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">
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        <div xml:id="echoid-div466" type="section" level="1" n="354">
          <p>
            <s xml:id="echoid-s18494" xml:space="preserve">
              <pb o="216" file="0238" n="243" rhead="APPARATVS"/>
            blemate ſubditur, quod erat faciendum; </s>
            <s xml:id="echoid-s18495" xml:space="preserve">in Theoremate vero, quod erat demonſtrandum, ſciendum præte-
              <lb/>
            rea Lemma eſſe quandam demonſtrationem in gratiam alterius demonſtrationis ne ipſa demonſtratio pro-
              <lb/>
            lixior euadat. </s>
            <s xml:id="echoid-s18496" xml:space="preserve">Vide Clauium duobus capit. </s>
            <s xml:id="echoid-s18497" xml:space="preserve">vltimis prolegom: </s>
            <s xml:id="echoid-s18498" xml:space="preserve">in Euclidem.</s>
            <s xml:id="echoid-s18499" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div467" type="section" level="1" n="355">
          <head xml:id="echoid-head374" style="it" xml:space="preserve">De Fallacijs, vel Paralogiſmis, vel Pſeudographijs.</head>
          <p>
            <s xml:id="echoid-s18500" xml:space="preserve">QVoniam Paralogiſmus, ſeu Pſeudographia, eſt fallax demonſ
              <unsure/>
            ſ
              <unsure/>
            ratio, ſequitur vt nunc de ea breuiter tra-
              <lb/>
            ctemus, hoc eſt de fallacijs, ſeu erratis, quæ aduerſus rectũ demonſtrandi vſum committi ſolẽt quarum.</s>
            <s xml:id="echoid-s18501" xml:space="preserve"/>
          </p>
          <figure number="123">
            <image file="0238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s18502" xml:space="preserve">Prima ſit, ſi quid ab Authoritate probetur; </s>
            <s xml:id="echoid-s18503" xml:space="preserve">hæc enim ratio, nec conuincit, nec Geo-
              <lb/>
            metrica eſt, ideſt, non procedit ex proprijs Geometriæ principijs, aut demonſtratis.</s>
            <s xml:id="echoid-s18504" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18505" xml:space="preserve">Secunda eſt, cum quis ratione, ſeu experientia ſenſus vtitur, vt ſi quis probaret in
              <lb/>
            præſenti triangulo lineam D E. </s>
            <s xml:id="echoid-s18506" xml:space="preserve">quæ eſt baſi B C. </s>
            <s xml:id="echoid-s18507" xml:space="preserve">paralella, eſſe eadem baſi minorem,
              <lb/>
            ex eo quod ipſius oculis id percipiatur, eſſet fallacia, quia Geometria tractat de mate-
              <lb/>
            ria intelligibili, non ſenſibili, nec ſenſus poteſt ſemper percipere inæqualitatem; </s>
            <s xml:id="echoid-s18508" xml:space="preserve">poteſt
              <lb/>
            enim linea D E. </s>
            <s xml:id="echoid-s18509" xml:space="preserve">eſſe adeo proxima baſi B C. </s>
            <s xml:id="echoid-s18510" xml:space="preserve">vt oculus vel linceus nullam cernat diſſe-
              <lb/>
            rentiam; </s>
            <s xml:id="echoid-s18511" xml:space="preserve">ſemper tamen Geometricè oſtendetur minor. </s>
            <s xml:id="echoid-s18512" xml:space="preserve">ad hanc fallaciam reducitur
              <lb/>
            menſuratio, vt ſi quis aut Circino, aut alio inſtrumento, vtranque, ex dictis lineis me-
              <lb/>
            tietur, indeque probaret illam eſſe minorem.</s>
            <s xml:id="echoid-s18513" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18514" xml:space="preserve">Tertia deceptio in qua Tyrones ferè omnes incidunt, eſt vti circulo ſenſibili ad oſtendendam æqualita-
              <lb/>
            tem linearum, v.</s>
            <s xml:id="echoid-s18515" xml:space="preserve">g. </s>
            <s xml:id="echoid-s18516" xml:space="preserve">in præſenti Iſoſcele A B C. </s>
            <s xml:id="echoid-s18517" xml:space="preserve">ducta D E. </s>
            <s xml:id="echoid-s18518" xml:space="preserve">paralella baſi B C. </s>
            <s xml:id="echoid-s18519" xml:space="preserve">probandum ſit duas lineas A D.
