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-s19973" xml:space="preserve">
              <pb o="288" file="0294" n="294" rhead="ALHAZEN OPTIC. LIB. VII."/>
            ſibilẽ.</s>
            <s xml:id="echoid-s19974" xml:space="preserve"> Ergo punctũ m eſt ultimus ſtatus, ad quẽ perueniũt uapores aſcendentes in altũ, & occurſus
              <lb/>
            lineæ d a e cõtingentis ſphærã terræ cũ linea h i.</s>
            <s xml:id="echoid-s19975" xml:space="preserve"> Quando ergo uolumus ſcire longitudinẽ eius à fa-
              <lb/>
            cie terrę, tũc nos deſcribemus altitudinis circulũ, tranſeuntẽ per centrũ ſolis, quãdo eius depreſsio
              <lb/>
            ab horizõte eſt 19 graduũ:</s>
            <s xml:id="echoid-s19976" xml:space="preserve"> & illud eſt a pud ortũ crepuſculi, ſuper quẽ ſint a, b, c, d:</s>
            <s xml:id="echoid-s19977" xml:space="preserve"> ſecabit ergo
              <gap/>
            ſphę-
              <lb/>
            ram terræ ſuper circulũ e f g h [per 1 the.</s>
            <s xml:id="echoid-s19978" xml:space="preserve"> 1 ſphær.</s>
            <s xml:id="echoid-s19979" xml:space="preserve"> Theodoſij] & linea a e k pertrãſeat per zenith ca-
              <lb/>
            pitum & per centrũ terræ, perpẽdicularis ſuper lineam b k d [per 11 p 1] ergo linea b k d ſecat terrã
              <lb/>
            in duo media, [per 17 d 1] apparẽs & occultũ.</s>
            <s xml:id="echoid-s19980" xml:space="preserve"> Apparẽs ergo eſt illud, quod eſt ſupra ipſam, ad partẽ
              <lb/>
            a, & occultum, quod eſt ad partẽ g:</s>
            <s xml:id="echoid-s19981" xml:space="preserve"> & nõ dicimus hoc, niſi dilatãdo & appropinquãdo.</s>
            <s xml:id="echoid-s19982" xml:space="preserve"> Veritas uerò
              <lb/>
            eſt, quòd apparẽs nõ eſt, niſi illud, quod eſt ſuper lineã p e q o protractã, contingentem ſphærã ſuper
              <lb/>
            punctũ uiſus:</s>
            <s xml:id="echoid-s19983" xml:space="preserve"> ueruntamen nõ eſt apud hũc or-
              <lb/>
              <figure xlink:label="fig-0294-01" xlink:href="fig-0294-01a" number="254">
                <variables xml:id="echoid-variables241" xml:space="preserve">n a d p e q o r f k h g b l c m</variables>
              </figure>
            bẽ terræ magna quãtitas.</s>
            <s xml:id="echoid-s19984" xml:space="preserve"> Et ponã arcum b c 19
              <lb/>
            graduũ, qui ſunt depreſsio ſolis apud ortũ cre-
              <lb/>
            puſculi.</s>
            <s xml:id="echoid-s19985" xml:space="preserve"> Super punctũ ergo c eſt centrum ſolis:</s>
            <s xml:id="echoid-s19986" xml:space="preserve">
              <lb/>
            faciã igitur illic ſuper ipſum punctũ, circulũ, cũ
              <lb/>
            lõgitudine quintupli & medietatis eius, quod
              <lb/>
            eſt æquale lineę e k:</s>
            <s xml:id="echoid-s19987" xml:space="preserve"> qui ſit circulus l m:</s>
            <s xml:id="echoid-s19988" xml:space="preserve"> & ſuper
              <lb/>
            ipſum ſcilicet punctũ c ſecat ſolẽ orbis a b c d:</s>
            <s xml:id="echoid-s19989" xml:space="preserve">
              <lb/>
            & continuabo lineã k g:</s>
            <s xml:id="echoid-s19990" xml:space="preserve"> deinde protrahã duas
              <lb/>
            lineas contingẽtes duos circulos ſolis & terræ
              <lb/>
            [per 17 p 3] continẽtes illuminatũ terræ à ſole,
              <lb/>
            quæ ſint m h n, l f n, cõtingẽtes terrã ſuper duo
              <lb/>
            puncta h & f:</s>
            <s xml:id="echoid-s19991" xml:space="preserve"> & ſunt termini pyramidis umbrę.</s>
            <s xml:id="echoid-s19992" xml:space="preserve">
              <lb/>
            Ergo linea m h n occurrit lineæ p o ſuper pun-
              <lb/>
            ctum q [per lẽma Procli ad 29 p 1:</s>
            <s xml:id="echoid-s19993" xml:space="preserve"> quia cõcur-
              <lb/>
            rit cũ b k d parallela ipſi p o per 28 p 1] ergo pũ-
              <lb/>
            ctum q, ſecundũ quod oſtẽdimus in figura, quę
              <lb/>
            eſt ante hãc, eſt locus luminoſus apud ortũ cre
