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

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          <p>
            <s xml:id="echoid-s16090" xml:space="preserve">
              <pb o="226" file="0232" n="232" rhead="ALHAZEN"/>
            cta:</s>
            <s xml:id="echoid-s16091" xml:space="preserve"> tuncilla ſuperficies, in qua eſſet illa linea recta & linea h t eſſet ſuperficies trianguli u h t:</s>
            <s xml:id="echoid-s16092" xml:space="preserve">
              <lb/>
            & illa ſuperficies eſſet illa, in qua ſunt duæ lineæ æquidiſtantes h t, d z:</s>
            <s xml:id="echoid-s16093" xml:space="preserve"> & ſic ſuperficies, in qua ſunt
              <lb/>
            duę lineæ h t, d z, eſſet ſuperficies trianguli h u t:</s>
            <s xml:id="echoid-s16094" xml:space="preserve"> & ſic axis eſſet in ſuperficie trianguli h u t:</s>
            <s xml:id="echoid-s16095" xml:space="preserve"> ſed axis
              <lb/>
            eſt æquidiſtans lineæ h t poſitione.</s>
            <s xml:id="echoid-s16096" xml:space="preserve"> Et axis ſecat duas lineas h u, t u:</s>
            <s xml:id="echoid-s16097" xml:space="preserve"> & linea t h eſt in ſuperficie trian
              <lb/>
            guli u e h, quæ eſt ſuperficies reflexionis:</s>
            <s xml:id="echoid-s16098" xml:space="preserve"> & linea communis huic ſuperficiei & ſuperficiei columnę,
              <lb/>
            eſt aliqua ſectio columnaris.</s>
            <s xml:id="echoid-s16099" xml:space="preserve"> Superficies ergo e u h ſecat axem columnæ in uno puncto, ſcilicet in d,
              <lb/>
            ut præoſten-
              <lb/>
              <figure xlink:label="fig-0232-01" xlink:href="fig-0232-01a" number="202">
                <variables xml:id="echoid-variables191" xml:space="preserve">t i n g y z x q m b c œ
                  <gap/>
                f h z r a d p e K o
                  <gap/>
                </variables>
              </figure>
            dimus [27 n.</s>
            <s xml:id="echoid-s16100" xml:space="preserve">]
              <lb/>
            Et ſi axis ſe-
              <lb/>
            cet lineá h u:</s>
            <s xml:id="echoid-s16101" xml:space="preserve">
              <lb/>
            punctum ſe-
              <lb/>
            ctionis cum
              <lb/>
            linea h u erit
              <lb/>
            in ſuperficie
              <lb/>
            trianguli u e
              <lb/>
            h:</s>
            <s xml:id="echoid-s16102" xml:space="preserve"> ſed in hac
              <lb/>
            ſuperficie nõ
              <lb/>
            eſt punctum,
              <lb/>
            per quod a-
              <lb/>
            xis tranſeat,
              <lb/>
            præter d:</s>
            <s xml:id="echoid-s16103" xml:space="preserve"> er-
              <lb/>
            go linea h u
              <lb/>
            iecat axem in d:</s>
            <s xml:id="echoid-s16104" xml:space="preserve"> & iam oſtendimus [24 n] quòd h u ſecat eum in puncto ſub d:</s>
            <s xml:id="echoid-s16105" xml:space="preserve"> quod eſt impoſsibile.</s>
            <s xml:id="echoid-s16106" xml:space="preserve">
              <lb/>
            Ergo axis d z eſt extra ſuperficiem u h t, & propinquior puncto e, quàm ſuperficies h u t.</s>
            <s xml:id="echoid-s16107" xml:space="preserve"> Superfi-
              <lb/>
            cies ergo, in qua ſunt lineæ h t, d z, eſt propinquior puncto e, quàm ſuperficies u h t:</s>
            <s xml:id="echoid-s16108" xml:space="preserve"> & c eſt in ſuper-
              <lb/>
            ficie, in qua ſunt h t, d z:</s>
            <s xml:id="echoid-s16109" xml:space="preserve"> quia eſt in linea q l:</s>
            <s xml:id="echoid-s16110" xml:space="preserve"> & q l eſt in ſuperficie, in qua ſunt h t, d z:</s>
            <s xml:id="echoid-s16111" xml:space="preserve"> [per 7 p 11] er-
              <lb/>
            go c eſt propinquius e, quàm s i:</s>
            <s xml:id="echoid-s16112" xml:space="preserve"> ſed c eſt in rectitudine e b [ut patuit.</s>
            <s xml:id="echoid-s16113" xml:space="preserve">] Si ergo e b exiue-
              <lb/>
            rit in parte b:</s>
            <s xml:id="echoid-s16114" xml:space="preserve"> perueniet ad c:</s>
