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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[221] a p h f l g e o k a n m e z q b
Page: 263
[222] a f h p g o e k d m n c q z b
Page: 263
[223] a f h p l g o e k d b m c q z n
Page: 264
[224] a f l p g e o k d b n m c z
Page: 264
[225] h a b g e f d e z
Page: 265
[226] h a b e d c z
Page: 265
[227] e a b d f c
Page: 265
[228] a r c p e h b z b d
Page: 266
[229] a n r l c x m h e p z g b b f d o k
Page: 267
[230] a l g h e z d k b t
Page: 268
[231] e a g e z b
Page: 269
[232] k o g e c n a d z f h m l p b
Page: 270
[233] e o k a c n g d z h m l p b
Page: 270
[234] a k r q c n g h l m d p z b
Page: 271
[235] ad m g p h l k q bn z c
Page: 277
[236] a d e i f p m h l k b z q o c
Page: 278
[237] a p k d m e l o g h b z c
Page: 279
[238] a q p k d m e g l o b z f c
Page: 279
[239] a d p m h e ſ g o k b n z c
Page: 280
[240] a h m g e n k z b c ſ d
Page: 281
[241] a h g m x e n k z l b c d
Page: 281
[242] a h g f m r e n k b p q d c ſ
Page: 281
[243] a f h m g e n k b p q d c l
Page: 282
[244] a h m g e r o n k b s z c l d
Page: 282
[245] a b g p e d z m h o h l c
Page: 283
[246] k q f b o r c l m e z f g
Page: 285
[247] b g f t n d h k z a m e
Page: 285
[248] b d g q h n k z o a p e m
Page: 286
[249] g a e h c d b z
Page: 290
[250] d a k g e c b z h
Page: 291
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          <p>
            <s xml:id="echoid-s20515" xml:space="preserve">
              <pb o="6" file="0308" n="308" rhead="VITELLONIS OPTICAE"/>
            ad lineam c f maiorem, quàm ad lineam c g minorem:</s>
            <s xml:id="echoid-s20516" xml:space="preserve"> eſt ergo maior proportio lineæ a b ad linea m
              <lb/>
            c d, quàm lineę a e ad lineam c f:</s>
            <s xml:id="echoid-s20517" xml:space="preserve"> & hoc eſt propoſitum.</s>
            <s xml:id="echoid-s20518" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div661" type="section" level="0" n="0">
          <head xml:id="echoid-head579" xml:space="preserve" style="it">5. Cum fuerit proportio primi ad ſecundum, tanquam tertij ad quartũ: erit è contrario pro-
            <lb/>
          portio ſecundi ad primum, ſicut quarti ad tertium. E' 13 def. & conſectario 4 p 5 element.</head>
          <p>
            <s xml:id="echoid-s20519" xml:space="preserve">Sit enim a primum, & b ſecundum, & ctertium, & d quartum:</s>
            <s xml:id="echoid-s20520" xml:space="preserve"> & ſit
              <lb/>
            proportio a ad b, ſicut c ad d.</s>
            <s xml:id="echoid-s20521" xml:space="preserve"> Dico, quòd erit è contrario proportio b ad
              <lb/>
              <figure xlink:label="fig-0308-01" xlink:href="fig-0308-01a" number="262">
                <variables xml:id="echoid-variables248" xml:space="preserve">a b c d</variables>
              </figure>
            a, ſicut d ad c.</s>
            <s xml:id="echoid-s20522" xml:space="preserve"> Quoniam enim eſt proportio a ad b, ſicut c ad d:</s>
            <s xml:id="echoid-s20523" xml:space="preserve"> erit per 16
              <lb/>
            p 5 permutatim proportio a ad c, ſicut b ad d:</s>
            <s xml:id="echoid-s20524" xml:space="preserve"> eſt ergo proportio b ad d,
              <lb/>
            ſicut a ad c:</s>
            <s xml:id="echoid-s20525" xml:space="preserve"> ergo iterum per 16 p 5 erit permutatim proportio b ad a, ſi-
              <lb/>
            cut d ad c, ſecundi uidelicet ad primum, ſicut quarti ad tertium:</s>
            <s xml:id="echoid-s20526" xml:space="preserve"> quod eſt
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s20527" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div663" type="section" level="0" n="0">
          <head xml:id="echoid-head580" xml:space="preserve" style="it">6. Cum fuerit quatuor quantitatum proportio primæ ad ſecundã
            <lb/>
          maior, quãtertiæ ad quartam: erit è contr ario minor proportio ſecun-
            <lb/>
          dæ ad primam, quàm quartæ ad tertiam. 26 p 5 element. in Campano.</head>
