Blancanus, Josephus, Sphaera mvndi, sev cosmographia demonstratiua , ac facile methodo tradita : in qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilaei, aliorumq' ; Astronomorum adinuentis continentur ; Accessere I. Breuis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Nouum instrumentum ad Horologia

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    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div154" type="section" level="1" n="97">
          <p>
            <s xml:id="echoid-s7632" xml:space="preserve">
              <pb o="76" file="0098" n="102" rhead="De Mundi Fabrica,"/>
            read eam proportionem, quam habet 17. </s>
            <s xml:id="echoid-s7633" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s7634" xml:space="preserve">& </s>
            <s xml:id="echoid-s7635" xml:space="preserve">è contra, diametrum Lunæ ad diametrum terræ, vt 5. </s>
            <s xml:id="echoid-s7636" xml:space="preserve">ad 17.
              <lb/>
            </s>
            <s xml:id="echoid-s7637" xml:space="preserve">habita igitur hac proportione eliciemus etiam ſphærarum proportionem. </s>
            <s xml:id="echoid-s7638" xml:space="preserve">Primò mechanicè ſic; </s>
            <s xml:id="echoid-s7639" xml:space="preserve">conſtruan-
              <lb/>
            tur duæ ſphæræ inæquales ex eadẽ materia, veluti ex plumbo, minoris diameter ſit 5. </s>
            <s xml:id="echoid-s7640" xml:space="preserve">digiti, maioris vero 17. </s>
            <s xml:id="echoid-s7641" xml:space="preserve">
              <lb/>
            iam vtriuſque pondus, earum proportionem manifeſtabit; </s>
            <s xml:id="echoid-s7642" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s7643" xml:space="preserve">minoris pondus vt 1. </s>
            <s xml:id="echoid-s7644" xml:space="preserve">maioris vero vt 40. </s>
            <s xml:id="echoid-s7645" xml:space="preserve">
              <lb/>
            Quapropter Luh
              <unsure/>
            a etiam quadragies à
              <unsure/>
            terra continebitur.</s>
            <s xml:id="echoid-s7646" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7647" xml:space="preserve">Secundo ve@o Geometricè per propoſ. </s>
            <s xml:id="echoid-s7648" xml:space="preserve">vlt. </s>
            <s xml:id="echoid-s7649" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7650" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s7651" xml:space="preserve">vbi Euclides probat binas ſphæras habere inuicẽ, nõ
              <lb/>
            c
              <unsure/>
            andem proportionem, quam habent earum diametri, ſed longe diuerſam; </s>
            <s xml:id="echoid-s7652" xml:space="preserve">habere videlicet proportionem,
              <lb/>
            quæ eſt triplicata ſuarum diametrorum proportio, ideſt, ſi diametrorum proportio triplicetur, tunc euadet
              <lb/>
            proportio ſphærarum; </s>
            <s xml:id="echoid-s7653" xml:space="preserve">triplicatur autem quæuis proportio hoc modo, ſit v.</s>
            <s xml:id="echoid-s7654" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7655" xml:space="preserve">propor@@o 1. </s>
            <s xml:id="echoid-s7656" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s7657" xml:space="preserve">triplicanda:
              <lb/>
            </s>
            <s xml:id="echoid-s7658" xml:space="preserve">accipia@tur, ſiue ſubdantur alij duo termini eandem rationem continuãtes, ita vt ſint 4. </s>
            <s xml:id="echoid-s7659" xml:space="preserve">numeri tales; </s>
