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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[141] f e t h k o b m a g n d
[142] f e t b m f a g d n
[143] l m a b g n d
[144] e b g q m d a o z h k
[145] a s c p c f d d e b
[146] e b g q l m d o a z n h k
[147] d z b t m l q r p h k f g e a
[148] s z o r x a h k g m u b d e t l f q p n
[149] a b h
[150] a l c q g d b h
[151] a g e u m q d o n z h p l
[152] a e u g d o p h q n k z i s t f
[153] f f e a z b h d g
[154] a f b m k q n e t h d z
[155] b a e p g d
[156] a b h z e p g d
[157] o z l h m n q t d a b e
[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
[159] i u r c z h t m g b n q f a
[160] i u r k c z l b d t m g n q f a
[161] l u r c z o d t m g b n k q f a s p x e s
[162] d t e h s n q b l q m f p a g
[163] e c h m z b d a
[164] e n c z b d g a
[165] c h z b d g a
[166] b e a d h z m g
[167] p o b c e l m t n a q k f d g
[168] b d a e h t z g f
[169] e b f a d m h t z g
[170] q e a b d m h z
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        <div xml:id="echoid-div218" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s6088" xml:space="preserve">
              <pb o="105" file="0111" n="111" rhead="OPTICAE LIBER IIII."/>
            nes ſemicirculi protractas, id eſt ad lineas tales ſemidiametro propinquiores.</s>
            <s xml:id="echoid-s6089" xml:space="preserve"> Pòſt ſecetur tabula
              <lb/>
            circa ſemicirculum maiorem, ut ſolum remaneat ſemicirculus:</s>
            <s xml:id="echoid-s6090" xml:space="preserve"> & ſecetur tabula ſub centro, ut cen-
              <lb/>
            tri locus acuatur quaſi punctum:</s>
            <s xml:id="echoid-s6091" xml:space="preserve"> hoc tamen modo, ut in eadem ſuperficie remaneat cum ſemicir-
              <lb/>
            culo & alijs lineis.</s>
            <s xml:id="echoid-s6092" xml:space="preserve"> Pòſt ſumatur tabula lignea plana excedens æneam in longitudine duobus digi-
              <lb/>
            tis:</s>
            <s xml:id="echoid-s6093" xml:space="preserve"> & ſit quadrata:</s>
            <s xml:id="echoid-s6094" xml:space="preserve"> & eius altitudo fiue ſpiſsitudo ſeptem digitorum.</s>
            <s xml:id="echoid-s6095" xml:space="preserve"> Signetur ergo in hac tabula
              <lb/>
            punctum medium:</s>
            <s xml:id="echoid-s6096" xml:space="preserve"> & ſuper ipſum fiat circulus excedens maiorem circulum tabulę æneæ, quanti-
              <lb/>
            tate digiti magni:</s>
            <s xml:id="echoid-s6097" xml:space="preserve"> & fiat ſuper idem centrum circulus, æqualis circulo minori tabulę æneę:</s>
            <s xml:id="echoid-s6098" xml:space="preserve"> & diui-
              <lb/>
            datur circulus maior in partes, in æqualitate reſpondentes partibus ſemicirculi tabulæ æneę:</s>
            <s xml:id="echoid-s6099" xml:space="preserve"> ut
              <lb/>
            ſcilicet prima reſpondeat primæ, ſecunda ſecundæ, & ſic de alijs:</s>
            <s xml:id="echoid-s6100" xml:space="preserve"> & circumquaque ſecetur ta-
              <lb/>
            bula lignea, ut ſolum remaneat maior circulus:</s>
            <s xml:id="echoid-s6101" xml:space="preserve"> & fiet hæc ſectio uſitato ſecandi modo.</s>
            <s xml:id="echoid-s6102" xml:space="preserve"> Secetur e-
              <lb/>
            tiam pars tabulæ minore circulo contenta:</s>
            <s xml:id="echoid-s6103" xml:space="preserve"> & modus ſectionis erit:</s>
            <s xml:id="echoid-s6104" xml:space="preserve"> uthuic tabulæ aſſocietur alia
              <lb/>
            tabula, ita ut linea à centro huius ad centrum illius tranſiens, ſit perpendicularis ſuper illam:</s>
            <s xml:id="echoid-s6105" xml:space="preserve"> & ad-
              <lb/>
            hibito tornatili inſtrumento centris earum, fiat ſectio partis circularis iam dictæ:</s>
            <s xml:id="echoid-s6106" xml:space="preserve"> (eſt autem alte-
              <lb/>
            rius tabulæ aſſociatio, ut fixa ſtet in ſectione) igitur reſtabit tabula quaſi annulus circularis, cuius
              <lb/>
            latitudo erit duorum digitorum:</s>
            <s xml:id="echoid-s6107" xml:space="preserve"> longitudo quatuordecim:</s>
            <s xml:id="echoid-s6108" xml:space="preserve"> altitudo ſeptem.</s>
            <s xml:id="echoid-s6109" xml:space="preserve"> Et ſit hæc altitudo
              <lb/>
              <figure xlink:label="fig-0111-01" xlink:href="fig-0111-01a" number="20">
                <image file="0111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/figures/0111-01"/>
              </figure>
            optimè circula-
              <lb/>
            ta ad modum, co
              <lb/>
            lumnę:</s>
            <s xml:id="echoid-s6110" xml:space="preserve"> remanẽt
              <lb/>
            autẽ in latitudi
              <lb/>
            ne huius annuli
              <lb/>
            lineę diuidentes
              <lb/>