          <p>
            <s xml:id="echoid-s20528" xml:space="preserve">Eſto proportio lineæ a ad lineam b maior, quàm lineæ c ad lineam d.</s>
            <s xml:id="echoid-s20529" xml:space="preserve"> Dico, quôd erit è contrario
              <lb/>
            minor proportio lineæ b ad lineam a, quàm lineæ d ad li-
              <lb/>
              <figure xlink:label="fig-0308-02" xlink:href="fig-0308-02a" number="263">
                <variables xml:id="echoid-variables249" xml:space="preserve">a b e c d</variables>
              </figure>
            neam c.</s>
            <s xml:id="echoid-s20530" xml:space="preserve"> Sit enim per 3 huius, ut, quæ eſt proportio lineæ c
              <lb/>
            ad lineam d, eadem ſit lineæ e ad lineam b.</s>
            <s xml:id="echoid-s20531" xml:space="preserve"> Quia ergo ma-
              <lb/>
            ior eſt proportio lineæ a ad lineam b, quàm lineæ c ad li-
              <lb/>
            neam d ex hypotheſi:</s>
            <s xml:id="echoid-s20532" xml:space="preserve"> patet, quòd minor eſt proportio li-
              <lb/>
            neæ e ad lineam b, quam lineę a ad lineã b:</s>
            <s xml:id="echoid-s20533" xml:space="preserve"> ergo per 10 p 5
              <lb/>
            linea a eſt maior quã linea e.</s>
            <s xml:id="echoid-s20534" xml:space="preserve"> Et quia eſt proportio lineæ e
              <lb/>
            ad lineam b, ſicut lineę c ad lineam d, erit per præmiſſam
              <lb/>
            eadem proportio lineę b ad lineã e, quę lineæ d ad lineam
              <lb/>
            c.</s>
            <s xml:id="echoid-s20535" xml:space="preserve"> Eſt autem per 8 p 5 minor proportio lineæ b ad lineam a,
              <lb/>
            quàm ad lineam e:</s>
            <s xml:id="echoid-s20536" xml:space="preserve"> eſt ergo minor proportio lineæ b ad lineam a, quàm lineę d ad lineam c:</s>
            <s xml:id="echoid-s20537" xml:space="preserve"> quod
              <lb/>
            eſt propoſitum.</s>
            <s xml:id="echoid-s20538" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div665" type="section" level="0" n="0">
          <head xml:id="echoid-head581" xml:space="preserve" style="it">7. Si quatuor quantitatum proportion alium prima fuerit maior quãſecunda, & tertia ma-
            <lb/>
          ior quã quarta: erit euerſim eadem proportio primæ ad augmentum ſui ſuper ſecundam, quæ ter
            <lb/>
          tiæ ad augmentum ſui ſuper quartam. E' 16 definit. & conſectario 19 p 5.</head>
          <p>
            <s xml:id="echoid-s20539" xml:space="preserve">Sint quatuor lineę proportionales a c prima:</s>
            <s xml:id="echoid-s20540" xml:space="preserve"> b c ſecunda:</s>
            <s xml:id="echoid-s20541" xml:space="preserve"> d ftertia:</s>
            <s xml:id="echoid-s20542" xml:space="preserve"> & e f quarta.</s>
            <s xml:id="echoid-s20543" xml:space="preserve"> Sitq́ue linea a b
              <lb/>
            maior quàm linea b c, & linea d f maior, quàm linea e f:</s>
            <s xml:id="echoid-s20544" xml:space="preserve"> ex-
              <lb/>
              <figure xlink:label="fig-0308-03" xlink:href="fig-0308-03a" number="264">
                <variables xml:id="echoid-variables250" xml:space="preserve">a b c d e f</variables>
              </figure>
            cedat quoque linea a c lineam b c, in linea a b, & linea d f
              <lb/>
            lineam e f, in linea d e.</s>
            <s xml:id="echoid-s20545" xml:space="preserve"> Dico, quòd eadem erit proportio
              <lb/>
            lineę a c ad lineam a b, quę lineę d f ad lineam d e.</s>
            <s xml:id="echoid-s20546" xml:space="preserve"> Quo-
              <lb/>
            niam enim eſt proportio lineę a c ad lineam b c, ſicut lineę
              <lb/>
            d f ad lineam e f:</s>
            <s xml:id="echoid-s20547" xml:space="preserve"> eſt ergo per 16 p 5 permutatim proportio
              <lb/>
            lineę a c ad lineam d f, ſicut lineę b c ad lineam e f:</s>
