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-s50642" xml:space="preserve">
              <pb o="452" file="0754" n="754" rhead="VITELLONIS OPTICAE"/>
            & 56 ſecunda, ſecundum quod arcus b c eſt partes 90 per 33 p 6:</s>
            <s xml:id="echoid-s50643" xml:space="preserve"> quoniam angulus b a c eſt rectus
              <lb/>
            per 34 p 1:</s>
            <s xml:id="echoid-s50644" xml:space="preserve"> angulus enim k h b eſt rectus:</s>
            <s xml:id="echoid-s50645" xml:space="preserve"> totus ergo arcus b d erit 90 partes, 13 minuta, & 56 ſecun-
              <lb/>
            da:</s>
            <s xml:id="echoid-s50646" xml:space="preserve"> ſed arcus d e eſt æqualis arcui d b:</s>
            <s xml:id="echoid-s50647" xml:space="preserve"> totus ergo arcus b c d e eſt 180 partes, 27 minuta, & 52 ſecun-
              <lb/>
            da.</s>
            <s xml:id="echoid-s50648" xml:space="preserve"> Quod quærebamus.</s>
            <s xml:id="echoid-s50649" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1891" type="section" level="0" n="0">
          <head xml:id="echoid-head1388" xml:space="preserve" style="it">60. Summorum uaporum conſiſtentiam ad quantum poßint eleuati pertingere, poßibile eſt
            <lb/>
          inueniri. Alhazen 6 n libri de crepuſculis.</head>
          <p>
            <s xml:id="echoid-s50650" xml:space="preserve">Ad hoc, quod hic proponitur, demonſtrandum, utemur conſuetis in ſcientia aſtrorum, ut in
              <lb/>
            præcedente.</s>
            <s xml:id="echoid-s50651" xml:space="preserve"> Sit itaq;</s>
            <s xml:id="echoid-s50652" xml:space="preserve"> per 69 th.</s>
            <s xml:id="echoid-s50653" xml:space="preserve"> 1 huius circulus, ſecundum quem ſuperficies plana tranſiens centrũ
              <lb/>
            ſolis & terræ, ſecat terram, circulus a b c:</s>
            <s xml:id="echoid-s50654" xml:space="preserve"> & ſit locus uiſus a:</s>
            <s xml:id="echoid-s50655" xml:space="preserve"> & ſit linea d a e contingens circulum.</s>
            <s xml:id="echoid-s50656" xml:space="preserve"> Et
              <lb/>
            quoniam angulus contingentiæ eſt indiuiſibilis, quia eſt minimus acutorum per 16 p 3:</s>
            <s xml:id="echoid-s50657" xml:space="preserve"> tunc patet
              <lb/>
            quòd uiſus non cadet ſub linea d a e, ſed tantùm ſupra illam.</s>
            <s xml:id="echoid-s50658" xml:space="preserve"> Et quoniam, ut patet per 27 th.</s>
            <s xml:id="echoid-s50659" xml:space="preserve"> 2 huius,
              <lb/>
            umbra terræ eſt pyramidalis:</s>
            <s xml:id="echoid-s50660" xml:space="preserve"> ſit illa pyramis umbrę terræ ante crepuſculum matutinum, quando
              <lb/>
            primò uidetur aer albeſcere in mane, c f e g:</s>
            <s xml:id="echoid-s50661" xml:space="preserve"> cuius uertex ſit f.</s>
            <s xml:id="echoid-s50662" xml:space="preserve"> Aer itaque cadens intra hanc pyrami-
              <lb/>
            dem non illuminatur à ſole, ſed radius ſolaris cadit ſuper omnem
              <lb/>
            aerem, qui eſt extra hanc pyramidem, quoniam ille nõ impeditur
              <lb/>
            per obſtaculum terræ.</s>
            <s xml:id="echoid-s50663" xml:space="preserve"> Non tamen uidetur uiſui illuminatum hoc,
              <lb/>
              <figure xlink:label="fig-0754-01" xlink:href="fig-0754-01a" number="884">
                <variables xml:id="echoid-variables861" xml:space="preserve">h f d a m e c i k y b</variables>
              </figure>
            quod eſt extra hãc pyramidem:</s>
            <s xml:id="echoid-s50664" xml:space="preserve"> quoniam (ut patet per 56 & 58 th.</s>
            <s xml:id="echoid-s50665" xml:space="preserve">
              <lb/>
            huius) non fit luminis reflexio ab aere puro & ſubtili.</s>
            <s xml:id="echoid-s50666" xml:space="preserve"> Tria ſunt er
              <lb/>
