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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[172] ſ k x b a s t c q f m o h z i g p d
[173] d a b e h z g
[174] d a b e h z g
[175] a d b b g
[176] a d f b ſ m e c z g
[177] h e m c u t s k o b z ſ q r f g a d
[178] h e m c u s t b o q z r f g a d
[179] i h e m c t z u s b o k q r f g a d
[180] n q e ſ g t f m o K d h c a s u p z b
[181] t n q z g m b ſ f h r a d e k o
[182] t i y n q g z x m b c ſ f h s r a d p e k o u
[183] f d b g t e h e
[184] e c s ſ o f i g m b k z d t q p h y n r u a x
[185] CIN EMATH EQUE FRANCAISE BIBLIOTHEQUE MUSEE
[186] a e t o f z h g d j c p k b q r
[187] a o u m h z t s n d ſ e q f p
[188] a o u p m h z t x b n y c q s l d g e K f r
[189] f u q b m t n e o z a
[190] f q b u g m c n K p a
[191] d g t K z b e a o ſ h
[192] d g t k n z u e b a o ſ h m r
[193] d g p i t k b e a o l f q h
[194] p d h t z f b g a ſ e k q
[195] t f h a ſ i k d r e z b c m o g
[196] q h f d u o g c r e a n m z b
[197] t f h a p k l i d e z b n r m o g q
[198] ſ m s q c d r b n p t a h e g u i f
[199] q s n p e f o x u m l b z k d h a
[200] k q t ſ n ſ g b o e u z d h a
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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>
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