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-div427" type="section" level="1" n="316">
          <pb o="205" file="0227" n="232"/>
        </div>
        <div xml:id="echoid-div429" type="section" level="1" n="317">
          <head xml:id="echoid-head335" xml:space="preserve">APPARATVS
            <lb/>
          AD MATHEMATICAS
            <lb/>
          ADDISCENDAS, ET PROMOVENDAS</head>
          <p>
            <s xml:id="echoid-s17472" xml:space="preserve">CVm ego tum in me ipſo, tum in alijs plunibus experientia didicerim quant is labori-
              <lb/>
            bus, quantiſque ſtudiorum diſpendijs, ij Mathematicis dent operam, qui eas nullo
              <lb/>
            doctore præuio, nullaq; </s>
            <s xml:id="echoid-s17473" xml:space="preserve">eræeedenti nſtructione aggrediuntur, breui hoc apparatu
              <lb/>
            huic malo remedium afferre decreui. </s>
            <s xml:id="echoid-s17474" xml:space="preserve">Qua in re fortè Gemio
              <unsure/>
            u mimitabor, qui vt
              <lb/>
            tradit Pappus lib. </s>
            <s xml:id="echoid-s17475" xml:space="preserve">8. </s>
            <s xml:id="echoid-s17476" xml:space="preserve">de Mathematicarum ordine ſeripſerat. </s>
            <s xml:id="echoid-s17477" xml:space="preserve">præ cæteris veroſcien-
              <lb/>
            tijs Mathematicæ prccipuè tali auxilio indigere videntur, tum propter earum mul-
              <lb/>
            titudinem, mutuam connexionem, ac depẽdentiam; </s>
            <s xml:id="echoid-s17478" xml:space="preserve">tum quod hac tempeſtate, qua
              <lb/>
            ipſę reuiuiſcere, ac reflorere incipiunt, perpauci, rariq; </s>
            <s xml:id="echoid-s17479" xml:space="preserve">ea@n profeſlores reperian-
              <lb/>
            tur, pauci ſſimique, qui earum totam Encyclopęd am p@ritè, ſcienterq; </s>
            <s xml:id="echoid-s17480" xml:space="preserve">percalleant,
              <lb/>
            quique varijs ſtudioſorum finibus latis facere queant, Verum (quod magis dolen-
              <lb/>
            dum eſt) plurimi paſſim reperiuntur, qui ſe Mathematicos venditant, propterea quòd ſphæræ circulos vt-
              <lb/>
            cunque nouerint, aut quod nudam Horologij deſcriptionem teneant. </s>
            <s xml:id="echoid-s17481" xml:space="preserve">quot ſunt qui totam Mutheſeos vim
              <lb/>
            in eo conſiſtere putant, vt ſciat quis, vt aiunt, alicuius Natiuitatem conſtruere? </s>
            <s xml:id="echoid-s17482" xml:space="preserve">totiq; </s>
            <s xml:id="echoid-s17483" xml:space="preserve">ſunt ferè omnes, vt Iu-
              <lb/>
            diciariam Aſtrologiam exiſtiment eſſe totius Matheſ@os columen, quæ tamen nuna ratione nomen ſcien-
              <lb/>
            tiæ Mathematicæ meretur. </s>
            <s xml:id="echoid-s17484" xml:space="preserve">Quam rari hodie Geome@ræ, qui Archimedis, Apollonij, Pappi, admiranda.
              <lb/>
            </s>
            <s xml:id="echoid-s17485" xml:space="preserve">monumenta perlegerint? </s>
            <s xml:id="echoid-s17486" xml:space="preserve">Quam @ari inter Arichmeticos ad Algebræ penetralia ſcienter perueniunt? </s>
            <s xml:id="echoid-s17487" xml:space="preserve">tan-
              <lb/>
            dem qui Muſici habentur, & </s>
            <s xml:id="echoid-s17488" xml:space="preserve">probantur, nulla Arithmeticæ aut Geometrię cognitione, nulla de Muſicæ na-
              <lb/>
            tura, officio, aut fine tractatione, eam tradunt, ac profitentur. </s>
            <s xml:id="echoid-s17489" xml:space="preserve">vnde reliqua noſtræ Muſicæ detrimẽta, de qui-
              <lb/>
            bus nos alibi diximus oriuntur. </s>
            <s xml:id="echoid-s17490" xml:space="preserve">Idem de reliquis Mathematicis dici poſlet, fed ne longior ſim, rem propo-
              <lb/>
            ſitam aggrediar, & </s>
            <s xml:id="echoid-s17491" xml:space="preserve">totum apparatum in quinque partes diſtribuam.</s>
            <s xml:id="echoid-s17492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17493" xml:space="preserve">Prima, erit Mathematicarum omnium expoſitio, & </s>
            <s xml:id="echoid-s17494" xml:space="preserve">diuiſio.</s>
            <s xml:id="echoid-s17495" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17496" xml:space="preserve">Secunda, Bibliotheca Authorum ſelectorum pro ſingulis Mathematicis.</s>
            <s xml:id="echoid-s17497" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17498" xml:space="preserve">Tertia, Variæ methodi earum addiſcenda@un.</s>
            <s xml:id="echoid-s17499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17500" xml:space="preserve">Quarta, Mathematici ſtudij promotio.</s>
            <s xml:id="echoid-s17501" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17502" xml:space="preserve">Quinta, Chronologia clarorum Mathematicorum, quam edidimus iam cum locis Mathematicis Ariſt.</s>
