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-div641" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s19915" xml:space="preserve">
              <pb o="287" file="0293" n="293" rhead="DE CREPVSCVLIS LIBER."/>
            prehenſus.</s>
            <s xml:id="echoid-s19916" xml:space="preserve"> Quare ſi æqualibus angulis æquales addãtur, æquabitur per 2 axio:</s>
            <s xml:id="echoid-s19917" xml:space="preserve"> totus angulus b a d
              <lb/>
            toti angulo e a d:</s>
            <s xml:id="echoid-s19918" xml:space="preserve"> & per 26 p 3 peripheria b d peripheriæ e d.</s>
            <s xml:id="echoid-s19919" xml:space="preserve">] Ergo totus arcus b c d e illuminatus à
              <lb/>
            ſole, eſt 180 partes & 27 minuta & quatuorquintæ & tertia quintæ unius minuti cũ propinquitate
              <lb/>
            [id eſt 52 ſecunda:</s>
            <s xml:id="echoid-s19920" xml:space="preserve"> nã ex arithmeticæ regulis {4/5} unius minuti ſunt 48 ſerupula ſecũda, & quinta pars
              <lb/>
            unius minuti ſunt 12 ſcrupula ſecunda, quorũ tertia pars, 4 ſcilicet ſcrupula ſecunda addιta cum 48
              <lb/>
            ſcrupulis ſecundis, efficiunt 52 ſcrupulà ſecunda.</s>
            <s xml:id="echoid-s19921" xml:space="preserve">] Et illud eſt, quod uoluimus declarare.</s>
            <s xml:id="echoid-s19922" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div643" type="section" level="0" n="0">
          <head xml:id="echoid-head552" xml:space="preserve" style="it">6. Poſit a peripheria maximi in terra circuli 2 4000 milliarium Italicorum: erit ſumma ua-
            <lb/>
          porum in nubem coactorum à terra altιtudo 5 2000 paſſuum. Vitell. 60 p 10.</head>
          <p>
            <s xml:id="echoid-s19923" xml:space="preserve">INcipiamus ergo nũc ex eo, quod intẽdimus de cauſſa apparition is crepuſculi, & formæ appari-
              <lb/>
            tionis eius nobis, & figurationis ipſius in horizonte oriẽtali.</s>
            <s xml:id="echoid-s19924" xml:space="preserve"> Ponam ergo circulũ ſignatum ſu-
              <lb/>
            per ſphærã terræ, & ſuper quã abſcindit terrã ſuperficies plana, trãſiens per zenιth capitũ & per
              <lb/>
              <gap/>
            centrũ terræ & ſolis circulũ a b, & locũ uiſus a:</s>
            <s xml:id="echoid-s19925" xml:space="preserve"> & faciã trãſire ſuper punctũ a lineam contingentẽ
              <lb/>
            circulũ [per 17 p 3] & prolongabo duas extremitates eius in duas partes, ſuper quas ſint d, e.</s>
            <s xml:id="echoid-s19926" xml:space="preserve"> Mani-
              <lb/>
            feſtum eſt igitur, quòd ſuper totũ;</s>
            <s xml:id="echoid-s19927" xml:space="preserve"> quod cadit ſub linea d a e ad partẽ b, nõ cadit uiſus, quoniã terra
              <lb/>
            abſcondit illud nobis:</s>
            <s xml:id="echoid-s19928" xml:space="preserve"> quia extẽſio uiſus nõ eſt, niſi ſuper lineã rectam [per primã hypotheſin opti-
              <lb/>
            corum Euclidis.</s>
            <s xml:id="echoid-s19929" xml:space="preserve">] Et Euclιdes quidẽiam declarauit [16 p 3] quòd nõ egreditur à puncto cõtactus
              <lb/>
            linea inter lineã cõtingent ẽ& circulũ.</s>
            <s xml:id="echoid-s19930" xml:space="preserve"> Viſus ergo nõ cadit ſub linea d a e, ſed cadit ſuper illud, quod
              <lb/>
            eleuatur ab ea.</s>
            <s xml:id="echoid-s19931" xml:space="preserve"> Et ponã formã pyramidis tenebrarũ euenientiũ ex umbra terræ, parum ante crepu-
              <lb/>
            ſculum, quãdo eſt depreſsio ſolis plus 19 gradibus per minutũ unũ, uerbi gratia;</s>
            <s xml:id="echoid-s19932" xml:space="preserve"> aut circiter:</s>
            <s xml:id="echoid-s19933" xml:space="preserve"> ſuper
              <lb/>