            <s xml:id="echoid-s16115" xml:space="preserve"> perueniet ergo ad c.</s>
            <s xml:id="echoid-s16116" xml:space="preserve"> His præoſtenſis, dico quòd linea s i, quæ eſt æ-
              <lb/>
            quidiſtans axi ſpeculi, cum fuerit in aliquo uiſibili, & uiſus fuerit in o ex parte concauitatis co-
              <lb/>
            lumnæ, & ſuperficies ſpeculata fuerit ſuperficies concaua:</s>
            <s xml:id="echoid-s16117" xml:space="preserve"> tunc s i comprehendetur ex o m ſpeculo
              <lb/>
            concauo a b g à linea a b g:</s>
            <s xml:id="echoid-s16118" xml:space="preserve"> & diuerſabuntur imagines eius ſecundum diuerſitatem diſtãtiæ ab axe,
              <lb/>
            cuius demonſtratio eſt.</s>
            <s xml:id="echoid-s16119" xml:space="preserve"> Quia angulus e b m eſt acutus [quia m b a eſt rectus ex theſi 26 n] ergo [per
              <lb/>
            15 p 1] l b c eſt acutus:</s>
            <s xml:id="echoid-s16120" xml:space="preserve"> & linea e b c eſt in ſuperficie circuli b f:</s>
            <s xml:id="echoid-s16121" xml:space="preserve"> & l b eſt diameter huius circuli [per 34
              <lb/>
            n 4.</s>
            <s xml:id="echoid-s16122" xml:space="preserve">] Ergo e b c ſecat circulum:</s>
            <s xml:id="echoid-s16123" xml:space="preserve"> ergo c b eſtintra concauitatem ſpeculi:</s>
            <s xml:id="echoid-s16124" xml:space="preserve"> & ſimiliter o b erit intra cõ-
              <lb/>
            cauitatem ſpeculi:</s>
            <s xml:id="echoid-s16125" xml:space="preserve"> quia angulus o b l eſt acutus, & duo anguli o b l, c b l ſunt æquales duobus angu
              <lb/>
            lis e b m, q b m:</s>
            <s xml:id="echoid-s16126" xml:space="preserve"> [quia per 15 p 1 æquantur angulis e b m, q b m, ęqualibus concluſis 27 n] & l b eſt
              <lb/>
            perpendicularis ſuper ſuperficiem, contingentem columnam, quæ tranſit per b.</s>
            <s xml:id="echoid-s16127" xml:space="preserve"> Forma ergo c
              <lb/>
            extenditur per c b, & peruenit ad b, & reflectitur per b o, & comprehenditur à uiſu in o [per 7 n
              <lb/>
            5.</s>
            <s xml:id="echoid-s16128" xml:space="preserve">] Item in quinto capitulo [27 n] cum fuimus locuti de ſpeculis columnaribus conuexis, decla-
              <lb/>
            rauimus, quod ſuperficies contingens columnam m g, erit ſub e:</s>
            <s xml:id="echoid-s16129" xml:space="preserve"> ergo e g ſecat ſuperficiem contin-
              <lb/>
            gentem:</s>
            <s xml:id="echoid-s16130" xml:space="preserve"> ſecat ergo lineam contingentem circum ferentiam ſectionis in g:</s>
            <s xml:id="echoid-s16131" xml:space="preserve"> ſecat ergo ſectionem, &
              <lb/>
            cadit intra ipſam:</s>
            <s xml:id="echoid-s16132" xml:space="preserve"> cadet ergo intra concauitatẽ ſpeculi:</s>
            <s xml:id="echoid-s16133" xml:space="preserve"> ergo duæ lineæ o g, g i ſunt intra concauita-
              <lb/>
            tem ſpeculi:</s>
            <s xml:id="echoid-s16134" xml:space="preserve"> & z g eſt perpendicularis ſuper ſuperficiem, contingentcm columnam in g [quia ex
              <lb/>
            theſi perpendicularis eſt a g lateri cylindraceo:</s>
            <s xml:id="echoid-s16135" xml:space="preserve"> & duo anguli o g z, i g z ſunt æquales:</s>
            <s xml:id="echoid-s16136" xml:space="preserve"> quia per 15 p 1
              <lb/>
            æquantur angulis e g n, t g n, æqualibus per 4 p 1.</s>
            <s xml:id="echoid-s16137" xml:space="preserve">] Ergo forma i extenditur per i g, & peruenit ad
              <lb/>
            g, & reflectitur per g o, & comprehenditur in o per lineam g o.</s>
            <s xml:id="echoid-s16138" xml:space="preserve"> Et ſimiliter s extenditur per s a, &
              <lb/>
            peruenit ad a, & reflectitur per a o, & comprehenditur in o.</s>
            <s xml:id="echoid-s16139" xml:space="preserve"> Et iam declarauimus, cum tractaui-
              <lb/>
            mus de fallacijs ſpeculorum columnarium conuexorum [27 n] quòd duæ lineæ h u, t u ſunt per-
              <lb/>
            pendiculares ſuper ſuperficies, contingentes ſectiones, tranſeuntes per duo puncta a, g.</s>
