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-s17589" xml:space="preserve">
              <pb o="252" file="0258" n="258" rhead="ALHAZEN"/>
            deinde poſueris inſtrumentum horarum in illa nocte ante ortum lunę, & ſciueris altitudinem lunę,
              <lb/>
            & obſeruaueris lunam uſq;</s>
            <s xml:id="echoid-s17590" xml:space="preserve"> ad ortum eius, & perueniat tempus in inſtrumento ad minutum idem
              <lb/>
            eiuſdem horæ, quod habet luna, & obſeruaueris altitudinem lunæ, quam habet in illa hora à uerti-
              <lb/>
            ce capitis, & obſeruaueris, ut inſtrumentum eleuationis ſit diuiſum per minuta, & per minora mi-
              <lb/>
            nutis, ſi poſsibile eſt:</s>
            <s xml:id="echoid-s17591" xml:space="preserve"> tunc inuenies diſtantiam lunæ à uertice capitis in illa hora per inſtrumen-
              <lb/>
            tum, minorem ſpatio remotionis à uertice capitis in illa hora per computationem.</s>
            <s xml:id="echoid-s17592" xml:space="preserve"> Ergo lux lunæ
              <lb/>
            non extenditur per duo foramina inſtrumenti, per quæ ſumpta eſt eleuatio rectè:</s>
            <s xml:id="echoid-s17593" xml:space="preserve"> tunc enim diſtan
              <lb/>
            tia eius à uertice capitis eſſet eadem cum illa, quę eſt inuenta per computationem:</s>
            <s xml:id="echoid-s17594" xml:space="preserve"> Sed diſtantia in-
              <lb/>
            uenta per computationem, differt à diſtantia per inſtrumentum.</s>
            <s xml:id="echoid-s17595" xml:space="preserve"> Ergo lux lunæ non extenditur à
              <lb/>
            cœlo ad aerem per lineas rectas:</s>
            <s xml:id="echoid-s17596" xml:space="preserve"> ergo ſecundum refractionem.</s>
            <s xml:id="echoid-s17597" xml:space="preserve"> Ex his ergo experimentationibus
              <lb/>
            patet, quòd uiſus comprehendit omnes ſtellas, quæ ſunt in cœlo refractè.</s>
            <s xml:id="echoid-s17598" xml:space="preserve"> Ergo uniuerſum cœlum
              <lb/>
            differt à diaphanitate aeris.</s>
            <s xml:id="echoid-s17599" xml:space="preserve"> Reſtat ergo declarare, quòd corpus cœli differt in ſubtilitate ab aere:</s>
            <s xml:id="echoid-s17600" xml:space="preserve"> &
              <lb/>
            hoc declarabitur per experimentationem prædictam.</s>
            <s xml:id="echoid-s17601" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div574" type="section" level="0" n="0">
          <head xml:id="echoid-head498" xml:space="preserve" style="it">16. Cœlum rari{us} eſt aere & igne. 50 p 10.</head>
          <p>
            <s xml:id="echoid-s17602" xml:space="preserve">SIt ergo circulus meridiei in loco experimentationis circulus a b g:</s>
            <s xml:id="echoid-s17603" xml:space="preserve"> & zenith capitis b:</s>
            <s xml:id="echoid-s17604" xml:space="preserve"> & polus
              <lb/>
            mundi d:</s>
            <s xml:id="echoid-s17605" xml:space="preserve"> & centrum mundi e:</s>
            <s xml:id="echoid-s17606" xml:space="preserve"> & continuemus b cum e:</s>
            <s xml:id="echoid-s17607" xml:space="preserve"> & ſit locus uiſus z:</s>
            <s xml:id="echoid-s17608" xml:space="preserve"> & circulus æquidi-
              <lb/>
            ſtans æquinoctiali (cuius diſtantia à poli mundi eſt illa, in qua inuenitur ſtella in hora certifica
              <lb/>
            tionis diſtantię primæ) circulus h t:</s>
            <s xml:id="echoid-s17609" xml:space="preserve"> & ſit locus ſtellæ in illa hora h:</s>
            <s xml:id="echoid-s17610" xml:space="preserve"> & ſit circulus æquidiſtans æqui
              <lb/>
            noctiali (cuius diſtantia à polo eſt illa, in qua inuenitur ſtella in ſecunda hora) circulus k b:</s>
            <s xml:id="echoid-s17611" xml:space="preserve"> iſte ergo
              <lb/>
            circulus erit ille, in quo requieſcet ſtella ſecundum uerticationem.</s>
            <s xml:id="echoid-s17612" xml:space="preserve"> Nam cum ſtella fuerit in uertice
              <lb/>
