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

< >
[141] f e t h k o b m a g n d
Page: 186
[142] f e t b m f a g d n
Page: 187
[143] l m a b g n d
Page: 187
[144] e b g q m d a o z h k
Page: 188
[145] a s c p c f d d e b
Page: 189
[146] e b g q l m d o a z n h k
Page: 189
[147] d z b t m l q r p h k f g e a
Page: 190
[148] s z o r x a h k g m u b d e t l f q p n
Page: 190
[149] a b h
Page: 192
[150] a l c q g d b h
Page: 192
[151] a g e u m q d o n z h p l
Page: 192
[152] a e u g d o p h q n k z i s t f
Page: 193
[153] f f e a z b h d g
Page: 195
[154] a f b m k q n e t h d z
Page: 196
[155] b a e p g d
Page: 196
[156] a b h z e p g d
Page: 196
[157] o z l h m n q t d a b e
Page: 197
[158] z i l m h n t d z a k g y c f b z r s u p a e x
Page: 198
[159] i u r c z h t m g b n q f a
Page: 201
[160] i u r k c z l b d t m g n q f a
Page: 201
[161] l u r c z o d t m g b n k q f a s p x e s
Page: 202
[162] d t e h s n q b l q m f p a g
Page: 203
[163] e c h m z b d a
Page: 204
[164] e n c z b d g a
Page: 204
[165] c h z b d g a
Page: 205
[166] b e a d h z m g
Page: 205
[167] p o b c e l m t n a q k f d g
Page: 206
[168] b d a e h t z g f
Page: 206
[169] e b f a d m h t z g
Page: 207
[170] q e a b d m h z
Page: 207
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page |< < (192) of 778 > >|
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            <s xml:id="echoid-s13081" xml:space="preserve">
              <pb o="192" file="0198" n="198" rhead="ALHAZEN"/>
            Igitur coniumctim [per 18 p 5] proportio o a ad a h, ſicut quadrati a i ad quadratũ a h:</s>
            <s xml:id="echoid-s13082" xml:space="preserve"> exceſſus enin
              <gap/>
              <lb/>
            quadrati a i ſupra quadratũ a h, cum quadrato a h efficit quadratum a i:</s>
            <s xml:id="echoid-s13083" xml:space="preserve"> igitur [per conuerſionẽ cõſe-
              <lb/>
            ctarij ad 20 p 6] i a erit media in proportione inter o a & a h.</s>
            <s xml:id="echoid-s13084" xml:space="preserve"> Igitur proportio o a ad i a, ſicut i a ad h a:</s>
            <s xml:id="echoid-s13085" xml:space="preserve">
              <lb/>
            & [per 19 p 5] eadem erit proportio reſidui ad reſiduum:</s>
            <s xml:id="echoid-s13086" xml:space="preserve"> id eſt o i ad i h.</s>
            <s xml:id="echoid-s13087" xml:space="preserve"> Amplius:</s>
            <s xml:id="echoid-s13088" xml:space="preserve"> ductus a d in h d
              <lb/>
            minor eſt quarta parte quadrati a d:</s>
            <s xml:id="echoid-s13089" xml:space="preserve"> [demonſtratum enim eſt rectangulum comprehenſum ſub a h
              <lb/>
            & h d, æquari quadranti quadrati a d:</s>
            <s xml:id="echoid-s13090" xml:space="preserve"> & a d minor eſt quàm a h per 9 ax:</s>
            <s xml:id="echoid-s13091" xml:space="preserve">] igitur h d eſt minor quarta
              <lb/>
            parte lineæ a d.</s>
            <s xml:id="echoid-s13092" xml:space="preserve"> [nam ſi æqualis eſſet:</s>
            <s xml:id="echoid-s13093" xml:space="preserve"> rectangulũ comprehenſum ſub a d & h d, æquaretur quadranti
              <lb/>
            quadrati a d per 1 p 6.</s>
            <s xml:id="echoid-s13094" xml:space="preserve">] Igitur h d eſt minor quinta parte a h.</s>
            <s xml:id="echoid-s13095" xml:space="preserve"> Cũ ergo a h ſit maior quàm quintupla ad
              <lb/>
            h d, & ductus eius in h t efficiat quadratũ h d:</s>
            <s xml:id="echoid-s13096" xml:space="preserve"> [per theſin] erit h t minor quinta parte h d:</s>
            <s xml:id="echoid-s13097" xml:space="preserve"> [nam per
              <lb/>
            theſin & 17 p 6 eſt, ut a h ad h d, ſic h d ad h t:</s>
            <s xml:id="echoid-s13098" xml:space="preserve"> ſed per proximã concluſionẽ a h maior eſt, quàm quintu
              <lb/>
            pla ipſius h d:</s>
