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-s6200" xml:space="preserve">
              <pb o="107" file="0113" n="113" rhead="OPTICAE LIBER IIII."/>
            regulæ.</s>
            <s xml:id="echoid-s6201" xml:space="preserve"> Deinceps in longiore parte illius lineæ circa punctum ſumptum, ſumatur altitudo me-
              <lb/>
            dij grani hordei, & fiat punctum.</s>
            <s xml:id="echoid-s6202" xml:space="preserve"> Dico quod illud eſt punctum medium regulæ, quod etiam cen-
              <lb/>
            tris foraminum opponitur rectè.</s>
            <s xml:id="echoid-s6203" xml:space="preserve"> Quoniam enim centra foraminum elongantur ſuper ſuperfi-
              <lb/>
            ciem tabulæ æneæ, in medij grani quantitate, & diſtant à ſuperficie annuli per duos digitos:</s>
            <s xml:id="echoid-s6204" xml:space="preserve"> lgi-
              <lb/>
            tur punctum illud diſtat ab eadem per duos digitos, & in quadrato concauo per digitum unum.</s>
            <s xml:id="echoid-s6205" xml:space="preserve">
              <lb/>
            Quare ab extremitatibus regulæ ad punctũ ſunt tres digiti.</s>
            <s xml:id="echoid-s6206" xml:space="preserve"> Quare punctũ illud erit mediũ.</s>
            <s xml:id="echoid-s6207" xml:space="preserve"> Super
              <lb/>
            hoc mediũ punctum producatur in utrãq;</s>
            <s xml:id="echoid-s6208" xml:space="preserve"> partẽ linea, ſecundũ latitudinẽ æquidiſtans extremιtati-
              <lb/>
            bus:</s>
            <s xml:id="echoid-s6209" xml:space="preserve"> & medietates lineæ longitudinis (ſuper quam eſt hæc perpendicularis) diuidãtur per æqua-
              <lb/>
            lia, per lineas latitudinis perpendiculares extremitatibus æquidiſtantes.</s>
            <s xml:id="echoid-s6210" xml:space="preserve"> Et ita diuiſa erit regula in
              <lb/>
            quatuor æquales partes.</s>
            <s xml:id="echoid-s6211" xml:space="preserve"> Similis fiat in alijs regulis operatio.</s>
            <s xml:id="echoid-s6212" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div222" type="section" level="0" n="0">
          <head xml:id="echoid-head254" xml:space="preserve" style="it">9. Sit{us} & collocatio ſpeculorum regulariũ in reflexionis organo.10.12.13.14.15.16.17 p 5.</head>
          <p>
            <s xml:id="echoid-s6213" xml:space="preserve">HIs completis, adaptetur ſpeculum planũ uni regularum:</s>
            <s xml:id="echoid-s6214" xml:space="preserve"> & eſt:</s>
            <s xml:id="echoid-s6215" xml:space="preserve"> ut ſit regula cauata ſecundũ
              <lb/>
            altitudinem ſpeculi, ita ut ſuperficies ſpeculi ſit in eadem ſuperficie cũ ſuperficie regulæ:</s>
            <s xml:id="echoid-s6216" xml:space="preserve"> &
              <lb/>
            ita, ut medium ſuperficiei ſpeculi punctũ, directè ſupponatur medio ſuperficiei regulæ pun
              <lb/>
            cto:</s>
            <s xml:id="echoid-s6217" xml:space="preserve"> & ita, ut linea diuidens ſuperficiẽ regulę in duo æqualia:</s>
            <s xml:id="echoid-s6218" xml:space="preserve"> diuidat etiã ſuperficiem ſpeculiper ę-
              <lb/>
            qualia, & ut cõtinuentur partes ſpeculi cũ linea diuidente:</s>
            <s xml:id="echoid-s6219" xml:space="preserve"> & hoc obſeruetur in poſsibilitatis fine.</s>
            <s xml:id="echoid-s6220" xml:space="preserve">
              <lb/>
            Deinde ſpeculum columnare politũ in facie applicetur alicui regulæ ita, ut mediũ punctũ eius ca-
              <lb/>
            dat ſuper mediũ regulæ punctũ, & ita, ut linea in longitudine ſpeculi ſumpta, diuidens ipſum per
              <lb/>
            æqualia, cõtinuetur cũ partibus lineæ lõgitudinis ſuperficiei regulæ æ què diuidenti, & ut media
              <lb/>
            longitudinis ſpeculi linea ſit in ſuperficie regulę.</s>
            <s xml:id="echoid-s6221" xml:space="preserve"> Et hoc ſic fieri poterit.</s>
