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-div635" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s19712" xml:space="preserve">
              <pb o="284" file="0290" n="290" rhead="ALHAZEN"/>
            diximus:</s>
            <s xml:id="echoid-s19713" xml:space="preserve"> nec eſt aer implens totam ſphęram:</s>
            <s xml:id="echoid-s19714" xml:space="preserve"> quoniam, ut præmiſimus, ſuper totum aerem aut plu-
              <lb/>
            rimum eius, ſemper cadit radius ſolis nocte & die:</s>
            <s xml:id="echoid-s19715" xml:space="preserve"> & nõ apparet illud in ipſo, propter ipſius ſubtili-
              <lb/>
            tatem.</s>
            <s xml:id="echoid-s19716" xml:space="preserve"> Et ſuper terram non eſt corpus ſpiſsius aere, niſi uapores aſcendẽtes, quibus non deeſt ſem-
              <lb/>
            per, quin illuminentur à ſole.</s>
            <s xml:id="echoid-s19717" xml:space="preserve"> Tunc uerò, quando pyramis umbræ ab eo remouetur, quod de uapo-
              <lb/>
            rum ſphæra terram continente uiſus noſtri conſequuntur, & recipit eos corpus ſolis, & cadunt ſu-
              <lb/>
            per eos radij eius, ſuſpenditur cum eo radius, & defert ipſum nobis, & conſequuntur ipſum uiſus
              <lb/>
            noſtri, & uidetur à nobis eius lumen, ſicut uidemus ipſum apparere in nubibus ex coloratione hu-
              <lb/>
            miditatum aſcen dentiũ, & ſicut colores, qui in roribus uidentur, in forma portionis circuli, & alio-
              <lb/>
            rum modorum.</s>
            <s xml:id="echoid-s19718" xml:space="preserve"> Quãdo ergo uolumus ſcire, quanta ſit ultima eleuatio illorũ uaporum à ſuperficie
              <lb/>
            terræ:</s>
            <s xml:id="echoid-s19719" xml:space="preserve"> tunc ad eam cognitionem præmittũtur quatuor res, quarum nulla excuſatur, & præter ipſas
              <lb/>
            nulla alia re indigemus, ita ut nõ poſsit fieri per minus, nec ſit neceſſarium plus.</s>
            <s xml:id="echoid-s19720" xml:space="preserve"> Illa autem quatuor
              <lb/>
            ſunt:</s>
            <s xml:id="echoid-s19721" xml:space="preserve"> corpus terræ:</s>
            <s xml:id="echoid-s19722" xml:space="preserve"> corpus ſolis:</s>
            <s xml:id="echoid-s19723" xml:space="preserve"> longitudo centri ſolis à centro terræ in omni ſitu:</s>
            <s xml:id="echoid-s19724" xml:space="preserve"> & quanta ſit de-
              <lb/>
            preſsio ſolis ab horizonte, donec appareat crepuſculum matutinum.</s>
            <s xml:id="echoid-s19725" xml:space="preserve"> Corpus autem terræ eſt ſicut
              <lb/>
            inſtrumentum omnium aliorum:</s>
            <s xml:id="echoid-s19726" xml:space="preserve"> & quantitas circuli magni continentis eam, ſecũdum quod dixe-
              <lb/>
            runt ſapientes, & ſignificauerunt illud per propoſitiones certas, eſt 24000 milliaria.</s>
            <s xml:id="echoid-s19727" xml:space="preserve"> Et dixerunt,
              <lb/>
            quòd per quãtitatem, qua medietas diametri terræ eſt pars una, eſt medietas diametri ſolis quinq;</s>
            <s xml:id="echoid-s19728" xml:space="preserve">
              <lb/>
            partes, & medietas partis:</s>
            <s xml:id="echoid-s19729" xml:space="preserve"> & per eam eſt longitudo centri ſolis à cẽtro terræ in longitudine media,
              <lb/>
            (non in omni ſitu) mille & centum & circiter decem partes:</s>
            <s xml:id="echoid-s19730" xml:space="preserve"> & quòd depreſsio ſolis ab horizonte,
              <lb/>
            cum oritur crepuſculum, eſt 18 gradus:</s>
            <s xml:id="echoid-s19731" xml:space="preserve"> & iã inuenitur ſuper 19:</s>
            <s xml:id="echoid-s19732" xml:space="preserve"> & ſuper hoc fabricabo ſupputatio-
              <lb/>
            nem noſtram:</s>
            <s xml:id="echoid-s19733" xml:space="preserve"> quoniã cum narrator rei eſt cũ additione in ea, dignior eſt, ut recipiatur ſermo eius,
              <lb/>