            <s xml:id="echoid-s13099" xml:space="preserve"> ergo h d maior eſt quàm quintupla ipſius h t:</s>
            <s xml:id="echoid-s13100" xml:space="preserve"> ide
              <gap/>
            q́;</s>
            <s xml:id="echoid-s13101" xml:space="preserve"> h t minor quinta parte ipſius h d]
              <lb/>
            & ita h t minor uiceſima quinta parte h a.</s>
            <s xml:id="echoid-s13102" xml:space="preserve"> [Quia enim ratio h a ad h d, & h d ad h t maior eſt ꝗ̃ quintu
              <lb/>
            pla, ut patuit:</s>
            <s xml:id="echoid-s13103" xml:space="preserve"> erit per 10 d 5 ratio a h ad h t maior, ꝗ̃ uicecupla quintupla:</s>
            <s xml:id="echoid-s13104" xml:space="preserve"> ideoq́;</s>
            <s xml:id="echoid-s13105" xml:space="preserve"> h t minor uiceſima
              <lb/>
            quinta parte ipſius a h.</s>
            <s xml:id="echoid-s13106" xml:space="preserve">] Sed proportio o i ad i h, ſicut i a ad a h, ut dictũ eſt.</s>
            <s xml:id="echoid-s13107" xml:space="preserve"> Igitur cõiunctim [per 18 p
              <lb/>
            5] o h ad i h, ſicut i a cũ a h ad a h.</s>
            <s xml:id="echoid-s13108" xml:space="preserve"> Igitur [per 15 p 5] tertia primę ad ſecũdã, ſicut tertia tertię ad quartã:</s>
            <s xml:id="echoid-s13109" xml:space="preserve">
              <lb/>
            ſed h t eſt tertia pars lineæ o h [nam per theſin h o tripla eſt ipſius h t.</s>
            <s xml:id="echoid-s13110" xml:space="preserve">] Igitur t h ad i h eſt, ſicut tertia
              <lb/>
            pars lineę i a, cũ tertia parte a h, ad lineã a h.</s>
            <s xml:id="echoid-s13111" xml:space="preserve"> Igitur t h ad i a, ſicut duę tertię lineę a h, cum tertia lineę i
              <lb/>
            h, ad lineã a h.</s>
            <s xml:id="echoid-s13112" xml:space="preserve"> Sed quoniã linea o i eſt maior i h:</s>
            <s xml:id="echoid-s13113" xml:space="preserve"> [oſtenſum enim eſt, ut o a ad ia, ſic o i ad i h:</s>
            <s xml:id="echoid-s13114" xml:space="preserve"> at per 9
              <lb/>
            ax:</s>
            <s xml:id="echoid-s13115" xml:space="preserve"> o a maior eſt i a:</s>
            <s xml:id="echoid-s13116" xml:space="preserve"> ergo o i maior eſt i h] erit i h minor medietate o h:</s>
            <s xml:id="echoid-s13117" xml:space="preserve"> & erit tertia i h minor ſexta par
              <lb/>
            te o h:</s>
            <s xml:id="echoid-s13118" xml:space="preserve"> & ita tertia i h erit minor medietate t h.</s>
            <s xml:id="echoid-s13119" xml:space="preserve"> Igitur duæ tertiæ a h, cum minore parte, quàm ſit me-
              <lb/>
            dietas h t, ſe habebunt ad a h, ſicut t h ad i h.</s>
            <s xml:id="echoid-s13120" xml:space="preserve"> Igitur [per conſectariũ 4 p 5] i h ad h t, ſicut a h ad duas
              <lb/>
            ſui tertias cum minore, quàm ſit medietas h t:</s>
            <s xml:id="echoid-s13121" xml:space="preserve"> ſed h t minor uiceſima quinta a h:</s>
            <s xml:id="echoid-s13122" xml:space="preserve"> & eius medietas mi
              <lb/>
            nor quàm medietas uiceſimæ quintæ partis.</s>
            <s xml:id="echoid-s13123" xml:space="preserve"> Sed linea a h in uigintiquinq;</s>
            <s xml:id="echoid-s13124" xml:space="preserve"> partes diuiſa:</s>
            <s xml:id="echoid-s13125" xml:space="preserve"> duæ tertiæ
              <lb/>
            cum medietate uiceſimæ quintæ partis non efficiunt octodecim eius partes.</s>
            <s xml:id="echoid-s13126" xml:space="preserve"> [Nam ex arithmeticæ
              <lb/>
            regulis intelliges {2/3} de 25 eſſe 16 integra, & ſupereſſe {2/3}, quæ additæ cum eo, quod minus eſt {1/2} uel etiã
              <lb/>
            cum {1/2}, efficiunt 1{1/6}.</s>
            <s xml:id="echoid-s13127" xml:space="preserve"> Itaq;</s>