            <s xml:id="echoid-s17503" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div430" type="section" level="1" n="318">
          <head xml:id="echoid-head336" style="it" xml:space="preserve">Mathematicarum diuiſio, & expl. catio. ‘Pars prima.</head>
          <p>
            <s xml:id="echoid-s17504" xml:space="preserve">COnueniens imo nec ſſarium omninò eſſe videtur, ante omnia breu@m quandam ac ſimplicem Mathe-
              <lb/>
            maticarum expl cationem tradere. </s>
            <s xml:id="echoid-s17505" xml:space="preserve">breuem m
              <unsure/>
            quam quoniam quamuis pluribus dequauis ſcienci@@ſ-
              <lb/>
            ſeratur, nunquam tamen naturam illius probè percipies, niſi ſcientiam ipſam animo totam compræhen-
              <lb/>
            deris.</s>
            <s xml:id="echoid-s17506" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17507" xml:space="preserve">Mathematicæ igitur ſcientiæ al@æ ſunt ſpeculatiuæ, aliæ practicæ; </s>
            <s xml:id="echoid-s17508" xml:space="preserve">item aliæ puræ, aliæ mediæ; </s>
            <s xml:id="echoid-s17509" xml:space="preserve">tandem
              <lb/>
            aliæ ſubalternantes, aliæ ſubalternatæ. </s>
            <s xml:id="echoid-s17510" xml:space="preserve">Per ſpeculatiuas eas intelligo quæ conſiderant quan@itatem a mate-
              <lb/>
            ria abſtractam, ideſt, nulla habita ratione mater æ in qua ipſa quantitas detinetur. </s>
            <s xml:id="echoid-s17511" xml:space="preserve">quod ſi quæ concretam
              <lb/>
            conſiderant, non tamen conſiderationem dirigunt ad opus.</s>
            <s xml:id="echoid-s17512" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div431" type="section" level="1" n="319">
          <head xml:id="echoid-head337" style="it" xml:space="preserve">Speculatiuæ Mathematicæ ſunt ſex ſequentes.</head>
          <p>
            <s xml:id="echoid-s17513" xml:space="preserve">1 GEometria quam primam facere libet, tractat de quantitate continua terminata, cuius ſunt tria gene-
              <lb/>
            ra, linea, ſuperficie, corpus: </s>
            <s xml:id="echoid-s17514" xml:space="preserve">uxta tres dimenſiones, longitudinem, latitudinem, & </s>
            <s xml:id="echoid-s17515" xml:space="preserve">profunditatem. </s>
            <s xml:id="echoid-s17516" xml:space="preserve">Li-
              <lb/>
            nea terminata eſt, v.</s>
            <s xml:id="echoid-s17517" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17518" xml:space="preserve">linea bipedalis, diameter alicuius circuli, vel quadrati, latus alicui
              <unsure/>
            us trianguli, quadra-
              <lb/>
            ti, rhombi, &</s>
            <s xml:id="echoid-s17519" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17520" xml:space="preserve">ſuperficies terminata eſt, v.</s>
            <s xml:id="echoid-s17521" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17522" xml:space="preserve">triangu um, quadratum, circulus, &</s>
            <s xml:id="echoid-s17523" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17524" xml:space="preserve">corpus terminatum eſt, vt
              <lb/>
            cubus, conus, cylindrus, ſphæra, &</s>
            <s xml:id="echoid-s17525" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17526" xml:space="preserve">de quibus omnibus ſubtiliſſime Geometria oſtendit admir
              <unsure/>
            abiles pro-
              <lb/>
            prietates. </s>
            <s xml:id="echoid-s17527" xml:space="preserve">pars quæ tractat de corporibus, ſeu ſolidis proprio no@ine dicitur Stereometria.</s>
            <s xml:id="echoid-s17528" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17529" xml:space="preserve">2 Arithmetica agit de quantitate diſcreta, finita, & </s>
            <s xml:id="echoid-s17530" xml:space="preserve">terminata, ſiue denumeris finicis, & </s>
            <s xml:id="echoid-s17531" xml:space="preserve">terminatis, vt
              <lb/>
            ſunt numeri quadrati, cubi, &</s>
            <s xml:id="echoid-s17532" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17533" xml:space="preserve">con@poſiti, incompoſiti, &</s>
            <s xml:id="echoid-s17534" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17535" xml:space="preserve">horum naturam, & </s>
            <s xml:id="echoid-s17536" xml:space="preserve">accidentiam, eoru@ que mu-
              <lb/>
            tuas actiones perſcrutatur.</s>
            <s xml:id="echoid-s17537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17538" xml:space="preserve">Hæ porrò duę dicuntur puræ, quod tractent de pura quantitate abſtracta a maleria, ideſt, Geometria con-
              <lb/>
            ſiderat triangulum ſecundum ſe, nulla habita ratione materię in qua ſit triangulum, ſiue enim ſit in ligno, ſi-
              <lb/>
            ue in ære, ſiue in cęlo, ſiue in terra, illud eodem modo conſiderat. </s>
            <s xml:id="echoid-s17539" xml:space="preserve">Similiter Arithmetica conſiderat </s>
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