            capitis, aut ualde prope:</s>
            <s xml:id="echoid-s17613" xml:space="preserve"> tunc uiſus comprehendet illam rectè:</s>
            <s xml:id="echoid-s17614" xml:space="preserve"> [per 13 n] quia linea recta, quæ tranſit
              <lb/>
            per uiſum & per uerticem capitis, eſt perpendicularis ſuper concauum ſphæræ cœli & perpendicu
              <lb/>
            laris ſuper conuexum aeris:</s>
            <s xml:id="echoid-s17615" xml:space="preserve"> & cum ſit perpendicularis ſuper utrumq;</s>
            <s xml:id="echoid-s17616" xml:space="preserve"> corpus:</s>
            <s xml:id="echoid-s17617" xml:space="preserve"> ergo uiſus compre-
              <lb/>
            hendit ſtellam, quæ eſt ſuper lineam hanc rectè, ſiue hæc duo corpora cœli & aeris fuerint diuerſæ
              <lb/>
            diaphanitatis, ſiue conſimilis.</s>
            <s xml:id="echoid-s17618" xml:space="preserve"> Cum ergo ſtella fuerit in uertice capitis, aut prope:</s>
            <s xml:id="echoid-s17619" xml:space="preserve"> uiſus comprehen-
              <lb/>
            dit illam in ſuo uero circulo æquidiſtante æquinoctiali, ſuper quẽ mouebatur ab initio noctis, quo-
              <lb/>
            uſq;</s>
            <s xml:id="echoid-s17620" xml:space="preserve"> peruenit ad circulum meridiei.</s>
            <s xml:id="echoid-s17621" xml:space="preserve"> Circulus ergo k b g eſt ille, in quo erat ſtella in experimentatio-
              <lb/>
            ne prima:</s>
            <s xml:id="echoid-s17622" xml:space="preserve"> & ſit circulus uerticationis, qui tranſit per ſtellam in hora experimentationis primæ cir-
              <lb/>
            culus b h k:</s>
            <s xml:id="echoid-s17623" xml:space="preserve"> & ſecet ille circulus circulum k b g in puncto k, & circulum h t in puncto h.</s>
            <s xml:id="echoid-s17624" xml:space="preserve"> Et quia di-
              <lb/>
            ſtantia ſtellę à polo mundi fuit in prima experimen
              <lb/>
              <figure xlink:label="fig-0258-01" xlink:href="fig-0258-01a" number="218">
                <variables xml:id="echoid-variables205" xml:space="preserve">k h b m z d e a t i g</variables>
              </figure>
            tatione minor, quàm in ſecũda:</s>
            <s xml:id="echoid-s17625" xml:space="preserve"> erit circulus h t pro
              <lb/>
            pinquior polo, circulo k b g:</s>
            <s xml:id="echoid-s17626" xml:space="preserve"> ergo punctũ h eſt pro-
              <lb/>
            pinquius zenith capitis, quàm punctum k:</s>
            <s xml:id="echoid-s17627" xml:space="preserve"> & conti
              <lb/>
            nuemus duas lineas h z, k z.</s>
            <s xml:id="echoid-s17628" xml:space="preserve"> Quia ergo ſtella com-
              <lb/>
            prehenditur à uiſu in hora experimentationis pri-
              <lb/>
            mę in puncto h:</s>
            <s xml:id="echoid-s17629" xml:space="preserve"> & tunc erat in ſuperficie circuli b h
              <lb/>
            k uerticalis:</s>
            <s xml:id="echoid-s17630" xml:space="preserve"> & ſtella erat in illa hora in circumferen
              <lb/>
            tia k b g:</s>
            <s xml:id="echoid-s17631" xml:space="preserve"> ergo ſtella erat in illa hora in puncto k:</s>
            <s xml:id="echoid-s17632" xml:space="preserve"> &
              <lb/>
            comprehenditur à uiſu in puncto h, & per rectitudi
              <lb/>
            nem lineæ z h:</s>
            <s xml:id="echoid-s17633" xml:space="preserve"> uiſus enim nihil comprehendit, niſi
              <lb/>
            per uerticationes linearum radialium, per quas for
              <lb/>
            mæ perueniunt ad uiſum.</s>
            <s xml:id="echoid-s17634" xml:space="preserve"> Viſus ergo cõprehendit
              <lb/>
            ſtellam in puncto h:</s>
            <s xml:id="echoid-s17635" xml:space="preserve"> quia forma peruenit ad illũ in
              <lb/>
            rectitudine lineæ h z.</s>
            <s xml:id="echoid-s17636" xml:space="preserve"> Et cum uiſus cõprehendat illam in rectitudine h z:</s>