            <s xml:id="echoid-s6222" xml:space="preserve"> Vtriuſq;</s>
            <s xml:id="echoid-s6223" xml:space="preserve"> baſis ſpeculi arcus
              <lb/>
            per æqualia diuidantur, & à puncto diuiſionis ſignato ad oppoſitũ ſignatum punctũ linea produca
              <lb/>
            tur, & lineę mediæ longitudinis aptetur & cõtinuetur.</s>
            <s xml:id="echoid-s6224" xml:space="preserve"> Speculũ columnare concauũ aptetur regu-
              <lb/>
            læ, ut media lõgitudinis eius linea ſecundũ æ qualẽ baſium arcuum diuiſionẽ ſumpta, æquidiſtãs
              <lb/>
            ſit line æ mediæ longitudinis regulæ:</s>
            <s xml:id="echoid-s6225" xml:space="preserve"> & etiã ut utriuſq, arcus chordę cũ lineæ lõgitudinis extremis
              <lb/>
            ſint in ſuperficie regulæ.</s>
            <s xml:id="echoid-s6226" xml:space="preserve"> Pyramidale ſpeculũ extrà politũ applicetur regulæ, ut acumen eius ſit in
              <lb/>
            termino line æ mediæ lõgitudinis regulæ, & linea diuidens portionẽ pyramidalis per æ qua, quę ſci
              <lb/>
            licet à uertice ad medium arcus baſis punctũ producitur, ſit in ſuperficie continuata cum parte re-
              <lb/>
            ſtante lineę mediæ, longitudinis regulæ.</s>
            <s xml:id="echoid-s6227" xml:space="preserve"> Speculum pyramidale concauum applicetur regulę ita, ut
              <lb/>
            acumen eius ſit in directo mediæ lineæ longitudinis regulæ, chorda uerò arcus baſis ſit in ſuperfi-
              <lb/>
            cie regulæ, & linea à uertice ad medium arcus baſis punctum ducta, ſit æ quidiſtans mediæ lineæ
              <lb/>
            longitudinis regulæ.</s>
            <s xml:id="echoid-s6228" xml:space="preserve"> Cum autem longitudo pyramidis ſit quatuor digitorum & dimidij:</s>
            <s xml:id="echoid-s6229" xml:space="preserve"> reſtabũt
              <lb/>
            ex longitudine regulæ digitus & dimidius.</s>
            <s xml:id="echoid-s6230" xml:space="preserve"> Ad aptandum regulæ ſpeculum ſphæricum extrà poli-
              <lb/>
            tum:</s>
            <s xml:id="echoid-s6231" xml:space="preserve"> fiat in regula circulus ſecundum quantitatem trium digitorum:</s>
            <s xml:id="echoid-s6232" xml:space="preserve"> eius centrum ſit medium re-
              <lb/>
            gulæ punctum:</s>
            <s xml:id="echoid-s6233" xml:space="preserve"> & aptetur ſpeculum, ut medium ſuperficiei eius punctum ſit in ſuperficie regulæ,
              <lb/>
            & in medio puncto mediæ lineæ longitudinis regulæ:</s>
            <s xml:id="echoid-s6234" xml:space="preserve"> quod quidẽ ſciri poterit per application em
              <lb/>
            alterius regulæ acutæ, æ qualis huic in longitudine, & diuiſæ per æ qualitatem, & applicatę mediæ
              <lb/>
            lineæ longitudinis regulæ, ita ut medium huius regulæ acutæ punctum, tangat medium ſpeculi
              <lb/>
            ſphærici punctum.</s>
            <s xml:id="echoid-s6235" xml:space="preserve"> Sphęricum concauum aptatur:</s>
            <s xml:id="echoid-s6236" xml:space="preserve"> facto in regula circulo ſecundum quantitatem
              <lb/>
            trium digitorum, cuius centrum medium regulæ punctum:</s>
            <s xml:id="echoid-s6237" xml:space="preserve"> Cauato circulo imponatur ita, ut circu
              <lb/>
            lus baſis ſpeculi ſit in ſuperficie regulæ, & punctum medium concauitatis ſpeculi, ſit directè oppo-
              <lb/>
            ſitũ medio regulæ puncto, & diameter baſis ſpeculi continuetur mediæ lineæ regulę:</s>
            <s xml:id="echoid-s6238" xml:space="preserve"> Quæita per-
              <lb/>
            pendetur.</s>
            <s xml:id="echoid-s6239" xml:space="preserve"> In regula acuta punctũ ſignetur:</s>