            <s xml:id="echoid-s7660" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7661" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7662" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7663" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7664" xml:space="preserve">
              <lb/>
            inter quos eſt eadem ratio, quæ inter duos priores; </s>
            <s xml:id="echoid-s7665" xml:space="preserve">eaque dicitur triplicata, quia ter ibi reperitur; </s>
            <s xml:id="echoid-s7666" xml:space="preserve">primo eſt
              <lb/>
            inter primos duos 1. </s>
            <s xml:id="echoid-s7667" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7668" xml:space="preserve">ſecundo inter ſecundum, & </s>
            <s xml:id="echoid-s7669" xml:space="preserve">tertium 2. </s>
            <s xml:id="echoid-s7670" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7671" xml:space="preserve">tertio inter tertium, & </s>
            <s xml:id="echoid-s7672" xml:space="preserve">quartum 4. </s>
            <s xml:id="echoid-s7673" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7674" xml:space="preserve">propor-
              <lb/>
            tio igitur primi ad vltimum hoc eſt 1. </s>
            <s xml:id="echoid-s7675" xml:space="preserve">ad 8. </s>
            <s xml:id="echoid-s7676" xml:space="preserve">eſt triplicata proportionis 1. </s>
            <s xml:id="echoid-s7677" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s7678" xml:space="preserve">quamobrem ſi ſint duæ ſphæræ,
              <lb/>
            quarũ diametri ſint vt 1. </s>
            <s xml:id="echoid-s7679" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s7680" xml:space="preserve">ſphæræ ipſe erunt inuicem, vt 1. </s>
            <s xml:id="echoid-s7681" xml:space="preserve">ad 8. </s>
            <s xml:id="echoid-s7682" xml:space="preserve">ideſt minor a maiore octies adæquabitur. </s>
            <s xml:id="echoid-s7683" xml:space="preserve">
              <lb/>
            hanc Euclidis propoſitionem experiri facilè poſſumus in ſphæris eiuſdem materię, & </s>
            <s xml:id="echoid-s7684" xml:space="preserve">vniformis quantitatis,
              <unsure/>
              <lb/>
            quia in hoc caſu maior ſphæra octies idem penderet, quod minor ſemel.</s>
            <s xml:id="echoid-s7685" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7686" xml:space="preserve">Cum igitur iam conſtet diametrum Lunæ ad diametrum terræ eſſe, vt 5. </s>
            <s xml:id="echoid-s7687" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s7688" xml:space="preserve">ſi hæc proportio triplice-
              <lb/>
            tur, vti modo docuimus, erunt hi 4. </s>
            <s xml:id="echoid-s7689" xml:space="preserve">numeri eam triplicantes 5. </s>
            <s xml:id="echoid-s7690" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7691" xml:space="preserve">57
              <emph style="super">4</emph>
              <emph style="super">5</emph>
            . </s>
            <s xml:id="echoid-s7692" xml:space="preserve">196. </s>
            <s xml:id="echoid-s7693" xml:space="preserve">ratio igitur primi 5. </s>
            <s xml:id="echoid-s7694" xml:space="preserve">ad vltimum
              <lb/>
            196. </s>
            <s xml:id="echoid-s7695" xml:space="preserve">erit triplicata priorum duorum, & </s>
            <s xml:id="echoid-s7696" xml:space="preserve">proinde erit proportio Lunę ad terram, vt 5. </s>
            <s xml:id="echoid-s7697" xml:space="preserve">ad 196. </s>
            <s xml:id="echoid-s7698" xml:space="preserve">primus autem 5.