            go, quæ in hac diſpoſitione res faciunt non uideri:</s>
            <s xml:id="echoid-s50667" xml:space="preserve"> ut ſi cadant ſub
              <lb/>
            linea contingente, & per uiſum tranſeunte:</s>
            <s xml:id="echoid-s50668" xml:space="preserve"> uel ſi cadant intra ſu-
              <lb/>
            perficiem conicam pyramidis umbræ terræ:</s>
            <s xml:id="echoid-s50669" xml:space="preserve"> uel ſi tanta ſit ſubtili-
              <lb/>
            tas materiæ corporum mediorum, ut ab ipſis non fiat reflexio ad
              <lb/>
            uiſum.</s>
            <s xml:id="echoid-s50670" xml:space="preserve"> Sit quoq;</s>
            <s xml:id="echoid-s50671" xml:space="preserve">, ut linea e a d contingens terram in puncto a cen
              <lb/>
            tro uiſus, ſecet ſuperficiem pyramidis illius umbrę in pũcto extra
              <lb/>
            pyramidem, quod ſit punctũe, ut propinquum umbræ.</s>
            <s xml:id="echoid-s50672" xml:space="preserve"> Aer ergo,
              <lb/>
            qui eſt apud punctum e, eſt inuiſibilis:</s>
            <s xml:id="echoid-s50673" xml:space="preserve"> non quòd cadat ſub linea
              <lb/>
            terram contingente:</s>
            <s xml:id="echoid-s50674" xml:space="preserve"> quoniam ille aer eſt in ſuperficie horizontis:</s>
            <s xml:id="echoid-s50675" xml:space="preserve">
              <lb/>
            nec quòd cadat intra ſuperficiem pyramidis umbræ terrę:</s>
            <s xml:id="echoid-s50676" xml:space="preserve"> quoniã
              <lb/>
            eſt extra illam:</s>
            <s xml:id="echoid-s50677" xml:space="preserve"> ſed manet inuiſibilis propter ſubtilitatem materię
              <lb/>
            ſuę, quia non habet admixtionem uaporis denſioris aere, à quo re
              <lb/>
            flectatur lumen ſolis ad uiſum, ut patet per 56 huius.</s>
            <s xml:id="echoid-s50678" xml:space="preserve"> Imaginemur
              <lb/>
            ergo moueri ſolem uſq;</s>
            <s xml:id="echoid-s50679" xml:space="preserve"> ad principiũ crepuſculi matutini.</s>
            <s xml:id="echoid-s50680" xml:space="preserve"> Et quo-
              <lb/>
            niam uertex pyramidis umbræ terræ ad locum nadir ſolis ſemper
              <lb/>
            procedit, ut patet per 27 th.</s>
            <s xml:id="echoid-s50681" xml:space="preserve"> 2 huius, & ex cauſſa eclipſium lunariũ:</s>
            <s xml:id="echoid-s50682" xml:space="preserve">
              <lb/>
            patet quòd illa pyramis omne corpus medium habet neceſſariò
              <lb/>
            tranſire.</s>
            <s xml:id="echoid-s50683" xml:space="preserve"> Sit ergo tunc pyramis umbræ terræ h i k:</s>
            <s xml:id="echoid-s50684" xml:space="preserve"> cuius uertex ſit
              <lb/>
            h:</s>
            <s xml:id="echoid-s50685" xml:space="preserve"> quæ interſecet lineam e d (quæ eſt diameter horizontis) in pũ
              <lb/>
            cto m.</s>
            <s xml:id="echoid-s50686" xml:space="preserve"> In hoc itaque puncto m, exſignificato ipſius nominis cre-
              <lb/>
            puſculi, primò uidebitur reflexum lumẽ ſolis, ut fiat ſenſibile.</s>
            <s xml:id="echoid-s50687" xml:space="preserve"> Hoc
              <lb/>
            autem neceſſe eſt accidere ex denſitate aeris inſpiſſati per natu-
              <lb/>
            ram uaporum:</s>
            <s xml:id="echoid-s50688" xml:space="preserve"> quia ab aere ſimplici non fit reflexio, ut patet ex
              <lb/>
            præmiſsis huius libri propoſitionibus:</s>
            <s xml:id="echoid-s50689" xml:space="preserve"> punctum ergo m eſt pun-
              <lb/>
            ctum altiſsim um, in quo conſiſtit eleuatio uaporum aerem ínſpiſ-
              <lb/>
            ſantium.</s>
            <s xml:id="echoid-s50690" xml:space="preserve"> Deſcribatur quoque conſequenter circulus alitudinis pertranſiens centrum ſolis in ho-