            <s xml:id="echoid-s16140" xml:space="preserve"> Imago er-
              <lb/>
            go s eſt in linea h u, & a o linea radialis, quæ extenditur ex uiſu ad punctum reflexionis:</s>
            <s xml:id="echoid-s16141" xml:space="preserve"> ergo ima-
              <lb/>
            go s eſt in a o:</s>
            <s xml:id="echoid-s16142" xml:space="preserve"> h ergo eſt imago s:</s>
            <s xml:id="echoid-s16143" xml:space="preserve"> [per 7 n 5] & ſic patet, quòd t eſt imago i.</s>
            <s xml:id="echoid-s16144" xml:space="preserve"> Et continuemus c l.</s>
            <s xml:id="echoid-s16145" xml:space="preserve">
              <lb/>
            Quiaergo c reflectitur ad o ex circumferentiæ puncto b:</s>
            <s xml:id="echoid-s16146" xml:space="preserve"> erit imago c in line a cl:</s>
            <s xml:id="echoid-s16147" xml:space="preserve"> & o b eſt linea ra-
              <lb/>
            dialis, quæ extenditur inter uiſum & punctum reflexionis.</s>
            <s xml:id="echoid-s16148" xml:space="preserve"> Ergo imago c eſt in puncto communi
              <lb/>
            c l & o b [per 7 n 5] nempe in puncto q.</s>
            <s xml:id="echoid-s16149" xml:space="preserve"> Sed in capitulo de imagine, cum tractauimus de imagini-
              <lb/>
            bus ſpeculorum ſphæricorum concauorum [60 n 5] patuit, quòd imago puncti, cuius forma refle-
              <lb/>
            ctitur à concauitate circuli, fortè concurret cum radiali linea, quæ eſt inter uiſum & punctum refle-
              <lb/>
            xionis, ultra ſpeculum:</s>
            <s xml:id="echoid-s16150" xml:space="preserve"> & fortè inter uiſum & ſpeculum:</s>
            <s xml:id="echoid-s16151" xml:space="preserve"> & fortè in centro uiſus:</s>
            <s xml:id="echoid-s16152" xml:space="preserve"> & fortè ultra cen-
              <lb/>
            trum uiſus:</s>
            <s xml:id="echoid-s16153" xml:space="preserve"> & fortè c l æquidiſtans erit o b.</s>
            <s xml:id="echoid-s16154" xml:space="preserve"> Et in illo capitulo [86 n 5] patuit, quòd fortè imago
              <lb/>
            erit unum punctum:</s>
            <s xml:id="echoid-s16155" xml:space="preserve"> aut duo:</s>
            <s xml:id="echoid-s16156" xml:space="preserve"> aut tria:</s>
            <s xml:id="echoid-s16157" xml:space="preserve"> aut quatuor.</s>
            <s xml:id="echoid-s16158" xml:space="preserve"> Imago ergo fortè erit in b q:</s>
            <s xml:id="echoid-s16159" xml:space="preserve"> fortè ultra o q:</s>
            <s xml:id="echoid-s16160" xml:space="preserve"> &
              <lb/>
            fortè in b o:</s>
            <s xml:id="echoid-s16161" xml:space="preserve"> & fortè in o:</s>
            <s xml:id="echoid-s16162" xml:space="preserve"> & fortè ultra:</s>
            <s xml:id="echoid-s16163" xml:space="preserve"> & fortè imago t q erit unum punctum:</s>
            <s xml:id="echoid-s16164" xml:space="preserve"> aut duo:</s>
            <s xml:id="echoid-s16165" xml:space="preserve"> aut tria:</s>
            <s xml:id="echoid-s16166" xml:space="preserve"> aut
              <lb/>
            quatuor.</s>
            <s xml:id="echoid-s16167" xml:space="preserve"> Si ergo imago c fuerit q:</s>
            <s xml:id="echoid-s16168" xml:space="preserve"> tũc h q t erit diameter imaginis s i.</s>
            <s xml:id="echoid-s16169" xml:space="preserve"> Si ergo omnes imagines s i fue
              <lb/>
            rint in linea h q t:</s>
            <s xml:id="echoid-s16170" xml:space="preserve"> tunc forma eius erit linea recta:</s>
            <s xml:id="echoid-s16171" xml:space="preserve"> nã mediũ eius eſt in rectitudine duarũ extremita-
              <lb/>
            tũ h t.</s>
            <s xml:id="echoid-s16172" xml:space="preserve"> Si aũt imago c fueritultra q:</s>
            <s xml:id="echoid-s16173" xml:space="preserve"> tunc imago s i erit ferè cõcaua ex parte uiſus.</s>
            <s xml:id="echoid-s16174" xml:space="preserve"> Et ſi imago c fuerint
              <lb/>
            plura puncta:</s>
            <s xml:id="echoid-s16175" xml:space="preserve"> tunc imago cerunt plures lineæ, quarum omnium extremitates cõiungentur in duo-
              <lb/>
            </s>
          </p>
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