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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        <div xml:id="echoid-div9" type="section" level="1" n="8">
          <pb o="1" file="0017" n="17"/>
        </div>
        <div xml:id="echoid-div10" type="section" level="1" n="9">
          <head xml:id="echoid-head11" xml:space="preserve">APPARATVS
            <lb/>
          AD SPHÆRAM.</head>
          <p>
            <s xml:id="echoid-s256" xml:space="preserve">QVoniam vt rectè Plato in Epin. </s>
            <s xml:id="echoid-s257" xml:space="preserve">dixit Geometria, & </s>
            <s xml:id="echoid-s258" xml:space="preserve">Arithmetica, veluti duabus ali@
              <lb/>
            Aſtronomia indiget, quibus ad Aſtra, atq́; </s>
            <s xml:id="echoid-s259" xml:space="preserve">adeò per vniuerſum Mundum euolare
              <lb/>
            poſſit, ideo</s>
          </p>
          <p>
            <s xml:id="echoid-s260" xml:space="preserve">Primo ſuppono auditorem, aut lectorem huius Sphæræ ex Geometria ſaltem Defi-
              <lb/>
            nitiones, reliquaque principia Geometriæ, quæ primo Euclidis libro pręmittun-
              <lb/>
            tur, percepiſſe. </s>
            <s xml:id="echoid-s261" xml:space="preserve">porrò quo pluribus Geometricis rebus fuerit inſtructus, eò melius,
              <lb/>
            ac facilius, quæ dicenda ſunt, arripiet: </s>
            <s xml:id="echoid-s262" xml:space="preserve">vnde in Academijs noſtræ Societatis, & </s>
            <s xml:id="echoid-s263" xml:space="preserve">
              <lb/>
            quidem optima Methodo, ſolent Noſtri ſaltem primum Euclidis Elementum,
              <lb/>
            auditoribus noſtris prælegere, antequam ad Sphæræ explicationẽ aggrediantur.
              <lb/>
            </s>
            <s xml:id="echoid-s264" xml:space="preserve">Secundo ex Arithmetica opus cſt, ſaltem numerorum Numerationem callere, nec-
              <lb/>
            non leuiter ſaltem intellexiſle, quid Additio, quid Subtractio, quid Multiplicatio, quid Diuiſio, quid Au-
              <lb/>
            rea regula, ſeu trium, quid radix quadrata. </s>
            <s xml:id="echoid-s265" xml:space="preserve">Demum Fractorum numerorum Numerationem, ſeu valorem
              <lb/>
            cognoſcere. </s>
            <s xml:id="echoid-s266" xml:space="preserve">Quapropter operæ pretium eſſet ante huius Sphæræ prælectiones ex Arithmetica practica
              <lb/>
            P.</s>
            <s xml:id="echoid-s267" xml:space="preserve">Clauij, quæ breuis, & </s>
            <s xml:id="echoid-s268" xml:space="preserve">clara eſt, iſta aliquatenus prælibaſſe.</s>
            <s xml:id="echoid-s269" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s270" xml:space="preserve">Ad hæc, vt ea, quæ dicturi ſumus, ea perſpicuitate demonſtrare poſſimus, quæ ab omnibus, vel Mathema-
              <lb/>
            tico puluere vix tinctis in telligi queant, opus ea eſt, quæ ſequuntur præmittere.</s>
            <s xml:id="echoid-s271" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div11" type="section" level="1" n="10">
          <head xml:id="echoid-head12" style="it" xml:space="preserve">Circulum datum iu partes, ſeu gradus 360. diuidere. # Præpoſ. 1.</head>
          <p>
            <s xml:id="echoid-s272" xml:space="preserve">SIT datus circulus B C D E. </s>
            <s xml:id="echoid-s273" xml:space="preserve">cuius centrum A. </s>
            <s xml:id="echoid-s274" xml:space="preserve">eum ſic in gradus 360. </s>
            <s xml:id="echoid-s275" xml:space="preserve">diuides. </s>
            <s xml:id="echoid-s276" xml:space="preserve">Primo per centrum A. </s>
            <s xml:id="echoid-s277" xml:space="preserve">du-
              <lb/>
            catur duæ diametri B D. </s>
            <s xml:id="echoid-s278" xml:space="preserve">& </s>
            <s xml:id="echoid-s279" xml:space="preserve">E C. </s>
            <s xml:id="echoid-s280" xml:space="preserve">quæ ſe mutuo ad angulos rectos ſecent: </s>
            <s xml:id="echoid-s281" xml:space="preserve">ſic enim circulus erit in quatuor
              <lb/>
            partes æquales diuiſus, quæ quadrantes appellantur, quorum quilibet gr. </s>
            <s xml:id="echoid-s282" xml:space="preserve">90. </s>
            <s xml:id="echoid-s283" xml:space="preserve">cõtinebit. </s>
            <s xml:id="echoid-s284" xml:space="preserve">Quod autem æquales
              <lb/>
              <figure xlink:label="fig-0017-01" xlink:href="fig-0017-01a" number="4">