              <lb/>
            ra dicti crepuſculi:</s>
            <s xml:id="echoid-s50691" xml:space="preserve"> qui ſit a b c d:</s>
            <s xml:id="echoid-s50692" xml:space="preserve"> qui per 69 th.</s>
            <s xml:id="echoid-s50693" xml:space="preserve"> 1 huius ſecabit ſphæram terræ ſecundum circulum:</s>
            <s xml:id="echoid-s50694" xml:space="preserve">
              <lb/>
            qui ſit e f g h, cuius centrum ſit k:</s>
            <s xml:id="echoid-s50695" xml:space="preserve"> ſitq́ue linea à centro terræ ad zenith capitis ducta, quæ ſit a e k:</s>
            <s xml:id="echoid-s50696" xml:space="preserve">
              <lb/>
            ſitq́ue linea b k d perpendicularis ſuper lineam a k ſemidiam etrum circuli altitudinis:</s>
            <s xml:id="echoid-s50697" xml:space="preserve"> eritq́ue linea
              <lb/>
            b k d diameter cuiuſdam circuli, cuius ſuperficies per 18 p 11 erit erecta ſuper ſuperficiem circuli al-
              <lb/>
            titudinis ſecans ſphæram terræ in duo hæmiſphæria:</s>
            <s xml:id="echoid-s50698" xml:space="preserve"> nec eſt differentia ſenſibilis ſuperficiei huius
              <lb/>
            circuli à ſuperficie circuli horizontis.</s>
            <s xml:id="echoid-s50699" xml:space="preserve"> Sit itaque corporis ſolis centrum in puncto c:</s>
            <s xml:id="echoid-s50700" xml:space="preserve"> eritq́ue per
              <lb/>
            acceptionem aſtronomicam, ſcilicet inſtrumentalem armillarum uel aſtrolabij, uel tabularum to-
              <lb/>
            talis arcus b c, quo diſtat centrum ſolis ab ipſa ſuperficie horizontis ferè 19 partes, ſecundum
              <lb/>
            quod circulus altitudinis eſt 360.</s>
            <s xml:id="echoid-s50701" xml:space="preserve"> Et quoniam diameter ſolis eſt quintupla diametro terræ, &
              <lb/>
            eius continens medietatem:</s>
            <s xml:id="echoid-s50702" xml:space="preserve"> fiat circa centrum c circulus l m ſecundum diametrum quintu-
              <lb/>
            plam & continentem medietatem lineæ e k, quæ eſt ſemidiameter terræ.</s>
            <s xml:id="echoid-s50703" xml:space="preserve"> Erit quoque, ut pa-
              <lb/>
            tet ex præmiſsis, circulus l m maximus circulorum corporis ſolaris:</s>
            <s xml:id="echoid-s50704" xml:space="preserve"> producaturq́ue linea c k à
              <lb/>
            centro ſolis ad centrum terræ, ſecans ſuperficiem terræ in puncto g.</s>
            <s xml:id="echoid-s50705" xml:space="preserve"> Et quoniam longior radius
              <lb/>
            à corpore ſolis exiens, & ad terram pertingens quaſi linea contingens eſt per 16 th.</s>
            <s xml:id="echoid-s50706" xml:space="preserve"> 2 huius:</s>
            <s xml:id="echoid-s50707" xml:space="preserve"> du-
              <lb/>
            cantur duæ lineæ contingentes ambos circulos, ſolis ſcilicet & terræ, quæ ſint l f n & m h n, ſecun-
              <lb/>
            dum quas lineas per 27 th.</s>
            <s xml:id="echoid-s50708" xml:space="preserve"> 2 huius, continetur illuminatio ſolis & umbra terræ.</s>
            <s xml:id="echoid-s50709" xml:space="preserve"> Producatur quo-
              <lb/>
            que linea contingens circulum terræ in puncto e, quæ ſit p o:</s>
            <s xml:id="echoid-s50710" xml:space="preserve"> ſecetq́;</s>
            <s xml:id="echoid-s50711" xml:space="preserve"> linea m h n lineam p o, in pũ-
              <lb/>
            cto q:</s>
            <s xml:id="echoid-s50712" xml:space="preserve"> eritq́;</s>
            <s xml:id="echoid-s50713" xml:space="preserve"> punctum q locus luminoſus in tempore crepuſculi.</s>
            <s xml:id="echoid-s50714" xml:space="preserve"> Et quoniã punctus n, qui eſt uertex
              <lb/>
            </s>
          </p>
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    </echo>
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