in
            <lb/>
          Campano.</head>
          <p>
            <s xml:id="echoid-s20579" xml:space="preserve">Sint quatuor lineæ a, b, c, d:</s>
            <s xml:id="echoid-s20580" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s20581" xml:space="preserve"> proportio a ad b maior, quàm c ad d.</s>
            <s xml:id="echoid-s20582" xml:space="preserve"> Dico, quòd erit permuta-
              <lb/>
            tim maior proportio lineæ a ad lineam c, quàm lineę b ad
              <lb/>
              <figure xlink:label="fig-0309-02" xlink:href="fig-0309-02a" number="267">
                <variables xml:id="echoid-variables253" xml:space="preserve">a b e c d</variables>
              </figure>
            lineam d.</s>
            <s xml:id="echoid-s20583" xml:space="preserve"> Sit enim per 3 huius proportio lineæ e ad lineã
              <lb/>
            b, ſicut lineæ c ad lineam d:</s>
            <s xml:id="echoid-s20584" xml:space="preserve"> erit ergo ex hypotheſi & ex 10
              <lb/>
            p 5 linea e minor quã linea a:</s>
            <s xml:id="echoid-s20585" xml:space="preserve"> ergo per 8 p 5 maior eſt pro-
              <lb/>
            portio lineæ a ad lineam c, quàm lineæ e ad lineam c.</s>
            <s xml:id="echoid-s20586" xml:space="preserve"> Eſt
              <lb/>
            autem ex præmiſsis & per 16 p 5 proportio lineę e ad li-
              <lb/>
            neam c, ſicut lineę b ad lineam d.</s>
            <s xml:id="echoid-s20587" xml:space="preserve"> Palàm ergo, quoniã ma-
              <lb/>
            ior eſt proportio lineę a ad lineã c, quàm lineę b ad lineã
              <lb/>
            d:</s>
            <s xml:id="echoid-s20588" xml:space="preserve"> quod eſt propoſitum.</s>
            <s xml:id="echoid-s20589" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div673" type="section" level="0" n="0">
          <head xml:id="echoid-head585" xml:space="preserve" style="it">11. Cum quatuor quantitatum maior fuerit propor
            <lb/>
          tio primæ ad ſecundam quàm tertiæ ad quartam: erit
            <lb/>
          coniunctim maior proportio primæ & ſecundæ ad ſecũdam, quàm tertiæ & quartæ ad quartã.
            <lb/>
          E' 14 definit. 18 p 5 element. 28 p 5 ele. in Campano.</head>
          <p>
            <s xml:id="echoid-s20590" xml:space="preserve">Eſto quatuor linearum a, b, c, d maior proportio a ad b, quàm c ad d.</s>
            <s xml:id="echoid-s20591" xml:space="preserve"> Dico, quòd totius lineę a b
              <lb/>
            ad lineã b maior erit proportio, quàm totius lineę c d ad
              <lb/>
              <figure xlink:label="fig-0309-03" xlink:href="fig-0309-03a" number="268">
                <variables xml:id="echoid-variables254" xml:space="preserve">a b e c d</variables>
              </figure>
            lineam d.</s>
            <s xml:id="echoid-s20592" xml:space="preserve"> Sit enim per 3 huius proportio lineę e ad lineam
              <lb/>
            b, quæ lineę c ad lineam d:</s>
            <s xml:id="echoid-s20593" xml:space="preserve"> eſt ergo ex hypotheſi maior ꝓ-
              <lb/>
            portio lineę a ad lineam b, quàm lineæ e ad lineam b:</s>
            <s xml:id="echoid-s20594" xml:space="preserve"> ergo
              <lb/>
            per 10 p 5 linea a eſt maior quàm lineae.</s>
            <s xml:id="echoid-s20595" xml:space="preserve"> Tota ergo linea
              <lb/>
            a b eſt maior quàm tota linea e b:</s>
            <s xml:id="echoid-s20596" xml:space="preserve"> ergo per 8 p 5 maior eſt
              <lb/>
            proportio totius lineæ a b ad lineã b, quàm totius lineę
              <lb/>
            e b ad lineã b:</s>
            <s xml:id="echoid-s20597" xml:space="preserve"> per 18 uerò 5 eſt proportio lineę e b ad line-
              <lb/>
            am b, quę lineę c d ad lineam d:</s>
