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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        <div xml:id="echoid-div225" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s6325" xml:space="preserve">
              <pb o="109" file="0115" n="115" rhead="OPTICAE LIBER IIII."/>
              <gap/>
            pparebit tamen lux reflecti ſuper foramen, ſimile eius deſcenſui, & medium lucis ſuper medium
              <lb/>
            foraminis, ſicut uiſum eſt in regula non declinata.</s>
            <s xml:id="echoid-s6326" xml:space="preserve"> Regulam, in qua ſitum eſt columnare concauum,
              <lb/>
            impones, ut deſcendat acumen tabulæ æneæ, donec tangat ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s6327" xml:space="preserve"> & declinabis hoc
              <lb/>
            ſpeculum ſecundum latus ſuum, ſicut declinaſti extrà politum.</s>
            <s xml:id="echoid-s6328" xml:space="preserve"> Idem in ſpeculis pyramidalibus con
              <lb/>
            cauis operaberis.</s>
            <s xml:id="echoid-s6329" xml:space="preserve"> Sphæricum concauũ aptetur, donec deſcendat acumen tabulæ æneæ in foramen
              <lb/>
            ſpeculi, factum ſecundum acuminis deſcenſum.</s>
            <s xml:id="echoid-s6330" xml:space="preserve"> Sphæricum extrà politum ſic imponatur, ut acu-
              <lb/>
            men tabulæ æneæ ſit in ſuperficie regulæ, & in eadem ſuperficie cum medio ſpeculi puncto:</s>
            <s xml:id="echoid-s6331" xml:space="preserve"> quod
              <lb/>
            ſic fieri poterit.</s>
            <s xml:id="echoid-s6332" xml:space="preserve"> Adhibeatur regula acuta regulę, & puncto ſpeculi medio, & deſcendat acumen tabu
              <lb/>
            læ æneæ, quouſq;</s>
            <s xml:id="echoid-s6333" xml:space="preserve"> ſit in directo acuitatis regulæ:</s>
            <s xml:id="echoid-s6334" xml:space="preserve"> & tunc cogatur ſiſtere.</s>
            <s xml:id="echoid-s6335" xml:space="preserve"> In ſpeculis columnaribus ui
              <lb/>
            debis reflexionem hoc modo.</s>
            <s xml:id="echoid-s6336" xml:space="preserve"> Aptetur ſpeculum, ſicut dictum eſt:</s>
            <s xml:id="echoid-s6337" xml:space="preserve"> & per foramen medium deſcen-
              <lb/>
            dat baculus columnaris, ſicut factũ eſt in ſpeculis planis:</s>
            <s xml:id="echoid-s6338" xml:space="preserve"> Cadet quidem baculus ſuper mediam lon
              <lb/>
            gitudinis ſpeculi lineam, & erit eius terminus in ſuperficie regulę.</s>
            <s xml:id="echoid-s6339" xml:space="preserve"> Super mediam igitur lineã ſigne-
              <lb/>
            tur punctum, in quod cadit:</s>
            <s xml:id="echoid-s6340" xml:space="preserve"> & ab hoc puncto in ſuperficie regulæ ſumatur longitudo ſemidiametri
              <lb/>
            circuli facti in regula, ad diſcernendum circularem lucis caſum:</s>
            <s xml:id="echoid-s6341" xml:space="preserve"> & ex alia parte puncti ſumatur lon-
              <lb/>
            gitudo eadem, & habebitur linea æqualis diametro prædicti circuli.</s>
            <s xml:id="echoid-s6342" xml:space="preserve"> Videbitur autem lux cadens,
              <lb/>
            extendi ſuper præd ctam lineam tantùm, & reflectetur ad foramen medium:</s>
            <s xml:id="echoid-s6343" xml:space="preserve"> & circa eius baſim in-
              <lb/>
            teriorem uidebitur lux circularis maior circulo interiori, ſicut in ſpeculis planis uiſum eſt.</s>
            <s xml:id="echoid-s6344" xml:space="preserve"> Idem in
              <lb/>
            ſpeculis pyramidalibus uidere poteris.</s>
            <s xml:id="echoid-s6345" xml:space="preserve"> Pari modo in ſpeculis ſphæricis, luce per foramen mediũ
              <lb/>
            deſcendente:</s>
            <s xml:id="echoid-s6346" xml:space="preserve"> fiat circulus in ſuperficie regulæ ad quantitatem circuli iam dicti:</s>
            <s xml:id="echoid-s6347" xml:space="preserve"> & uidebitur lux ex-
              <lb/>
            tendi ſuper hunc circulum, & reflecti ad foramen medium modo iam dicto.</s>
            <s xml:id="echoid-s6348" xml:space="preserve"> Et apparebit in his o-
              <lb/>
            mnibus rectis reflexionibus, linea perpendicularis in interiore ſuperficie annuli ſecare lucẽ circu-