            quam ſint g, e, f, c:</s>
            <s xml:id="echoid-s19934" xml:space="preserve"> totũ enim, quod cadit in hac pyramιde deſignata (cuius caput eſt f, & baſis ipſius
              <lb/>
            terra) eſt rectum ſoli, nõ apparẽs ei, neq;</s>
            <s xml:id="echoid-s19935" xml:space="preserve"> illuminatũ ab eo, & eſt in ueritate tenebroſum:</s>
            <s xml:id="echoid-s19936" xml:space="preserve"> & quod ca-
              <lb/>
            dit exterius ab ea, eſt apparẽs ſoli, & ſuper ipſum cadũt radij eius & lumẽ eius.</s>
            <s xml:id="echoid-s19937" xml:space="preserve"> Veruntamẽ quod ex
              <lb/>
            corporib.</s>
            <s xml:id="echoid-s19938" xml:space="preserve"> eſt ſubtile ualde, nõ perducit ad uiſus noſtros illud, quod
              <lb/>
              <figure xlink:label="fig-0293-01" xlink:href="fig-0293-01a" number="253">
                <variables xml:id="echoid-variables240" xml:space="preserve">h
                  <gap/>
                d a m e c k z g b</variables>
              </figure>
            ex radιo induit, ꝓpterea quòd æquãtur in uiſibus noſtris illud, qđ
              <lb/>
            ex aere ſubtile eſt intra pyramidẽ, & qđ eſt extra ipſum:</s>
            <s xml:id="echoid-s19939" xml:space="preserve"> & uidetur
              <lb/>
            æther totus in forma luminis & tenebrarum.</s>
            <s xml:id="echoid-s19940" xml:space="preserve"> Et nos quidẽ ſcimus,
              <lb/>
            quòd illud, quod cõtinet nos ex aere, & quod eſt propinquũ nobis,
              <lb/>
            eſt tenebroſum, nõ apparẽs ſoli:</s>
            <s xml:id="echoid-s19941" xml:space="preserve"> & quod procedιt in inceſſu in altũ,
              <lb/>
            aut dextrorſum, aut ſiniſtrorſum, & anterius & poſterius, eſt lumi-
              <lb/>
            noſum, apparẽs ſoli:</s>
            <s xml:id="echoid-s19942" xml:space="preserve"> & ſunt ambo cũ illo apud nos æqualiter in tota
              <lb/>
            cõprehenſione uiſus:</s>
            <s xml:id="echoid-s19943" xml:space="preserve"> & nõ apparet aliquid uiſibus noſtris ante ortũ
              <lb/>
            ſolis, & poſt occaſum ſolis, niſi ſit eleuatũ à ſuperficie horizontis, &
              <lb/>
            niſi ſit extra pyramidẽ umbræ, & niſi ſit ſpiſsius aere ſubtili.</s>
            <s xml:id="echoid-s19944" xml:space="preserve"> Manife-
              <lb/>
            ſtum eſt igitur, quòd nõ apparet uiſibus noſtris aliquid in habitudi-
              <lb/>
            ne ſplẽdoris & illuminationis, niſi per aggregationẽ triũ conditio-
              <lb/>
            num in eo:</s>
            <s xml:id="echoid-s19945" xml:space="preserve"> quarũ una eſt, ut nõ ſit ſub lιnea d a e:</s>
            <s xml:id="echoid-s19946" xml:space="preserve"> quoniã ſi eſt ſub ea,
              <lb/>
            prohibet ſphęra terræ inter ipſum & uiſum:</s>
            <s xml:id="echoid-s19947" xml:space="preserve"> quia nõ comprẽhendιt
              <lb/>
            ipſum uiſus luminoſum neq;</s>
            <s xml:id="echoid-s19948" xml:space="preserve"> tenebroſum.</s>
            <s xml:id="echoid-s19949" xml:space="preserve"> Et alia eſt, ut nõ ſit in py-
              <lb/>
            ramide umbræ:</s>
            <s xml:id="echoid-s19950" xml:space="preserve"> nã ſi eſt in ea, eſt tenebroſum, propterea quòd priua
              <lb/>
            tũ eſt facie ſolis & illuminatione ſua ab eo.</s>
            <s xml:id="echoid-s19951" xml:space="preserve"> Et alia eſt ut ſit ſpiſsius
              <lb/>
            aere ſubtili implẽte ſphæram:</s>
            <s xml:id="echoid-s19952" xml:space="preserve"> quoniã iam ſciuimus, quòd aer altior
              <lb/>
            extra pyramidẽ, cadit ſuper lineã d a e:</s>
            <s xml:id="echoid-s19953" xml:space="preserve"> & cũ illo non apparet nobis