                <image file="0017-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0017-01"/>
              </figure>
            ſint, patet ex ſcholio 27. </s>
            <s xml:id="echoid-s285" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s286" xml:space="preserve">3. </s>
            <s xml:id="echoid-s287" xml:space="preserve">Euclidis, quod etiã circino exacte
              <lb/>
            acuminato experiri potes. </s>
            <s xml:id="echoid-s288" xml:space="preserve">Enimuero perſpicuitatis cauſa vtemur
              <lb/>
            huiuſmodi probationibus ab experientia deſumptis, quæ quamu@s
              <lb/>
            Geometricam illam præciſionẽ non aſſe quantur, nihilominus eui-
              <lb/>
            dentiam ac certitudinẽ nullo negotio inducunt. </s>
            <s xml:id="echoid-s289" xml:space="preserve">Etenim in rebus
              <lb/>
            Geometricis, & </s>
            <s xml:id="echoid-s290" xml:space="preserve">Arithmetricis ſiue in Magnitudin bus & </s>
            <s xml:id="echoid-s291" xml:space="preserve">Nume-
              <lb/>
            ris, experientiæ demonſtrationibus æquiualent. </s>
            <s xml:id="echoid-s292" xml:space="preserve">Non omnino à
              <lb/>
            Geometricis tamen rationibus abſtinebimus, ſed in gratiam eorũ,
              <lb/>
            qui Geometrica callent, citabimus vbique, cũ è re noſtra fuerit, eas
              <lb/>
            Geometrarũ demonſtrationes, ex quibus res propoſica comproba-
              <lb/>
            tur, vti in præſentia fecimus.</s>
            <s xml:id="echoid-s293" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s294" xml:space="preserve">Circinum poſtea exacte acuminatũ dilata ad interuallum ſemi-
              <lb/>
            diametri A B. </s>
            <s xml:id="echoid-s295" xml:space="preserve">quo interuallo ſeruato pone alterum circini pedem
              <lb/>
            n B. </s>
            <s xml:id="echoid-s296" xml:space="preserve">altero verò nota hinc inde duo puncta F G. </s>
            <s xml:id="echoid-s297" xml:space="preserve">eodem modo po-
              <lb/>
            ſito altero pede in C. </s>
            <s xml:id="echoid-s298" xml:space="preserve">alia duo pũcta hinc, & </s>
            <s xml:id="echoid-s299" xml:space="preserve">inde notabis H I. </s>
            <s xml:id="echoid-s300" xml:space="preserve">idem
              <lb/>
            fac ex puncto D. </s>
            <s xml:id="echoid-s301" xml:space="preserve">ſignando duo puncta N K. </s>
            <s xml:id="echoid-s302" xml:space="preserve">& </s>
            <s xml:id="echoid-s303" xml:space="preserve">tandem alia duo ex
              <lb/>
            E. </s>
            <s xml:id="echoid-s304" xml:space="preserve">vtrinque, quæ ſint L M. </s>
            <s xml:id="echoid-s305" xml:space="preserve">hoc modo erit totus circulus in 12. </s>
            <s xml:id="echoid-s306" xml:space="preserve">par-
              <lb/>
            tes æquales diuiſus, vt experientia conſtat. </s>
            <s xml:id="echoid-s307" xml:space="preserve">ratio vero eſt, quia in-
              <lb/>
            teruallũ ſemidiametri ſexies ſuam periferiam percurrit, ex quarti Euclidis Elem. </s>
            <s xml:id="echoid-s308" xml:space="preserve">quare arcus B F. </s>
            <s xml:id="echoid-s309" xml:space="preserve">contine-
              <lb/>
            bit gr. </s>
            <s xml:id="echoid-s310" xml:space="preserve">60. </s>
            <s xml:id="echoid-s311" xml:space="preserve">quia arcus B F. </s>
            <s xml:id="echoid-s312" xml:space="preserve">eſt ſexta circuli pars, & </s>
            <s xml:id="echoid-s313" xml:space="preserve">in toto circulo, continentur gr. </s>
            <s xml:id="echoid-s314" xml:space="preserve">360. </s>
            <s xml:id="echoid-s315" xml:space="preserve">quorum pars ſexta, pa-
              <lb/>
            riter eſt gr. </s>
            <s xml:id="echoid-s316" xml:space="preserve">60. </s>
            <s xml:id="echoid-s317" xml:space="preserve">totidem etiam continebit ar us C I. </s>
            <s xml:id="echoid-s318" xml:space="preserve">quare tres arcus B I. </s>
            <s xml:id="echoid-s319" xml:space="preserve">I F. </s>
            <s xml:id="echoid-s320" xml:space="preserve">F C. </s>
            <s xml:id="echoid-s321" xml:space="preserve">ſinguli continebunt gr. </s>
            <s xml:id="echoid-s322" xml:space="preserve">30.