            <s xml:id="echoid-s20598" xml:space="preserve"> eſt enim ex pręmiſsis pro-
              <lb/>
            portio lineę e ad lineam b, ſicut lineę c ad lineam d.</s>
            <s xml:id="echoid-s20599" xml:space="preserve"> Eſt
              <lb/>
            ergo maior proportio lineę a b ad lineã b, quàm lineę c d
              <lb/>
            ad lineam d:</s>
            <s xml:id="echoid-s20600" xml:space="preserve"> quod eſt propoſitum.</s>
            <s xml:id="echoid-s20601" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div675" type="section" level="0" n="0">
          <head xml:id="echoid-head586" xml:space="preserve" style="it">12. Si quatuor quantitatum proportio primæ & ſecundæ ad ſecundam ſit maior, quàm ter-
            <lb/>
          tiæ & quartæ ad quartam: erit diſiunctim maior proportio primæ ad ſecundam, quàm tertiæ
            <lb/>
          ad quartam. E' 15 definit. 17 p 5 element. 29 p 5 elem. in Campano.</head>
          <p>
            <s xml:id="echoid-s20602" xml:space="preserve">Sit proportio totius lineę a b ad eius partem lineam b maior, quàm totius lineæ c d ad eius par-
              <lb/>
            tem d.</s>
            <s xml:id="echoid-s20603" xml:space="preserve"> Dico, quòd erit diſiunctim proportio lineę a ad line-
              <lb/>
              <figure xlink:label="fig-0309-04" xlink:href="fig-0309-04a" number="269">
                <variables xml:id="echoid-variables255" xml:space="preserve">a b c e d</variables>
              </figure>
            a m b maior, quàm lineę c ad lineam d.</s>
            <s xml:id="echoid-s20604" xml:space="preserve"> Sit en im per 3 huius
              <lb/>
            proportio lineę e b ad lineam b, ſicut lineę c d ad lineam d:</s>
            <s xml:id="echoid-s20605" xml:space="preserve">
              <lb/>
            erit ergo ex hypotheſi maior proportio lineę a b ad lineam
              <lb/>
            b, quàm lineę e b ad eandem lineam b:</s>
            <s xml:id="echoid-s20606" xml:space="preserve"> ergo per 10 p 5 erit
              <lb/>
            linea a b maior quàm linea e b:</s>
            <s xml:id="echoid-s20607" xml:space="preserve"> a blata ergo utrobique linea
              <lb/>
            b communi, relinquitur linea a maior quàm linea e.</s>
            <s xml:id="echoid-s20608" xml:space="preserve"> Eſt er-
              <lb/>
            go per 8 p 5 maior proportio lineę a ad lineam b, quàm li-
              <lb/>
            neę e ad eandem lineam b:</s>
            <s xml:id="echoid-s20609" xml:space="preserve"> ſed per pręmiſſa eſt proportio li
              <lb/>
            neę e b ad lineam b, ſicut lineę c d ad lineam d:</s>
            <s xml:id="echoid-s20610" xml:space="preserve"> ergo per 17
              <lb/>
            p 5 eſt proportio lineę e ad lineã b, ſicut lineę c ad lineam d.</s>
            <s xml:id="echoid-s20611" xml:space="preserve"> Erit ergo maior proportio lineę a ad li-
              <lb/>
            neam b.</s>
            <s xml:id="echoid-s20612" xml:space="preserve"> quàm lineę c ad lineam d:</s>
            <s xml:id="echoid-s20613" xml:space="preserve"> & hoc eſt propoſitum.</s>
            <s xml:id="echoid-s20614" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div677" type="section" level="0" n="0">
          <head xml:id="echoid-head587" xml:space="preserve" style="it">13. Quarumlibet trium quantitatum quocun ordine diſpoſitarum, quarum mediæ ad
            <lb/>
          utram extremarum nota ſit proportio: erit proportio primæ adtertiam compoſit a ex propor-
            <lb/>
          tione primæ ad ſecũdam, & ſecundæ ad tertiam. Ex quo patet, quòd proportio extremorum ad
            <lb/>
          inuicem componitur ſemper ex proportione mediorum ad inuicem & adipſa extrema. E' ſcho-
            <lb/>
          </head>
        </div>
      </text>
    </echo>
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