              <lb/>
            in eo aliquid luminis, propter tenuitatem & ſubtilitatẽ ſuam, & pro
              <lb/>
            pterea quod uidemus in hoc loco, & eſt parum ante crepuſculũ, il-
              <lb/>
            lud, quod comprehẽdimus de ſphæra, tectum, nõ illuminatũ, & non
              <lb/>
            diuerſificatur pars eius à parte.</s>
            <s xml:id="echoid-s19954" xml:space="preserve"> Et ſcimus, quòd nõ eſt in eo punctũ
              <lb/>
            neq;</s>
            <s xml:id="echoid-s19955" xml:space="preserve"> locus unus, in quo aggregentur iſtæ cõditiones tres.</s>
            <s xml:id="echoid-s19956" xml:space="preserve"> Sed pun
              <lb/>
            ctum e eſt:</s>
            <s xml:id="echoid-s19957" xml:space="preserve"> ubi occurrit ultιmo ſtatui pyramidis linea d a e:</s>
            <s xml:id="echoid-s19958" xml:space="preserve"> & iã po-
              <lb/>
            ſuimus in eo duas conditiones:</s>
            <s xml:id="echoid-s19959" xml:space="preserve"> quoniã nõ eſt ſub linea d a e, nec in-
              <lb/>
            tra pyramidẽ:</s>
            <s xml:id="echoid-s19960" xml:space="preserve"> ergo cadit ſuper ipſum radius ſolis.</s>
            <s xml:id="echoid-s19961" xml:space="preserve"> Nõ ergo facit ne-
              <lb/>
            ceſſariam tenebroſitatẽ eius in oculis noſtris tũc, niſi priuatio eius à conditione tertia, quę eſt ſpiſ-
              <lb/>
            ſitudo.</s>
            <s xml:id="echoid-s19962" xml:space="preserve"> Iam ergo certificatur, quòd aer, ubi eſt punctũ e, in hoc loco eſt ſubtilis, & non perueniũt ad
              <lb/>
            ipſum uapores ſpiſsi, aſeendentes de terra, qui ſunt ſpiſsiores aere.</s>
            <s xml:id="echoid-s19963" xml:space="preserve"> Deinde poſtquã eleuatur ſol pa-
              <lb/>
            rum, & fit depreſsio eius ab horizonte 19 graduũ tantùm, & fit forma pyramidis & figura eius, ſicut
              <lb/>
            illa, ſuper quã ſunt i, m, h, k, & apparet in horizõte res luminoſa, & nõ fuerat antè illic res lum inoſa:</s>
            <s xml:id="echoid-s19964" xml:space="preserve">
              <lb/>
            ſeimus quòd ille eſt primus locorũ & hoſpitiorũ, in quo aggregãtur cõditiones tres prędictæ:</s>
            <s xml:id="echoid-s19965" xml:space="preserve"> quo-
              <lb/>
            niã ante illud parũ per illud, cuι nõ eſt quantitas, nõ fuit illic aliquid de lumine:</s>
            <s xml:id="echoid-s19966" xml:space="preserve"> & primus locorũ, in
              <lb/>
            quo aggregatur, ut non ſit ſub linea d a e, nec intret pyramidein tenebrarum, eſt punctum m.</s>
            <s xml:id="echoid-s19967" xml:space="preserve"> Ergo
              <lb/>
            punctũ m eſt primus locorũ, in quo inuẽta eſt cõditio rertia, & eſt illic ſpiſsitudo aeris.</s>
            <s xml:id="echoid-s19968" xml:space="preserve"> Ergo pũctũ
              <lb/>
            in eſt ultimus ſtatus uaporũ, & ſumma aſcẽſio eorũ:</s>
            <s xml:id="echoid-s19969" xml:space="preserve"> & nõ abbreuiãtur ab eo, neq;</s>
            <s xml:id="echoid-s19970" xml:space="preserve"> pertrãſeũt ipſum.</s>
            <s xml:id="echoid-s19971" xml:space="preserve">
              <lb/>
            Quoniã ſi abbreuiarẽtur ab eo, eſſet punctũ m in aere ſubt li, & nõ appareret nobis in eo aliquid de
              <lb/>
            lumine, ſicut nõ apparet in eo, qui eſt poſt ipſum, ad partem e:</s>
            <s xml:id="echoid-s19972" xml:space="preserve"> & ſi pertrãſirent ipſum, illuminaretur
              <lb/>
            nobis punctũ e ante hoc:</s>
            <s xml:id="echoid-s19973" xml:space="preserve"> quoniã nõ ponimus in eo, quod eſt inter m & e, in his duobus locis rẽ ſen-
              <lb/>
            </s>
          </p>
        </div>
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