              <lb/>
            </s>
            <s xml:id="echoid-s7699" xml:space="preserve">continetur in ſecundo 196. </s>
            <s xml:id="echoid-s7700" xml:space="preserve">tricies, & </s>
            <s xml:id="echoid-s7701" xml:space="preserve">nouies, & </s>
            <s xml:id="echoid-s7702" xml:space="preserve">paulo plus, vt patet per diuiſionem maioris per minorem. </s>
            <s xml:id="echoid-s7703" xml:space="preserve">
              <lb/>
            Eſt igitur Lunæ globus quadrageſima ferè pars terreſtris globi, ſiu
              <unsure/>
            e terra adęquat Lunam quadragies. </s>
            <s xml:id="echoid-s7704" xml:space="preserve">quod
              <lb/>
            c
              <unsure/>
            rat vltimus ſcopus. </s>
            <s xml:id="echoid-s7705" xml:space="preserve">Cur ergo videtur tantum pedalis? </s>
            <s xml:id="echoid-s7706" xml:space="preserve">reſpondent optici id prouenire ex nimia a nobis di-
              <lb/>
            ſtantia, experimur enim quotidie, quæ a longè videntur parua videri, & </s>
            <s xml:id="echoid-s7707" xml:space="preserve">quò
              <unsure/>
            magis à longè, eo minora ap-
              <lb/>
            parere.</s>
            <s xml:id="echoid-s7708" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7709" xml:space="preserve">Cur præterea ſæpe prope horizontem, vel in nebula, vel fumo, maior ſpectatur? </s>
            <s xml:id="echoid-s7710" xml:space="preserve">reſpondent optici ea,
              <lb/>
            quæ videntur per diuerſa media, ideſt, diuerſæ tranſparentiæ, ita vt craſſius fit ad obiectum, rarius ad ocu-
              <lb/>
            lum, tunc maiora ſolito videri. </s>
            <s xml:id="echoid-s7711" xml:space="preserve">ſic quæ exiſtũt in aqua maiora quam ſint apparent, quia videntur per aquam
              <lb/>
            primo quæ craſſior eſt aere.</s>
            <s xml:id="echoid-s7712" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div158" type="section" level="1" n="98">
          <head xml:id="echoid-head108" style="it" xml:space="preserve">De altitudine Lunarium Montium. Cap. I X.</head>
          <p>
            <s xml:id="echoid-s7713" xml:space="preserve">SV perius probauimus Lunæ faciem, quæ terras deſpectat eſſe montibus, ac concauitatibus aſperam. </s>
            <s xml:id="echoid-s7714" xml:space="preserve">ſunt
              <lb/>
            @amen nonnulli, qui adeo ab Lunæ inæqualitatibus abhorreant, vt propterea velint has eminentias, atq;
              <lb/>
            </s>
            <s xml:id="echoid-s7715" xml:space="preserve">depreſſiones ſaluari poſſe per partes denſiores, ac rariores; </s>
            <s xml:id="echoid-s7716" xml:space="preserve">quæ omnes vnica Lunæ ſphæricitate cõpræhen-
              <lb/>
            dantur. </s>
            <s xml:id="echoid-s7717" xml:space="preserve">quidquid ſit haſce eminentias, ſiue montes, menſurare aggredimur. </s>
            <s xml:id="echoid-s7718" xml:space="preserve">Vtautem ſupra dictum eſt; </s>
            <s xml:id="echoid-s7719" xml:space="preserve">ver-
              <lb/>
            tices horum montium intra partem adhuc tenebroſam exiſtentes, lumine Solis præuenti, ſicque cęteris par-
              <lb/>
            @ibus prius illuſtrati, ſe produnt. </s>
            <s xml:id="echoid-s7720" xml:space="preserve">tantaq; </s>
            <s xml:id="echoid-s7721" xml:space="preserve">eſt eorum diſtantia a confinio luminis, & </s>
            <s xml:id="echoid-s7722" xml:space="preserve">vmbrę, vt ſit quaſi pars vi-
              <lb/>
            geſima totius lunaris diametri, vt diligenti inſpectori conſtare po-
              <lb/>
            reſt. </s>
            <s xml:id="echoid-s7723" xml:space="preserve">hoc aſſumpto intelligatur lunaris globus C A E. </s>