              <lb/>
            larem reflexam, & diuidere circulum eius per medium.</s>
            <s xml:id="echoid-s6349" xml:space="preserve"> Quod autem dictum eſt de luce naturali:</s>
            <s xml:id="echoid-s6350" xml:space="preserve"> ui-
              <lb/>
            deri poterit in luce accidentali.</s>
            <s xml:id="echoid-s6351" xml:space="preserve"> Domus unici foraminis opponatur parieti, in quem deſcendit ra-
              <lb/>
            dius ſolis, & applicetur inſtrumentum foramini.</s>
            <s xml:id="echoid-s6352" xml:space="preserve"> Cum ergo intrauerit lux accidentalis per foramen
              <lb/>
            non medium, uidebitur reflecti per eius oppoſitum:</s>
            <s xml:id="echoid-s6353" xml:space="preserve"> & ſi aptetur inſtrumentum, utintret per duo
              <lb/>
            foramina, reflectetur per duo ſimilia.</s>
            <s xml:id="echoid-s6354" xml:space="preserve"> Verùm ut poſsis perpendere lucem, cum intrauerit directè:</s>
            <s xml:id="echoid-s6355" xml:space="preserve">
              <lb/>
            appone ſuperius pergamenum album, & inclina inſtrumentum, donec uideas locem cadentem ſu-
              <lb/>
            per pergamenum:</s>
            <s xml:id="echoid-s6356" xml:space="preserve"> in ſpeculis enim non plenè comprehenditur lucis accidentalis caſus, propter de-
              <lb/>
            bilitatẽ eius.</s>
            <s xml:id="echoid-s6357" xml:space="preserve"> Idem autem in hac luce patebit, quod in naturali patuit:</s>
            <s xml:id="echoid-s6358" xml:space="preserve"> non enim eſt diuerſitas in ea-
              <lb/>
            rum natura, niſi quòd una'
              <unsure/>
            fortis eſt, & alia debilis.</s>
            <s xml:id="echoid-s6359" xml:space="preserve"> Palàm ergo, quòd luces per diuerſas lineas ad ſpe
              <lb/>
            cula accedentes, per diuerſas reflectuntur lineas:</s>
            <s xml:id="echoid-s6360" xml:space="preserve"> & quòd ſecundum rectam perpendicularem in-
              <lb/>
            cidentes, ſecundum eandem regrediuntur:</s>
            <s xml:id="echoid-s6361" xml:space="preserve"> & quòd declinatio linearũ reflexionis, eſt æqualis decli
              <lb/>
            nationi linearum acceſſus.</s>
            <s xml:id="echoid-s6362" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div226" type="section" level="0" n="0">
          <head xml:id="echoid-head258" xml:space="preserve" style="it">13. Superficies reflexionis eſt perpendicularis plano ſpeculum in reflexionis puncto tan-
            <lb/>
          genti. 25 p 5.</head>
          <p>
            <s xml:id="echoid-s6363" xml:space="preserve">ET planũ, quòd lineæ lucis reflexæ & aduenientis, ſunt in eadem ſuperficie orthogonali ſuper
              <lb/>
            ſuperficiem politi, aut ſuperficiem contingentem punctum politi, a quo fit reflexio:</s>
            <s xml:id="echoid-s6364" xml:space="preserve"> & ſi lux ſu
              <lb/>
            per perpendicularem uenerit, reflectitur ſuper perpendicularem:</s>
            <s xml:id="echoid-s6365" xml:space="preserve"> & in quodcunq;</s>
            <s xml:id="echoid-s6366" xml:space="preserve"> punctum
              <lb/>
            ceciderit, reflectitur in ſuperficie perpendiculari, ſuper ſuperficiem tangentem illud punctum:</s>
            <s xml:id="echoid-s6367" xml:space="preserve"> &
              <lb/>
            ſemper linea reflexa cum perpendiculari ſuper illud punctum, æqualem tenet angulum, angulo,
              <lb/>
            quem includit linea ueniens cum eadem perpendiculari.</s>
            <s xml:id="echoid-s6368" xml:space="preserve"> Et huius rei probatio eſt.</s>
            <s xml:id="echoid-s6369" xml:space="preserve"> Quia palàm [per
              <lb/>
            10.</s>
            <s xml:id="echoid-s6370" xml:space="preserve">11.</s>
            <s xml:id="echoid-s6371" xml:space="preserve">12.</s>
            <s xml:id="echoid-s6372" xml:space="preserve">n] quòd ſi deſcendat lux quæcunq;</s>
            <s xml:id="echoid-s6373" xml:space="preserve"> per foramen aliquod:</s>
            <s xml:id="echoid-s6374" xml:space="preserve"> reflectitur per aliud ipſum reſpi-
              <lb/>
            ciens:</s>
            <s xml:id="echoid-s6375" xml:space="preserve"> & ſi conſtrin gatur foramen, ut reſtet quaſi ſolus axis:</s>