              <lb/>
            </s>
            <s xml:id="echoid-s323" xml:space="preserve">cum enim arcus B F. </s>
            <s xml:id="echoid-s324" xml:space="preserve">complectatur gr. </s>
            <s xml:id="echoid-s325" xml:space="preserve">60. </s>
            <s xml:id="echoid-s326" xml:space="preserve">reliquus arcus F C. </s>
            <s xml:id="echoid-s327" xml:space="preserve">reliquos 30. </s>
            <s xml:id="echoid-s328" xml:space="preserve">continebit, qui ſuperſunt vſq; </s>
            <s xml:id="echoid-s329" xml:space="preserve">ad
              <lb/>
            quadrantis B C. </s>
            <s xml:id="echoid-s330" xml:space="preserve">complementum, hoc eſt, vſque ad 90. </s>
            <s xml:id="echoid-s331" xml:space="preserve">eadem ratione arcus B I. </s>
            <s xml:id="echoid-s332" xml:space="preserve">comprehendet gr. </s>
            <s xml:id="echoid-s333" xml:space="preserve">30. </s>
            <s xml:id="echoid-s334" xml:space="preserve">& </s>
            <s xml:id="echoid-s335" xml:space="preserve">con
              <lb/>
            ſequenter reliquus arcus I C. </s>
            <s xml:id="echoid-s336" xml:space="preserve">reis quos 30. </s>
            <s xml:id="echoid-s337" xml:space="preserve">gradus habebit: </s>
            <s xml:id="echoid-s338" xml:space="preserve">totus igitur circulus erit in 12. </s>
            <s xml:id="echoid-s339" xml:space="preserve">æquas partes diui-
              <lb/>
            ſus, quarum ſingulæ tricenos gradus continebunt. </s>
            <s xml:id="echoid-s340" xml:space="preserve">Rurſus vnamquamq; </s>
            <s xml:id="echoid-s341" xml:space="preserve">earum diuide bifariam, ſeu in duas-
              <lb/>
            parte, æquas, vt vide factum in quadrante B C. </s>
            <s xml:id="echoid-s342" xml:space="preserve">in punctis n. </s>
            <s xml:id="echoid-s343" xml:space="preserve">o. </s>
            <s xml:id="echoid-s344" xml:space="preserve">p. </s>
            <s xml:id="echoid-s345" xml:space="preserve">ſicque tota periferia erit ſecta in 24. </s>
            <s xml:id="echoid-s346" xml:space="preserve">partes
              <lb/>
            quarum ſingulæ gr. </s>
            <s xml:id="echoid-s347" xml:space="preserve">15. </s>
            <s xml:id="echoid-s348" xml:space="preserve">comprehendent. </s>
            <s xml:id="echoid-s349" xml:space="preserve">Rurſus harum quælibet in partes 3. </s>
            <s xml:id="echoid-s350" xml:space="preserve">æquas ſubdiuidue, vt in parte
              <lb/>
            B. </s>
            <s xml:id="echoid-s351" xml:space="preserve">factum in cernis, quare quælibet earum quinis gradibus conſtabit: </s>
            <s xml:id="echoid-s352" xml:space="preserve">tandem eas ſingulas in 5. </s>
            <s xml:id="echoid-s353" xml:space="preserve">partes æquat
              <lb/>
            exactè partire, eritque vnaquęque earum gradus vnus, hacq; </s>
            <s xml:id="echoid-s354" xml:space="preserve">ratione tota circũferentia, diuiſa erit in gr. </s>
            <s xml:id="echoid-s355" xml:space="preserve">360. </s>
            <s xml:id="echoid-s356" xml:space="preserve">
              <lb/>
            quod erat faciendum. </s>
            <s xml:id="echoid-s357" xml:space="preserve">Nos tamen ob paruitatẽ figuræ nequiuimus ſubdiuidere tres partesarcus B n. </s>
            <s xml:id="echoid-s358" xml:space="preserve">in ſuos
              <lb/>
            5. </s>
            <s xml:id="echoid-s359" xml:space="preserve">gradus. </s>
            <s xml:id="echoid-s360" xml:space="preserve">Si verò adhuc exactius operari velis, id aſſequeris per latus Pentangoni in dato circulo delcriben-
              <lb/>
            di, hac ratione, ſit ſemidiameter E. </s>
            <s xml:id="echoid-s361" xml:space="preserve">A. </s>
            <s xml:id="echoid-s362" xml:space="preserve">diuiſa bifariam in puncto T. </s>
            <s xml:id="echoid-s363" xml:space="preserve">poſtea altero circini crure in T. </s>
            <s xml:id="echoid-s364" xml:space="preserve">poſito, </s>
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      </text>
    </echo>
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