            <s xml:id="echoid-s7724" xml:space="preserve">centrũ E. </s>
            <s xml:id="echoid-s7725" xml:space="preserve">di-
              <lb/>
              <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a" number="73">
                <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0098-01"/>
              </figure>
            metiens C F. </s>
            <s xml:id="echoid-s7726" xml:space="preserve">quę ad terrę diametrum eſt ferè, vt 2. </s>
            <s xml:id="echoid-s7727" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s7728" xml:space="preserve">cum autem
              <lb/>
            terræ ſemidiam. </s>
            <s xml:id="echoid-s7729" xml:space="preserve">contineat milliar a aſtronomica 3,436, {1/2}. </s>
            <s xml:id="echoid-s7730" xml:space="preserve">erit ſemi-
              <lb/>
            diam. </s>
            <s xml:id="echoid-s7731" xml:space="preserve">E C. </s>
            <s xml:id="echoid-s7732" xml:space="preserve">iuxta allatam rationem 981. </s>
            <s xml:id="echoid-s7733" xml:space="preserve">milliaria. </s>
            <s xml:id="echoid-s7734" xml:space="preserve">ſit autem pars fi-
              <lb/>
            guræ vbi C. </s>
            <s xml:id="echoid-s7735" xml:space="preserve">ea Lunæ pars, quã nos
              <unsure/>
            quotidie videmus, ſeu quę deor-
              <lb/>
            ſum vergit, & </s>
            <s xml:id="echoid-s7736" xml:space="preserve">per punctum C. </s>
            <s xml:id="echoid-s7737" xml:space="preserve">tranſeat E C. </s>
            <s xml:id="echoid-s7738" xml:space="preserve">confinium lucis, & </s>
            <s xml:id="echoid-s7739" xml:space="preserve">te-
              <lb/>
            nebrarum. </s>
            <s xml:id="echoid-s7740" xml:space="preserve">linea G C D. </s>
            <s xml:id="echoid-s7741" xml:space="preserve">referat radium Sol
              <unsure/>
            is exiſtẽtis ad partes G.
              <lb/>
            </s>
            <s xml:id="echoid-s7742" xml:space="preserve">tangentem Lunam in C. </s>
            <s xml:id="echoid-s7743" xml:space="preserve">vbi non ſunt montes; </s>
            <s xml:id="echoid-s7744" xml:space="preserve">qui vlterius produ-
              <lb/>
            ctus occurrat vertici D. </s>
            <s xml:id="echoid-s7745" xml:space="preserve">exiſtenti adhuc in parte tenebroſa, eumq; </s>
            <s xml:id="echoid-s7746" xml:space="preserve">
              <lb/>
            illuſtret. </s>
            <s xml:id="echoid-s7747" xml:space="preserve">ducatur linea E A D. </s>
            <s xml:id="echoid-s7748" xml:space="preserve">linea D C. </s>
            <s xml:id="echoid-s7749" xml:space="preserve">eſt diſtãtia verticis à
              <unsure/>
            con-
              <lb/>
            finio, quam ponimus eſſe partem vigeſimam totius C F. </s>
            <s xml:id="echoid-s7750" xml:space="preserve">ſiue deci-
              <lb/>
            mam ipſius C E. </s>
            <s xml:id="echoid-s7751" xml:space="preserve">erit igitur milliaria ferè 98. </s>
            <s xml:id="echoid-s7752" xml:space="preserve">cum tota E C. </s>
            <s xml:id="echoid-s7753" xml:space="preserve">ſit mil-
              <lb/>
            liaria 981. </s>
            <s xml:id="echoid-s7754" xml:space="preserve">in triangulo igitur E C D. </s>
            <s xml:id="echoid-s7755" xml:space="preserve">rectangulo, quia angulus ad C. </s>
            <s xml:id="echoid-s7756" xml:space="preserve">eſt rectus per 16. </s>
            <s xml:id="echoid-s7757" xml:space="preserve">tertij Elem. </s>
            <s xml:id="echoid-s7758" xml:space="preserve">notum eſt
              <lb/>
            latus E C. </s>
            <s xml:id="echoid-s7759" xml:space="preserve">981. </s>