              <lb/>
            puſculi:</s>
            <s xml:id="echoid-s19994" xml:space="preserve"> & eſt ultimus ſtatus aſcenſionis uapo-
              <lb/>
            rum.</s>
            <s xml:id="echoid-s19995" xml:space="preserve"> Cum ergo uolumus cognoſcere longitu-
              <lb/>
            dinem eius à ſuperficie terræ:</s>
            <s xml:id="echoid-s19996" xml:space="preserve"> tũc continuabi-
              <lb/>
            mus k cũ q per lineã k r q:</s>
            <s xml:id="echoid-s19997" xml:space="preserve"> & continuabo k cum
              <lb/>
            h.</s>
            <s xml:id="echoid-s19998" xml:space="preserve"> Ergo portio h g f eſt illuminata:</s>
            <s xml:id="echoid-s19999" xml:space="preserve"> quia facie ad
              <lb/>
            faciẽ reſpicit ſolem.</s>
            <s xml:id="echoid-s20000" xml:space="preserve"> Iam ergo oſtẽdimus [præ-
              <lb/>
            cedente numero] quòd ea eſt 180 grad.</s>
            <s xml:id="echoid-s20001" xml:space="preserve"> & 27
              <lb/>
            min.</s>
            <s xml:id="echoid-s20002" xml:space="preserve"> & 52 ſecũd.</s>
            <s xml:id="echoid-s20003" xml:space="preserve"> & arcus g h eſt medietas eius:</s>
            <s xml:id="echoid-s20004" xml:space="preserve">
              <lb/>
            [Quia enim l n, m n tangunt peripheriã circuli
              <lb/>
            e f g h in punctis f & h per fabricationem, erunt
              <lb/>
            anguli ad f & h recti per 18 p 3.</s>
            <s xml:id="echoid-s20005" xml:space="preserve"> Si igitur ſemidia-
              <lb/>
            metros k l, k m circuli a b c d ductas cogites:</s>
            <s xml:id="echoid-s20006" xml:space="preserve">
              <lb/>
            æquabuntur quadrata linearũ f l, f k quadrato
              <lb/>
            ſemidiametri k l per 47 p 1, per quam etiã qua-
              <lb/>
            drata linearum h m, h k æquabuntur quadrato
              <lb/>
            ſemidiametri k m:</s>
            <s xml:id="echoid-s20007" xml:space="preserve"> ſubductis igitur quadratis
              <lb/>
            ipſarũ f k, h k per 5 d 1 æqualibus, à quadratis k l, k m ſimiliter per 15 d 1 æqualibus:</s>
            <s xml:id="echoid-s20008" xml:space="preserve"> relinquẽtur qua-
              <lb/>
            drata ipſarũ f l, h m æqualia, & iccirco rectę f l, h m æquales.</s>
            <s xml:id="echoid-s20009" xml:space="preserve"> Quare cũ triangula f k l, h k m ſint æqui-
              <lb/>
            latera, erunt æquiangula, & angulus f k l æqualis angulo h k m per 8 p 1.</s>
            <s xml:id="echoid-s20010" xml:space="preserve"> Rurſus ſi ſemidiametros l c,
              <lb/>
            m c circuli l m ductas animo concipias:</s>
            <s xml:id="echoid-s20011" xml:space="preserve"> erũt triangula l k c, m k c æquilatera & æquiangula, & angu-
              <lb/>
            lus l k c æqualis angulo m k c.</s>
            <s xml:id="echoid-s20012" xml:space="preserve"> Quamobrem ſi angulis f k l, h k m è concluſo æqualibus addas angu-
              <lb/>
            los l k c, m k c æquales:</s>
            <s xml:id="echoid-s20013" xml:space="preserve"> totus angulus f k g æquabitur toti angulo h k g per 2 axio:</s>
            <s xml:id="echoid-s20014" xml:space="preserve"> & peripheria f g
              <lb/>
            peripheriæ h g per 26 p 3] & eſt grad.</s>
            <s xml:id="echoid-s20015" xml:space="preserve"> 90 & 13 min.</s>
            <s xml:id="echoid-s20016" xml:space="preserve"> & 56 ſecun.</s>
            <s xml:id="echoid-s20017" xml:space="preserve"> & illud eſt quãtitas anguli h k g:</s>
            <s xml:id="echoid-s20018" xml:space="preserve"> & iã
              <lb/>
            fuit angulus b k c 19 grad quoniã eſt depreſsio ſolis:</s>
            <s xml:id="echoid-s20019" xml:space="preserve"> ergo remanet angulus h k b 71 grad.</s>
            <s xml:id="echoid-s20020" xml:space="preserve"> 13 min.</s>
            <s xml:id="echoid-s20021" xml:space="preserve"> 56
              <lb/>
            ſecun.</s>
            <s xml:id="echoid-s20022" xml:space="preserve"> ſed angulus e k b eſt 90:</s>