            <s xml:id="echoid-s6376" xml:space="preserve"> reflectitur per axem reſpicientis:</s>
            <s xml:id="echoid-s6377" xml:space="preserve"> & ſi
              <lb/>
            fiat alteratio deſcenſus lucis:</s>
            <s xml:id="echoid-s6378" xml:space="preserve"> reflectitur per lineas, per quas prius deſcenderat.</s>
            <s xml:id="echoid-s6379" xml:space="preserve"> Et palàm [ex inſtru-
              <lb/>
            menti reflexionis cõſtructione] quòd foramina ſe reſpicientia eundem habent ſitum, reſpectu me-
              <lb/>
            dij.</s>
            <s xml:id="echoid-s6380" xml:space="preserve"> Et cum non procedat lux, niſi per rectas lineas:</s>
            <s xml:id="echoid-s6381" xml:space="preserve"> palam, quòd reflectitur per lineas eiuſdem ſitus,
              <lb/>
            reſpectu medij foraminis, cum lineis deſcenſus:</s>
            <s xml:id="echoid-s6382" xml:space="preserve"> Vnde cũ accedit per orthogonalẽ, per eam reflecti-
              <lb/>
            tur ſolam.</s>
            <s xml:id="echoid-s6383" xml:space="preserve"> Quare ſemper lineæ reflexionis eundem ſeruant ſitum cum lineis deſcenſus, reſpectu ſu-
              <lb/>
            perficiei contingentis punctum reflexionis.</s>
            <s xml:id="echoid-s6384" xml:space="preserve"> Et hoc uerum eſt ſiue in ſubſtantiali ſiue in accidenta-
              <lb/>
            li luce, ſiue forti ſiue debili:</s>
            <s xml:id="echoid-s6385" xml:space="preserve"> & generaliter in omni.</s>
            <s xml:id="echoid-s6386" xml:space="preserve"> Et nos oſtendemus identitatẽ ſitus.</s>
            <s xml:id="echoid-s6387" xml:space="preserve"> Iam ſcimus,
              <lb/>
            quòd ſuperficies regulæ cadit ſuper tabulam, in qua quadratum fecimus, orthogonaliter.</s>
            <s xml:id="echoid-s6388" xml:space="preserve"> Igitur li-
              <lb/>
            nea media tabulæ quadrati orthogonalis eſt ſuper lineam communem ſectioni ipſius & regulæ, &
              <lb/>
            ſuper lineam latitudinis regulæ:</s>
            <s xml:id="echoid-s6389" xml:space="preserve"> Et tabula quadrati æquidiſtat æneæ tabulæ, & linea eius, id eſt, ta-
              <lb/>
            bulæ quadratæ concauæ media, æquidiſtat lineæ mediæ tabulæ æneæ, quę eſt linea à centro tabu-
              <lb/>
            læ æneæ producta, & diuidens ſemicirculum per æqualia.</s>
            <s xml:id="echoid-s6390" xml:space="preserve"> Linea autem comunis ſuperficιei tabulę
              <lb/>
            æneæ & ſuperficiei regulæ, in qua eſt linea latitudinis, eſt æquidiſtãs lineæ communi concauę tabu
              <lb/>
            læ & regulæ [per 28 p 1:</s>
            <s xml:id="echoid-s6391" xml:space="preserve"> linea enim longitudinis regulæ rectè ſecat latitudinis lineas.</s>
            <s xml:id="echoid-s6392" xml:space="preserve">] Quare linea
              <lb/>
            media tabulæ æneæ cadet perpendiculariter ſuper lineam cõmunem regulæ & tabulę æneæ.</s>
            <s xml:id="echoid-s6393" xml:space="preserve"> Et re-
              <lb/>
            gula perpendicularis eſt ſuper ſuperficiem quadrati, & ſuperficies quadrati æquidiſtans ſuperficiei
              <lb/>
            tabulæ æneę Quare ſuperficies tabulę æneę orthogonalis eſt ſuper ſuperficiem regulę:</s>
            <s xml:id="echoid-s6394" xml:space="preserve"> & linea me-
              <lb/>
            dia latitudinis regulę, eſt perpendicularis ſuper mediam longitudinis regulæ lineam:</s>
            <s xml:id="echoid-s6395" xml:space="preserve"> & ſimiliter li-
              <lb/>
            nea media tabulę æneę, eſt perpendicularis ſuper eandẽ.</s>
            <s xml:id="echoid-s6396" xml:space="preserve"> Et ita media linea tabulę æneæ eſt perpen
              <lb/>
            dicularis ſuper ſuperficiem regulæ, & ſuper mediam longitudinis eius lineam:</s>
            <s xml:id="echoid-s6397" xml:space="preserve"> Eſt ergo perpendicu
              <lb/>
              <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a" number="22">
                <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/figures/0115-01"/>
              </figure>
            </s>
          </p>
        </div>
      </text>
    </echo>
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