            <s xml:id="echoid-s7760" xml:space="preserve">milliariorum. </s>
            <s xml:id="echoid-s7761" xml:space="preserve">latus vero C D. </s>
            <s xml:id="echoid-s7762" xml:space="preserve">98. </s>
            <s xml:id="echoid-s7763" xml:space="preserve">mill. </s>
            <s xml:id="echoid-s7764" xml:space="preserve">& </s>
            <s xml:id="echoid-s7765" xml:space="preserve">angulus ad C. </s>
            <s xml:id="echoid-s7766" xml:space="preserve">notus, quia rectus. </s>
            <s xml:id="echoid-s7767" xml:space="preserve">ſi igitur fiat trian-
              <lb/>
            gulum paruum rectangulum, habens latera circa angulum rectum prædictis analoga, erit totum triangulum
              <lb/>
            proport onale triangulo magno lunari per 6. </s>
            <s xml:id="echoid-s7768" xml:space="preserve">ſexti Elem. </s>
            <s xml:id="echoid-s7769" xml:space="preserve">quod etiam experientia conf@rmari poteſt. </s>
            <s xml:id="echoid-s7770" xml:space="preserve">in hoc
              <lb/>
            igitur paruo triangulo per circinum diligenter expendatur pars A D. </s>
            <s xml:id="echoid-s7771" xml:space="preserve">quot ſcilicet milliar. </s>
            <s xml:id="echoid-s7772" xml:space="preserve">contineat ex ijs,
              <lb/>
            quæ ſunt in latere D C. </s>
            <s xml:id="echoid-s7773" xml:space="preserve">vel E C. </s>
            <s xml:id="echoid-s7774" xml:space="preserve">parui trianguli, & </s>
            <s xml:id="echoid-s7775" xml:space="preserve">m
              <unsure/>
            anife
              <unsure/>
            ſta erit altitudo montis A D. </s>
            <s xml:id="echoid-s7776" xml:space="preserve">eritque quaſi mil-
              <lb/>
            liaria quatuor.</s>
            <s xml:id="echoid-s7777" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7778" xml:space="preserve">Aliter geometricè ſic; </s>
            <s xml:id="echoid-s7779" xml:space="preserve">quadrata laterum in numeris congnitorum E C. </s>
            <s xml:id="echoid-s7780" xml:space="preserve">C D. </s>
            <s xml:id="echoid-s7781" xml:space="preserve">accipiantur, ſimulque addan-
              <lb/>
            tur, efficientque hunc numer. </s>
            <s xml:id="echoid-s7782" xml:space="preserve">971,965. </s>
            <s xml:id="echoid-s7783" xml:space="preserve">qui per 47. </s>
            <s xml:id="echoid-s7784" xml:space="preserve">primi Elem. </s>
            <s xml:id="echoid-s7785" xml:space="preserve">erit æqualis quadra@o numero lineæ E D.</s>
            <s xml:id="echoid-s7786" xml:space="preserve">
              <unsure/>
              <lb/>
            qua propter radix quadrata prædicti numeri, quæ eſt 985. </s>
            <s xml:id="echoid-s7787" xml:space="preserve">ferè, erit ipſa linea E D. </s>
            <s xml:id="echoid-s7788" xml:space="preserve">continens mill
              <unsure/>
            iaria 985.</s>
            <s xml:id="echoid-s7789" xml:space="preserve">
              <unsure/>
              <lb/>
            à qua ab@ata linea E A. </s>
            <s xml:id="echoid-s7790" xml:space="preserve">milliaria 981. </s>
            <s xml:id="echoid-s7791" xml:space="preserve">remanet ipſa A D. </s>
            <s xml:id="echoid-s7792" xml:space="preserve">quatuor ferè miliar. </s>
            <s xml:id="echoid-s7793" xml:space="preserve">pro altitudine montis. </s>
            <s xml:id="echoid-s7794" xml:space="preserve">Eadem
              <lb/>
            ratiocinatione poſſumus inueſtigare profunditatem concauitatum illarum, quæ ſunt in parte illuminata
              <lb/>
            propè confinium.</s>
            <s xml:id="echoid-s7795" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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