              <lb/>
            </s>
            <s xml:id="echoid-s18520" xml:space="preserve">A E. </s>
            <s xml:id="echoid-s18521" xml:space="preserve">abſcindi æquales, & </s>
            <s xml:id="echoid-s18522" xml:space="preserve">ad id conſtruat quis circulum ex A. </s>
            <s xml:id="echoid-s18523" xml:space="preserve">interuallo A D. </s>
            <s xml:id="echoid-s18524" xml:space="preserve">hic circulus tranſibit etiam per
              <lb/>
              <figure xlink:label="fig-0238-02" xlink:href="fig-0238-02a" number="124">
                <image file="0238-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-02"/>
              </figure>
            E. </s>
            <s xml:id="echoid-s18525" xml:space="preserve">ad ſenſum euidenter. </s>
            <s xml:id="echoid-s18526" xml:space="preserve">ſi igitur diſcurat ſic, lineæ A D. </s>
            <s xml:id="echoid-s18527" xml:space="preserve">A E. </s>
            <s xml:id="echoid-s18528" xml:space="preserve">ſunt ductæ à centro
              <lb/>
            A. </s>
            <s xml:id="echoid-s18529" xml:space="preserve">ad circumferentiam D E. </s>
            <s xml:id="echoid-s18530" xml:space="preserve">ergo ſunt æquales. </s>
            <s xml:id="echoid-s18531" xml:space="preserve">erit fallacia ſenſus quia inde pro-
              <lb/>
            bat, quia oculo id cernit. </s>
            <s xml:id="echoid-s18532" xml:space="preserve">certum quidem eſt lineam A D. </s>
            <s xml:id="echoid-s18533" xml:space="preserve">pertinere à centro ad
              <lb/>
            circumferentiam, ſed auxilio ſenſus non eſt certum lineam A E. </s>
            <s xml:id="echoid-s18534" xml:space="preserve">præcisè terminari
              <lb/>
            in ipſa circumferentia, quia non eſt ducta poſt deſcriptum circulum, nec ſupponi-
              <lb/>
            tur circulum tranſire per E. </s>
            <s xml:id="echoid-s18535" xml:space="preserve">& </s>
            <s xml:id="echoid-s18536" xml:space="preserve">quamuis Euclides in Prima, & </s>
            <s xml:id="echoid-s18537" xml:space="preserve">alijs, vtatur circulo
              <lb/>
            ad oſtendas lineas æquales, id bene habet, quia in Prima lineæ ducuntur ſaltem.
              <lb/>
            </s>
            <s xml:id="echoid-s18538" xml:space="preserve">vna poſt factum circulum, qui per extremum alterius lineæ tranſit ex hypotheſi. </s>
            <s xml:id="echoid-s18539" xml:space="preserve">
              <lb/>
            in Secunda vero propoſitione ductis iam lineis circulus deſcribitur interuallo mi-
              <lb/>
            noris ſecans maiorem, quare pars maioris intra circulum intercepta neceſſario ducitur à cẽtro ad circumfe-
              <lb/>
            rentiam, & </s>
            <s xml:id="echoid-s18540" xml:space="preserve">ſic illæ duæ probantur æquales.</s>
            <s xml:id="echoid-s18541" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18542" xml:space="preserve">Quartò, fallaciter demonſtramus, quando in conſtructione aſſumitur aliquid, cuius conſtructio ignora-
              <lb/>
            tur, vt ſi ad quadrandum circulum dicat quis, ſumatur linea recta æqualis peripherię circuli; </s>
            <s xml:id="echoid-s18543" xml:space="preserve">hoc enim Geo-
              <lb/>
            metricè non dum inuentum eſt, & </s>
            <s xml:id="echoid-s18544" xml:space="preserve">ſi mechanicè, vel organicè fiat nititur ſenſu; </s>
            <s xml:id="echoid-s18545" xml:space="preserve">ſimiliter peccant omnes de-
              <lb/>
            monſtrationes in quibus vſui ſunt lineę punctuales, vt eſt linea Cõchiodis Nicodemis apud Clauium in Geo-
              <lb/>
            metria pract. </s>
            <s xml:id="echoid-s18546" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18547" xml:space="preserve">8. </s>
            <s xml:id="echoid-s18548" xml:space="preserve">pag. </s>
            <s xml:id="echoid-s18549" xml:space="preserve">25. </s>
            <s xml:id="echoid-s18550" xml:space="preserve">& </s>
            <s xml:id="echoid-s18551" xml:space="preserve">linea Quadratix apud Clauium ad finem 6. </s>
            <s xml:id="echoid-s18552" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s18553" xml:space="preserve">huiuſmodi enim lineæ non
              <lb/>
            ſunt quid continuum, cum ex punctis conoſcent, & </s>