            <s xml:id="echoid-s20548" xml:space="preserve"> ergo per
              <lb/>
            19 p 5 erit proportio lineę a b ad lineam d e, ſicut lineę a c
              <lb/>
            ad lineam d f:</s>
            <s xml:id="echoid-s20549" xml:space="preserve"> ergo per 16 p 5 erit proportio lineę a b ad lineam a c.</s>
            <s xml:id="echoid-s20550" xml:space="preserve"> ſicut lineę d e ad lineam d f.</s>
            <s xml:id="echoid-s20551" xml:space="preserve"> Ergo
              <lb/>
            per 5 huius erit proportio lineę a c ad lineam a b, ſicut lineę d fad lineam d e:</s>
            <s xml:id="echoid-s20552" xml:space="preserve"> quod eſt propoſitum.</s>
            <s xml:id="echoid-s20553" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div667" type="section" level="0" n="0">
          <head xml:id="echoid-head582" xml:space="preserve" style="it">8. Si quatuor quantit atum prima fuerit maior ſecunda, & tertia maior quarta: erit maior
            <lb/>
          proportio primæ ad quartam, quàm ſecundæ ad tertiam. Conſectarium ex 8 p 5 element.</head>
          <p>
            <s xml:id="echoid-s20554" xml:space="preserve">Sint quatuor lineę a, b, c, d:</s>
            <s xml:id="echoid-s20555" xml:space="preserve"> & ſit a prima maior quàm b ſecũda, & ſit c tertia maior, quàm d quar-
              <lb/>
            ta.</s>
            <s xml:id="echoid-s20556" xml:space="preserve"> Dico, quòd maior eſt proportio lineæ a, ad lineam d, quàm
              <lb/>
              <figure xlink:label="fig-0308-04" xlink:href="fig-0308-04a" number="265">
                <variables xml:id="echoid-variables251" xml:space="preserve">a b c d</variables>
              </figure>
            lineę b ad lineam c.</s>
            <s xml:id="echoid-s20557" xml:space="preserve"> Quia enim linea c eſt maior quàm linea d
              <lb/>
            ex hypotheſi:</s>
            <s xml:id="echoid-s20558" xml:space="preserve"> patet per 8 p 5:</s>
            <s xml:id="echoid-s20559" xml:space="preserve"> quoniam maior eſt proportio li-
              <lb/>
            neę a ad lineam d, quàm ad lineam c:</s>
            <s xml:id="echoid-s20560" xml:space="preserve"> minor uero eſt proportio
              <lb/>
            lineę b ad lineã c, quàm lineę a, ad lineam c per eandem 8 p 5:</s>
            <s xml:id="echoid-s20561" xml:space="preserve">
              <lb/>
            quoniam ut pręmiſſum eſt linea a eſt maior quàm linea b.</s>
            <s xml:id="echoid-s20562" xml:space="preserve"> Et
              <lb/>
            quoniam quicquid eſt maius maiore, eſt maius minore:</s>
            <s xml:id="echoid-s20563" xml:space="preserve"> patet,
              <lb/>
            quòd maior eſt proportio lineę a ad lineam d, quàm lineę b ad
              <lb/>
            lineam c:</s>
            <s xml:id="echoid-s20564" xml:space="preserve"> patet ergo propoſitum.</s>
            <s xml:id="echoid-s20565" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div669" type="section" level="0" n="0">
          <head xml:id="echoid-head583" xml:space="preserve" style="it">9. Cum quatuor quantitatum prima fuerit maior quàm
            <lb/>
          tertia, & ſecunda minor quàm quarta: maior erit proportio primæ ad ſecundam, quàm tertiæ
            <lb/>
          ad quartam. Conſectarium ex 8 p 5 element.</head>
          <p>
            <s xml:id="echoid-s20566" xml:space="preserve">Sint quatuor lineę a prima:</s>
            <s xml:id="echoid-s20567" xml:space="preserve"> b ſecũda:</s>
            <s xml:id="echoid-s20568" xml:space="preserve"> c tertia:</s>
            <s xml:id="echoid-s20569" xml:space="preserve"> d quarta:</s>
            <s xml:id="echoid-s20570" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s20571" xml:space="preserve"> a maior quàm c, & ſit b minor quã d.</s>
            <s xml:id="echoid-s20572" xml:space="preserve">
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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