            <s xml:id="echoid-s20023" xml:space="preserve"> quia rectus exiſtit.</s>
            <s xml:id="echoid-s20024" xml:space="preserve"> Ergo remanet angulus e k h 18 grad.</s>
            <s xml:id="echoid-s20025" xml:space="preserve"> 46 min.</s>
            <s xml:id="echoid-s20026" xml:space="preserve"> 4 ſe-
              <lb/>
            cun.</s>
            <s xml:id="echoid-s20027" xml:space="preserve"> Et quia linea k q diuidit eũ in duo media, & illud eſt manifeſtũ:</s>
            <s xml:id="echoid-s20028" xml:space="preserve"> [Quia enim e k, h k:</s>
            <s xml:id="echoid-s20029" xml:space="preserve"> item e q, h q
              <lb/>
            æquãtur:</s>
            <s xml:id="echoid-s20030" xml:space="preserve"> illæ per 15 d 1, quia circuli e f g h ſunt ſemidiametri:</s>
            <s xml:id="echoid-s20031" xml:space="preserve"> hæ per ſecundũ conſectariũ 36 p 3, quia
              <lb/>
            ab eodẽ puncto q peripheriã e f g h tangunt:</s>
            <s xml:id="echoid-s20032" xml:space="preserve"> & cõmunis eſt k q:</s>
            <s xml:id="echoid-s20033" xml:space="preserve"> æquabitur angulus e k q angulo h k
              <lb/>
            q per 8 p 1.</s>
            <s xml:id="echoid-s20034" xml:space="preserve"> Quare angulus e k h bifariã ſectus eſt per rectã q k] angulus igitur q k e eſt 9 grad.</s>
            <s xml:id="echoid-s20035" xml:space="preserve"> 23.</s>
            <s xml:id="echoid-s20036" xml:space="preserve"> mi.</s>
            <s xml:id="echoid-s20037" xml:space="preserve">
              <lb/>
            2 ſecund.</s>
            <s xml:id="echoid-s20038" xml:space="preserve"> ergo angulus k q e eſt cõplementũ recti [per 32 p 1:</s>
            <s xml:id="echoid-s20039" xml:space="preserve"> quia angulus ad e rectus eſt per 18 p 3]
              <lb/>
            & illud eſt 80 grad.</s>
            <s xml:id="echoid-s20040" xml:space="preserve"> 36 min.</s>
            <s xml:id="echoid-s20041" xml:space="preserve"> 58 ſecun.</s>
            <s xml:id="echoid-s20042" xml:space="preserve"> Chorda ergo eius, quę eſt linea e k, eſt 59 grad.</s>
            <s xml:id="echoid-s20043" xml:space="preserve"> 11 min.</s>
            <s xml:id="echoid-s20044" xml:space="preserve"> 48 ſecun.</s>
            <s xml:id="echoid-s20045" xml:space="preserve">
              <lb/>
            per quantitatẽ, qua eſt linea k q 60 grad.</s>
            <s xml:id="echoid-s20046" xml:space="preserve"> [ut monſtrat tabula rectarũ ſubtenſarũ in circulo.</s>
            <s xml:id="echoid-s20047" xml:space="preserve">] Verun
              <lb/>
            tamen per quantitatẽ, qua eſt linea k e 60 grad.</s>
            <s xml:id="echoid-s20048" xml:space="preserve"> erit q r k 60 grad.</s>
            <s xml:id="echoid-s20049" xml:space="preserve"> & 48 min.</s>
            <s xml:id="echoid-s20050" xml:space="preserve"> & quinq;</s>
            <s xml:id="echoid-s20051" xml:space="preserve"> ſextorũ unius
              <lb/>
            minuti:</s>
            <s xml:id="echoid-s20052" xml:space="preserve"> ſed linea k r ex illis eſt 60 grad.</s>
            <s xml:id="echoid-s20053" xml:space="preserve"> ergo remanet r q 48 min.</s>
            <s xml:id="echoid-s20054" xml:space="preserve"> & 50 ſecun.</s>
            <s xml:id="echoid-s20055" xml:space="preserve"> & eſt illud ex miliari-
              <lb/>
            bus (quibus circumferentia terræ continet 24000) milliaria, 51 & 47 minut.</s>
            <s xml:id="echoid-s20056" xml:space="preserve"> & 34 ſecun.</s>
            <s xml:id="echoid-s20057" xml:space="preserve"> & 6
              <lb/>
            partes ex 11 partib.</s>
            <s xml:id="echoid-s20058" xml:space="preserve"> ſecundis.</s>
            <s xml:id="echoid-s20059" xml:space="preserve"> Et illud eſt ultimũ, ad quod eleuantur & perueniũt
              <lb/>
            uapores aſcendentes ex terra.</s>
            <s xml:id="echoid-s20060" xml:space="preserve"> Et illud eſt, quod uoluimus.</s>
            <s xml:id="echoid-s20061" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div645" type="section" level="0" n="0">
          <head xml:id="echoid-head553" xml:space="preserve">FINIS.</head>
        </div>
      </text>
    </echo>
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