            <s xml:id="echoid-s6240" xml:space="preserve"> & ab illo puncto lõgitudo ſemidiametri baſis ſpeculi no
              <lb/>
            retur ex utra que parte, & ita hæc acuta regula mediæ lineæ regulæ applicetur, ut punctum ſignatũ
              <lb/>
            in ea, directè opponatur medio cõcauitatis ſpeculi puncto, & diameter in ea facta ſimul ſit cum ba-
              <lb/>
            fis diametro.</s>
            <s xml:id="echoid-s6241" xml:space="preserve"> His peractis in ſemidiametro tabulæ æneæ triangulum per æqualia diuidente:</s>
            <s xml:id="echoid-s6242" xml:space="preserve"> ſigne-
              <lb/>
            tur ab acumine eius longitudo, æqualis axi huius ſpeculi concaui, & fiat punctum.</s>
            <s xml:id="echoid-s6243" xml:space="preserve"> Axis autem ſic
              <lb/>
            dignoſcitur.</s>
            <s xml:id="echoid-s6244" xml:space="preserve"> Regula acuta ſuperficiei ſpeculi applicetur, ut acuitas directè ſit ſuper mediam longi-
              <lb/>
            tudinis lineam, puncto eius ſuper medium concaui ſpeculi punctum directè ſtatuto:</s>
            <s xml:id="echoid-s6245" xml:space="preserve"> deinde acus
              <lb/>
            recta & ſubtilis ſuper illud regulæ acutæ punctum perpendiculariter cadat in ſpeculum:</s>
            <s xml:id="echoid-s6246" xml:space="preserve"> deſcen-
              <lb/>
            det quidem ſuper medium concaui punctum:</s>
            <s xml:id="echoid-s6247" xml:space="preserve"> ſignetur autem in acu punctum, quod poſt ſuum
              <lb/>
            deſcẽſum tangat concauitas regulæ:</s>
            <s xml:id="echoid-s6248" xml:space="preserve"> & ſit modicum declinata regula, ut certius poſsit fieri in acu
              <lb/>
            ſignum.</s>
            <s xml:id="echoid-s6249" xml:space="preserve"> Poſtea ſecun dum longitudinem acus à puncto ſignato in ea, metire ab acumine tabulæ æ-
              <lb/>
            neæ in linea triangulum diuidente, & fac punctum.</s>
            <s xml:id="echoid-s6250" xml:space="preserve"> Deinceps hanc regulam facias intrare quadra-
              <lb/>
            tum concauum, ita ut acumen tabulæ æneæ deſcendat ſupra ſpeculum, & adhibeatur regula acu-
              <lb/>
            ta, ut ſignetur punctum in linea diuidente triangulum, quod tetigerit ex ea regula acuta, cum a-
              <lb/>
            cumen trianguli deſeenderit uſque ad ſuperficiem concaui:</s>
            <s xml:id="echoid-s6251" xml:space="preserve"> Signa igitur punctum:</s>
            <s xml:id="echoid-s6252" xml:space="preserve"> hoc uerò ſe-
              <lb/>
            cundum punctum minus diſtabit ab acumine quàm primum.</s>
            <s xml:id="echoid-s6253" xml:space="preserve"> Superficies enim tabulæ æneæ di-
              <lb/>
            ſtat à ſuperficie annuli ſiue tabulæ, in qua eſt quadratum concauum, per duos digitos minus me-
              <lb/>
            dietate grani hordei:</s>
            <s xml:id="echoid-s6254" xml:space="preserve"> punctum autem medium regulæ directè eſt oppoſitum medio ſpeculi conca-
              <lb/>
            ui puncto:</s>
            <s xml:id="echoid-s6255" xml:space="preserve"> quod quidem diſtat ab eadem ſuperficie tabulæ per duos digitos.</s>
            <s xml:id="echoid-s6256" xml:space="preserve"> Cum ergo acumen ta-
              <lb/>
            bulę orthogonaliter deſcendat:</s>
            <s xml:id="echoid-s6257" xml:space="preserve"> nõ cadet ſuper mediũ cõcaui punctũ, quod eſt terminus axis, ſed in
              <lb/>
            punctũ altius.</s>
            <s xml:id="echoid-s6258" xml:space="preserve"> Quare patet propoſitũ.</s>
            <s xml:id="echoid-s6259" xml:space="preserve"> Signetur uerò in ſpeculo cõcauo pũctũ, in qđ incidit acumẽ
              <lb/>
            tabulæ æneæ, & extracto in pũcto illo foramine, orthogonaliter deſcẽdẽte & modico, ad hãc quidẽ
              <lb/>
            </s>
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