            <s xml:id="echoid-s13128" xml:space="preserve"> {2/3} cum {1/2} de 25, ſunt 17{1/6}.</s>
            <s xml:id="echoid-s13129" xml:space="preserve">] Igitur proportio i h ad h t maior eſt, quàm ſit pro-
              <lb/>
            portio 25 ad 18.</s>
            <s xml:id="echoid-s13130" xml:space="preserve"> Item cum h t ſit minor uiceſima quinta parte a h:</s>
            <s xml:id="echoid-s13131" xml:space="preserve"> erit at maior uigintiquatuor parti-
              <lb/>
            bus, quarum a h eſt uigintiquinq;</s>
            <s xml:id="echoid-s13132" xml:space="preserve">. Sed linea i h minor eſt medietate o h:</s>
            <s xml:id="echoid-s13133" xml:space="preserve"> & ita minor medietate h t:</s>
            <s xml:id="echoid-s13134" xml:space="preserve">
              <lb/>
            [quia h t & eius ſemiſsis efficiunt ſemiſſem ipſius o h:</s>
            <s xml:id="echoid-s13135" xml:space="preserve"> quo i h minor concluſa eſt] & ita minor una
              <lb/>
            & dimidia uigintiquinq;</s>
            <s xml:id="echoid-s13136" xml:space="preserve"> partium a h:</s>
            <s xml:id="echoid-s13137" xml:space="preserve"> & i a ita minor 26{1/2}, ſumptis partibus ſecundum diuiſionem a
              <lb/>
            h.</s>
            <s xml:id="echoid-s13138" xml:space="preserve"> Ergo proportio i a ad a t, ſicut minoris lineæ 26{1/2} ad maiorem 24.</s>
            <s xml:id="echoid-s13139" xml:space="preserve"> Igitur proportio i a ad a t mi-
              <lb/>
            nor eſt, quàm 26{1/2} ad 24.</s>
            <s xml:id="echoid-s13140" xml:space="preserve"> Sed proportio i h ad h t maior eſt, quàm 25 ad 18:</s>
            <s xml:id="echoid-s13141" xml:space="preserve"> igitur proportio i h ad h t
              <lb/>
            maior eſt, quàm i a ad a t [ratio enim 25 ad 18 maior eſt, ꝗ̃ 26{1/2} ad 24, ut patet ex arithmethica.</s>
            <s xml:id="echoid-s13142" xml:space="preserve">] Sit
              <lb/>
            proportio i m ad m t, ſicut i a ad a t:</s>
            <s xml:id="echoid-s13143" xml:space="preserve"> [id autem efficies:</s>
            <s xml:id="echoid-s13144" xml:space="preserve"> ſirectæ ex i a & a t compoſitæ ſegmenta ſu-
              <lb/>
            mas i a, a t:</s>
            <s xml:id="echoid-s13145" xml:space="preserve"> i t uerò inſectam ſimiliter ſeces per 10 p 6] cadet quidem m inter i & h.</s>
            <s xml:id="echoid-s13146" xml:space="preserve"> [Quia enim ra-
              <lb/>
            tio lineæ i h ad h t maior eſt, quàm i m ad m t:</s>
            <s xml:id="echoid-s13147" xml:space="preserve"> erit i m minor i h:</s>
            <s xml:id="echoid-s13148" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s13149" xml:space="preserve"> punctum m cadit inter i & h:</s>
            <s xml:id="echoid-s13150" xml:space="preserve"> e-
              <lb/>
            ritq́;</s>
            <s xml:id="echoid-s13151" xml:space="preserve"> per 9 ax:</s>
            <s xml:id="echoid-s13152" xml:space="preserve"> m t maior m h.</s>
            <s xml:id="echoid-s13153" xml:space="preserve">] Item maior erit proportio i m ad m h, quàm i a ad a t:</s>
            <s xml:id="echoid-s13154" xml:space="preserve"> [Quia enim li-
              <lb/>
            nea m t maior eſt m h è proxima concluſione:</s>
            <s xml:id="echoid-s13155" xml:space="preserve"> erit per 8 p 5 ratio i m ad m h maior, quàm ad m t:</s>
            <s xml:id="echoid-s13156" xml:space="preserve"> at
              <lb/>
            ratio i m ad m t, eſt ratio i a ad a t per fabricationẽ.</s>
            <s xml:id="echoid-s13157" xml:space="preserve"> Qua-
              <lb/>
              <figure xlink:label="fig-0198-01" xlink:href="fig-0198-01a" number="158">
                <variables xml:id="echoid-variables148" xml:space="preserve">
                  <gap/>
                z i l
                  <gap/>
                m h n t d z a
                  <gap/>
                k g y c f b z r s u p a