            circulũ eius ſe
              <lb/>
            cundum diuiſio
              <lb/>
            nẽ ſemicirculi ta
              <lb/>
            bulæ æneę.</s>
            <s xml:id="echoid-s6111" xml:space="preserve"> À
              <unsure/>
            ca
              <lb/>
            pitibus autem li
              <lb/>
            nearum harũ ꝓ-
              <lb/>
            ducantur lineæ
              <lb/>
            in ſuperficie al
              <lb/>
            titudinis exteri
              <lb/>
            oris, perpẽdicu
              <lb/>
            lares ſuper ſu-
              <lb/>
            perficiem latitu
              <lb/>
            dinis:</s>
            <s xml:id="echoid-s6112" xml:space="preserve"> & poterit
              <lb/>
            hoc modo fieri.</s>
            <s xml:id="echoid-s6113" xml:space="preserve">
              <lb/>
            Quæratur regu-
              <lb/>
            la bene aeuta, cu
              <lb/>
            ius capiti linéæ
              <lb/>
            adhibeantur, &
              <lb/>
            regula mouea-
              <lb/>
            tur, donec tran
              <lb/>
            ſeat ſuperficiẽ al
              <lb/>
            titudinis, in qua
              <lb/>
            libet parte acu-
              <lb/>
            minis:</s>
            <s xml:id="echoid-s6114" xml:space="preserve"> Signa e-
              <lb/>
            ius capita, & fac
              <lb/>
            lineam, quoniam illa erit perpendicularis, quam quæris.</s>
            <s xml:id="echoid-s6115" xml:space="preserve"> Aliter poterit hoc idem fieri.</s>
            <s xml:id="echoid-s6116" xml:space="preserve"> Ponatur pes
              <lb/>
            circini ſuper terminũ lineæ diuidentis circulũ, & fiat ſemicirculus ſecũdũ altitudinẽ annuli, qui di
              <lb/>
            uidatur per æqualia, & protrahatur à puncto in punctũ linea, & ita de ſingulis.</s>
            <s xml:id="echoid-s6117" xml:space="preserve"> Pari modo à termi-
              <lb/>
            nis illarum diuidentium protrahantur perpẽdiculares ex parte interioris altitudinis.</s>
            <s xml:id="echoid-s6118" xml:space="preserve"> Amplius:</s>
            <s xml:id="echoid-s6119" xml:space="preserve"> ſu
              <lb/>
            matur in altitudine interiori ex parte faciei non diuiſę, altitudo duorum digitorum:</s>
            <s xml:id="echoid-s6120" xml:space="preserve"> & in perpen-
              <lb/>
            dicularibus fiat ſignum, & in ſignis illis fiat circulus, æquidiſtans faciei annuli hoc modo.</s>
            <s xml:id="echoid-s6121" xml:space="preserve"> Tabula
              <lb/>
            aliqua plana fiat circularis, æqualis circulo minori tabulę æneę:</s>
            <s xml:id="echoid-s6122" xml:space="preserve"> & ſecetur ex ea pars aliqua uſque
              <lb/>
            ad centrum, quaſitriangulum ex duabus ſemidiametris & arcu circuli, ſecundum quod libuerit,
              <lb/>
            ut poſsis tabulam cum manu imponere, & locis aſsignatis aptare.</s>
            <s xml:id="echoid-s6123" xml:space="preserve"> Apta ergo locis illis, ut ſit æqui-
              <lb/>
            diſtans faciei annuli, & fac circulum ſecundum ipſam.</s>
            <s xml:id="echoid-s6124" xml:space="preserve"> Sumatur etiam infra hunc circulum altitu-
              <lb/>
            do medietatis grani hordei, & fiant ſigna, & in punctis aſsignatis fiat circulus per aptationem ta-
              <lb/>
            bulę.</s>
            <s xml:id="echoid-s6125" xml:space="preserve"> Et in hoc poſtremo circulo fiat circularis concauitas, & ſit unius digiti eius profunditas, &
              <lb/>
            altitudo tanquam altitudo tabulę æneę:</s>
            <s xml:id="echoid-s6126" xml:space="preserve"> & ſit hęc altitudo intra altitudinem duorum digitorum, ut
              <lb/>
            eadem ſit poſtremi circuli & cõcauitatis ſpecies.</s>
            <s xml:id="echoid-s6127" xml:space="preserve"> Aptetur autem huic concauitati tabula ęnea, quę
              <lb/>
            quidem intret concauitatem uſq;</s>
            <s xml:id="echoid-s6128" xml:space="preserve"> ad circulum minorem.</s>
            <s xml:id="echoid-s6129" xml:space="preserve"> Et cum diſtantia minoris à maiori ſit uni-
              <lb/>
            us digiti, & concauitas ſimiliter:</s>
            <s xml:id="echoid-s6130" xml:space="preserve"> igitur circulo poſtremo & tabulę ęneę communis erit ſuperficies:</s>
            <s xml:id="echoid-s6131" xml:space="preserve">
              <lb/>
            & line æ perpendiculares in altitudine annuli, tangent lineas diuiſionis tabulæ æneæ, & cadent
              <lb/>
            perpendiculariter ſuper tabulam ęneam.</s>
            <s xml:id="echoid-s6132" xml:space="preserve"> Sit autem ſuperficies tabulę ęneę diuiſa ex parte faciei
              <lb/>
            </s>
          </p>
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