            cum non contradicit ei alius:</s>
            <s xml:id="echoid-s19734" xml:space="preserve"> quandoquidem narrator cũ additione ſcit, quod non ſcit alius, & con
              <lb/>
            ſequitur, quod non conſequitur alius.</s>
            <s xml:id="echoid-s19735" xml:space="preserve"> Nã qui narrat de aliquo, quod uiderit illud, antequam uiderit
              <lb/>
            ipſum alius, dignior eſt, ut conſequatur, quod intendit, quando nõ exiſtimatur de eo ſuſpicio.</s>
            <s xml:id="echoid-s19736" xml:space="preserve"> Præ-
              <lb/>
            mittam igitur ad illud, quod inter manus meas eſt, propoſitiones quaſdam multi iuuaminis.</s>
            <s xml:id="echoid-s19737" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div636" type="section" level="0" n="0">
          <head xml:id="echoid-head548" xml:space="preserve" style="it">2. Si ſphæricũ luminoſum illuminet opacum æquale: hemiſphæriũ illuminabit. Vitell. 26 p 2.</head>
          <p>
            <s xml:id="echoid-s19738" xml:space="preserve">DIco ergo, quòd omnium duarum ſphærarum æqualium, inter
              <lb/>
              <figure xlink:label="fig-0290-01" xlink:href="fig-0290-01a" number="249">
                <variables xml:id="echoid-variables236" xml:space="preserve">g a e h c d b z</variables>
              </figure>
            quas non eſt aliud corpus, quod unam earum alteri abſcondat:</s>
            <s xml:id="echoid-s19739" xml:space="preserve">
              <lb/>
            illud, quod ex unaquaq;</s>
            <s xml:id="echoid-s19740" xml:space="preserve"> earum uerſa facie reſpicit alteram, eſt
              <lb/>
            medietas eius æqualiter.</s>
            <s xml:id="echoid-s19741" xml:space="preserve"> Et ſignifico per uerſam faciẽ unius reſpectu
              <lb/>
            alterius:</s>
            <s xml:id="echoid-s19742" xml:space="preserve"> quòd ſi una earum eſt luminoſa, & altera recipiẽs lumen, illu-
              <lb/>
            minatur, & relucet medietas recipientis lumen.</s>
            <s xml:id="echoid-s19743" xml:space="preserve"> Cuius exemplum eſt,
              <lb/>
            ut ſint duæ ſphæræ a & b æquales:</s>
            <s xml:id="echoid-s19744" xml:space="preserve"> & pono, ut aliqua ſuperficies plana
              <lb/>
            tranſeat per centrũ utriuſq;</s>
            <s xml:id="echoid-s19745" xml:space="preserve">: ſecabit ergo duas ſphæras ſuper duos cir-
              <lb/>
            culos æquales, & in ſuperficie una [per 1th.</s>
            <s xml:id="echoid-s19746" xml:space="preserve"> 1 ſphær.</s>
            <s xml:id="echoid-s19747" xml:space="preserve"> Theodoſij.</s>
            <s xml:id="echoid-s19748" xml:space="preserve">] Sint
              <lb/>
            ergo illi duo circuli a g h, b d c:</s>
            <s xml:id="echoid-s19749" xml:space="preserve"> & cõtinuabo a cum b:</s>
            <s xml:id="echoid-s19750" xml:space="preserve"> & protrahã duas
              <lb/>
            lineas a g, b d perpendiculares ſuper lineam a b:</s>
            <s xml:id="echoid-s19751" xml:space="preserve"> [per 11 p 1] ergo ipſæ
              <lb/>
            ſunt æquidiſtantes [per 28 p 1] & continuabo g cum d.</s>
            <s xml:id="echoid-s19752" xml:space="preserve"> Et quoniã duæ
              <lb/>
            lineæ a g, b d ſunt ęquales [per 15 d 1:</s>
            <s xml:id="echoid-s19753" xml:space="preserve"> quia ſunt ſemidiametri ęqualium
              <lb/>
            circulorum] & æquidiſtantes [è cõcluſo] duæ lineæ a b, g d ſimiliter
              <lb/>
            erunt æquales & æquidiſtantes:</s>
            <s xml:id="echoid-s19754" xml:space="preserve"> [per 33 p 1] ergo duo] anguli ad g & d
              <lb/>
            ſunt recti:</s>
            <s xml:id="echoid-s19755" xml:space="preserve"> [per ſecundam partem 34 p 1] ergo linea g d eſt contingens
              <lb/>
            duos circulos [per conſectarium 16 p 3.</s>
            <s xml:id="echoid-s19756" xml:space="preserve">] Et quando nos protrahemus
              <lb/>