                  <gap/>
                e x</variables>
              </figure>
            re per 11 p 5 ratio i m ad m h maior eſt, quàm i a ad a t]
              <lb/>
            & ita maior, quàm i a ad a h.</s>
            <s xml:id="echoid-s13158" xml:space="preserve"> [Quoniam enim ratio i m
              <lb/>
            ad m h maior eſt, quàm i a ad a t è ſuperiore conclu-
              <lb/>
            ſione:</s>
            <s xml:id="echoid-s13159" xml:space="preserve"> ratio uerò i a ad a t maior eſt, quàm ad a h per
              <lb/>
            8 p 5:</s>
            <s xml:id="echoid-s13160" xml:space="preserve"> cum a t ſit maior ipſa a h per 9 ax.</s>
            <s xml:id="echoid-s13161" xml:space="preserve"> Ratio igitur i m
              <lb/>
            ad m h multò maior eſt, quàm ratio i a ad a h.</s>
            <s xml:id="echoid-s13162" xml:space="preserve">] Sit igi-
              <lb/>
            tur proportio il ad lh, ſicut i a ad a h:</s>
            <s xml:id="echoid-s13163" xml:space="preserve"> [per 10 p 6] ca-
              <lb/>
            det quidem linter m & i.</s>
            <s xml:id="echoid-s13164" xml:space="preserve"> Amplius à punctis l, m ducan-
              <lb/>
            tur contingentes l b, m g [per 17 p 3] & ducantur lineæ
              <lb/>
            i b, h b, i g, t g, a b, a g:</s>
            <s xml:id="echoid-s13165" xml:space="preserve"> quæ duæ ultimæ producantur uſ-
              <lb/>
            que ad exteriorem circulum:</s>
            <s xml:id="echoid-s13166" xml:space="preserve"> & habebitur ex quarto li-
              <lb/>
            bro, quòd angulus i b z ſit æqualis angulo h b a [conti-
              <lb/>
            nuata enim h b in x:</s>
            <s xml:id="echoid-s13167" xml:space="preserve"> æquabuntur anguli i b z & x b z
              <lb/>
            per 12 n 4:</s>
            <s xml:id="echoid-s13168" xml:space="preserve"> item x b z & h b a per 15 p 1:</s>
            <s xml:id="echoid-s13169" xml:space="preserve"> itaq;</s>
            <s xml:id="echoid-s13170" xml:space="preserve"> per 1 ax.</s>
            <s xml:id="echoid-s13171" xml:space="preserve"> an-
              <lb/>
            guli i b z, h b a æquantur.</s>
            <s xml:id="echoid-s13172" xml:space="preserve">] Cum igitur ſit proportio il
              <lb/>
            ad l h, ſicut i a ad a h [per ſuperiorem fabricatio-
              <lb/>
            nem] erit [per 18 n 5] h locus imaginis i, dum reflecti-
              <lb/>
            tur à puncto b.</s>
            <s xml:id="echoid-s13173" xml:space="preserve"> Et ſi dicatur cõtrarium, & ſumatur alius
              <lb/>
            locus imaginis i:</s>
            <s xml:id="echoid-s13174" xml:space="preserve"> probabis per impoſsibile, ſumpta im-
              <lb/>
            poſsibilitate à proportione, quam non eſt uerum eſſe i
              <lb/>
            a ad lineam à puncto imaginis ductam ad punctum a,
              <lb/>
            ſicut i l ad lineam à puncto l ad locum imaginis.</s>
            <s xml:id="echoid-s13175" xml:space="preserve"> Cum
              <lb/>
            igitur h ſit locus imaginis:</s>
            <s xml:id="echoid-s13176" xml:space="preserve"> & l b contingat circulum in
              <lb/>
            b:</s>
            <s xml:id="echoid-s13177" xml:space="preserve"> producta a b faciet angulum l b z æqualem ſuo collaterali [a b l:</s>
            <s xml:id="echoid-s13178" xml:space="preserve"> quia uterq;</s>
            <s xml:id="echoid-s13179" xml:space="preserve"> per 18 p 3 rectus eſt.</s>
            <s xml:id="echoid-s13180" xml:space="preserve">]
              <lb/>
            Et quoniã l b perpendicularis ſuper a b z [per 18 p 3] reſtabit angulus i b l æ qualis angulo l b h.</s>
            <s xml:id="echoid-s13181" xml:space="preserve"> [Nam
              <lb/>
            </s>
          </p>
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