            <s xml:id="echoid-s17637" xml:space="preserve"> & linea recta, quæ eſt inter
              <lb/>
            ſtellam & uiſum, ſit linea k z:</s>
            <s xml:id="echoid-s17638" xml:space="preserve"> manifeſtum eſt ergo, quòd uiſus non comprehendit ſtellam, quæ eſt in
              <lb/>
            puncto k rectè:</s>
            <s xml:id="echoid-s17639" xml:space="preserve"> ergo refractè.</s>
            <s xml:id="echoid-s17640" xml:space="preserve"> Sit ergo locus refractionis m:</s>
            <s xml:id="echoid-s17641" xml:space="preserve"> & continuemus k m:</s>
            <s xml:id="echoid-s17642" xml:space="preserve"> & protrahamus ab
              <lb/>
            m rectã uſq;</s>
            <s xml:id="echoid-s17643" xml:space="preserve"> ad z.</s>
            <s xml:id="echoid-s17644" xml:space="preserve"> Forma ergo ſtellæ, quæ peruenit ad z, ex qua uiſus comprehendit ſtellam:</s>
            <s xml:id="echoid-s17645" xml:space="preserve"> extendi
              <lb/>
            tur à ſtella perlineam k m, & refringitur per lineam m z:</s>
            <s xml:id="echoid-s17646" xml:space="preserve"> & non refringuntur formæ, niſi cum occur-
              <lb/>
            rit corpus diuerſæ diaphanitatis à diaphanitate corporis, in quo exiſtit.</s>
            <s xml:id="echoid-s17647" xml:space="preserve"> Ergo corpus, in quo eſt ſtel
              <lb/>
            la, ſcilicet cœlum, eſt diaphanũ differens in diaphanitate ab aere.</s>
            <s xml:id="echoid-s17648" xml:space="preserve"> Et quia locus refractionis eſt apud
              <lb/>
            ſuperficiem, quæ tranſit in duo corpora, quæ differunt in diaphanitate:</s>
            <s xml:id="echoid-s17649" xml:space="preserve"> punctum ergo m eſt pun-
              <lb/>
            ctum in concauitate cœli.</s>
            <s xml:id="echoid-s17650" xml:space="preserve"> Et continuemus lineam inter e, m:</s>
            <s xml:id="echoid-s17651" xml:space="preserve"> & ſit diameter ſphærę cœli:</s>
            <s xml:id="echoid-s17652" xml:space="preserve"> erit ergo li-
              <lb/>
            nea e m perpendicularis ſuper ſuperficiem cœli concauam contingentem aerem, & ſuper ſuperfi-
              <lb/>
            ciem aeris conuexam:</s>
            <s xml:id="echoid-s17653" xml:space="preserve"> [ut demonſtratum eſt 25 n 4.</s>
            <s xml:id="echoid-s17654" xml:space="preserve">] Et cum forma ſtellæ, quæ eſt in puncto k, exten
              <lb/>
            datur per lineam m k, & refringatur in aere per lineam m z:</s>
            <s xml:id="echoid-s17655" xml:space="preserve"> patet, quòd hæc refractio eſt ad lineam,
              <lb/>
            in qua eſt perpendicularis e m, quæ tranſit per punctum refractionis, quæ eſt perpendicularis ſu-
              <lb/>
            per ſuperficiem aeris.</s>
            <s xml:id="echoid-s17656" xml:space="preserve"> Et cum refractio in aere ſit ad partem perpendicularis exeuntis à loco refra-
              <lb/>
            ctionis:</s>
            <s xml:id="echoid-s17657" xml:space="preserve"> ergo corpus aeris eſt groſsius corpore cœli.</s>
            <s xml:id="echoid-s17658" xml:space="preserve"> Patet ergo, quòd hoc, qùod inuenimus per ex-
              <lb/>
            perimentationẽ ſtellarũ, ſignificat demõſtratiuè, quòd uiſus nõ comprehendit ſtellas, niſi refractè:</s>
            <s xml:id="echoid-s17659" xml:space="preserve">
              <lb/>
            & quòd corpus aeris eſt groſsius corpore cœli:</s>
            <s xml:id="echoid-s17660" xml:space="preserve"> & quòd corpus cœli eſt ſubtilius corpore aeris.</s>
            <s xml:id="echoid-s17661" xml:space="preserve"> Ex
              <lb/>
            his ergo omnibus patet, quòd omnia, quę cõprehendũtur à uiſu ultra corpora diaphana, quorũ dia
              <lb/>
            phanitas differt à diaphanitate aeris (ſi uiſus fuerit obliquus à perpendicularibus egredientibus ex
              <lb/>
            ipſis ſuper ſuperficiem diaphanorum corporum, in quibus conſiſtunt) comprehenduntur refractè.</s>
            <s xml:id="echoid-s17662" xml:space="preserve"/>
          </p>
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