            g a & b d ſecundum rectitudinem, ad duas circumferentias duorũ cir-
              <lb/>
            culorum, uſq;</s>
            <s xml:id="echoid-s19757" xml:space="preserve"> ad duo puncta e & z, deinde cõtinuabimus e cum z:</s>
            <s xml:id="echoid-s19758" xml:space="preserve"> erit
              <lb/>
            recta linea e z contingens duos circulos [ijſdem de cauſsis, quibus d g
              <lb/>
            tangere oſtenſa eſt:</s>
            <s xml:id="echoid-s19759" xml:space="preserve">] & erit una quæq;</s>
            <s xml:id="echoid-s19760" xml:space="preserve"> duarum portionum g h e, d c z,
              <lb/>
            quarum una eſt uerſa facie ad alterã, medietas circuli [per 17 d 1] quo-
              <lb/>
            niam unam quamq;</s>
            <s xml:id="echoid-s19761" xml:space="preserve"> earum fecat diameter circuli.</s>
            <s xml:id="echoid-s19762" xml:space="preserve"> Et ſimiliter cõtingit
              <lb/>
            in omnibus ſuperficiebus planis, quæ tranſeunt per duo centra duarũ
              <lb/>
            ſphærarum.</s>
            <s xml:id="echoid-s19763" xml:space="preserve"> Iam igitur declaratum eſt, quòd lineæ egredientes ex una duarum ſphærarum ad alte-
              <lb/>
            ram, contingunt utraſq;</s>
            <s xml:id="echoid-s19764" xml:space="preserve"> ſimul, & comprehendunt ex unaquaque earum medietatem.</s>
            <s xml:id="echoid-s19765" xml:space="preserve"> Et illud eſt,
              <lb/>
            quod declarare uoluimus.</s>
            <s xml:id="echoid-s19766" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div638" type="section" level="0" n="0">
          <head xml:id="echoid-head549" xml:space="preserve" style="it">3. Si ſphæricum luminoſum illuminet opacum min{us}: pl{us} hemiſphærio illuminabit. Vi-
            <lb/>
          tell. 27 p 2.</head>
          <p>
            <s xml:id="echoid-s19767" xml:space="preserve">QVòd ſi una duarum ſphærarum eſt maior altera:</s>
            <s xml:id="echoid-s19768" xml:space="preserve"> tũc illud, quod ex minore uerſa facie reſpi-
              <lb/>
            cit maiorem, eſt plus medietate minoris:</s>
            <s xml:id="echoid-s19769" xml:space="preserve"> & quod ex maiore uerſa facie reſpicit minorem,
              <lb/>
            eſt minus medietate maioris.</s>
            <s xml:id="echoid-s19770" xml:space="preserve"> Cuius exemplum eſt, ut ſint duæ ſphæræ a & b:</s>
            <s xml:id="echoid-s19771" xml:space="preserve"> & ſphæra a ſit
              <lb/>
            maior.</s>
            <s xml:id="echoid-s19772" xml:space="preserve"> Protrahã ergo ſuperficiẽ planã, tranſeuntẽ per cẽtra utriuſq;</s>
            <s xml:id="echoid-s19773" xml:space="preserve">: ſecabit ergo utrãq;</s>
            <s xml:id="echoid-s19774" xml:space="preserve"> earũ in duo
              <lb/>
            media ſuք duos circulos a g d, b e z [per 1 the.</s>
            <s xml:id="echoid-s19775" xml:space="preserve"> 1 ſphęr.</s>
            <s xml:id="echoid-s19776" xml:space="preserve">] & cõtinuabo a cũ b, & protrahã ipſam ſecũdũ
              <lb/>
            rectitudinẽ in partẽ h:</s>
            <s xml:id="echoid-s19777" xml:space="preserve"> & ponã proportionẽ medietatis diametri circuli a g d ad medietatẽ diametri
              <lb/>
            circuli b e z, ſicut ꝓportio a h ad b h.</s>
            <s xml:id="echoid-s19778" xml:space="preserve"> Eius uerò acceptio eſt prõpta ex tractatu ſexto & ꝗnto Eucli-
              <lb/>
            dis [ſi enim trib.</s>
            <s xml:id="echoid-s19779" xml:space="preserve"> rectis datis, differẽtia nẽpe ſemidiametrorũ circulorũ a & b:</s>
            <s xml:id="echoid-s19780" xml:space="preserve"> ſemidiametro b c mi-
              <lb/>
            noris circuli, & ipſa a b, inueniatur ք 12 p 6 quarta ꝓportionalis b h:</s>
            <s xml:id="echoid-s19781" xml:space="preserve"> erit ք 18 p 5 ut a d ſemidiameter
              <lb/>
            </s>
          </p>
        </div>
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