            <s xml:id="echoid-s18554" xml:space="preserve">propterea nequeunt partes ipſarum præcisè haberi, cum
              <lb/>
            incertum ſit vbinam ſint puncta lineam conſtituentia. </s>
            <s xml:id="echoid-s18555" xml:space="preserve">in Quadrantice præterea vltimum punctum haberi
              <lb/>
            nequit. </s>
            <s xml:id="echoid-s18556" xml:space="preserve">Nicodemes paralogizat ducens lineam quandam quæ terminatur ad Conchilem punctualem, quia
              <lb/>
            incertum eſt an ad vnum ex punctis illis deſinat, ſecus terminari ab ea nequit.</s>
            <s xml:id="echoid-s18557" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18558" xml:space="preserve">Quinta, eſt cum vtimur communibus principis aliarum ſcientiarum, ſic Bryſo in quadrando circulo vte-
              <lb/>
            batur, hoc principio, quæcunque ſunt ſimul maiora, & </s>
            <s xml:id="echoid-s18559" xml:space="preserve">minora ijſdem, ſunt inuicem æqualia, quod com-
              <lb/>
            mune eſt magnitudinibus, numeris temporibus, & </s>
            <s xml:id="echoid-s18560" xml:space="preserve">qualitatibus, & </s>
            <s xml:id="echoid-s18561" xml:space="preserve">ideo ab Ariſt. </s>
            <s xml:id="echoid-s18562" xml:space="preserve">repræhenditur text. </s>
            <s xml:id="echoid-s18563" xml:space="preserve">primi
              <lb/>
            poſter. </s>
            <s xml:id="echoid-s18564" xml:space="preserve">vide noſtram illius loci explicationem: </s>
            <s xml:id="echoid-s18565" xml:space="preserve">Hinc etiam non licet Geometræ vti illo principio quæ ſunt
              <lb/>
            eadem vni tertio ſunt eadem inter ſe, quia eſt cõmune alijs ſcientijs, ſed pro eo vt debet hoc; </s>
            <s xml:id="echoid-s18566" xml:space="preserve">quæ ſunt æqua-
              <lb/>
            lia vni tertio, &</s>
            <s xml:id="echoid-s18567" xml:space="preserve">c.</s>
            <s xml:id="echoid-s18568" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18569" xml:space="preserve">Sexta, Rationes probabiles apud Geometras habentur pro paralogiſmis, vt ſi quis probaret ſuperiorcm li-
              <lb/>
            neam D E quæ eſt baſi æquidiſtans, eſſe minorem baſi B C. </s>
            <s xml:id="echoid-s18570" xml:space="preserve">ex eo, quod ſit in anguſtiori loco, quam ſit baſis;
              <lb/>
            </s>
            <s xml:id="echoid-s18571" xml:space="preserve">deciperetur quia ibi poni poteſt linea maior baſi, quæ tamen non ſit ei æquidiſtans.</s>
            <s xml:id="echoid-s18572" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18573" xml:space="preserve">Septima, Dicitur principij petitio, eſtque, quando in diſcurſu aſſumitur pro vero id, quod eſt demon-
              <lb/>
            ſtrandum, ideſt, quod in principio poſitum eſt, Ariſt. </s>
            <s xml:id="echoid-s18574" xml:space="preserve">2. </s>
            <s xml:id="echoid-s18575" xml:space="preserve">priorum cap. </s>
            <s xml:id="echoid-s18576" xml:space="preserve">31. </s>
            <s xml:id="echoid-s18577" xml:space="preserve">af
              <unsure/>
            ſ
              <unsure/>
            ert hoc exemplum; </s>
            <s xml:id="echoid-s18578" xml:space="preserve">vult quiſpiam
              <lb/>
              <figure xlink:label="fig-0238-03" xlink:href="fig-0238-03a" number="125">
                <image file="0238-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-03"/>
              </figure>
            oſtendere duas in ſequenti figura lineas A B. </s>
            <s xml:id="echoid-s18579" xml:space="preserve">C D. </s>
            <s xml:id="echoid-s18580" xml:space="preserve">eſſe paralellas,
              <lb/>
            quod faciant angulos alternos A G H. </s>
            <s xml:id="echoid-s18581" xml:space="preserve">G H D. </s>
            <s xml:id="echoid-s18582" xml:space="preserve">æquales, nam hoc
              <lb/>
            poſito per vigeſimam ſeptimam primi, id ſequitur volens poſtea
              <lb/>
            probare tales angulos eſſe æquales, id probat, ex eo quòd ſunt pa-
              <lb/>
            ralellæ, quod ſequitur per 29. </s>
            <s xml:id="echoid-s18583" xml:space="preserve">primi, petit quod in principio poſi-
              <lb/>
            tum eſt pro bandum, ſcilicet, lineas A B. </s>
            <s xml:id="echoid-s18584" xml:space="preserve">C D. </s>
            <s xml:id="echoid-s18585" xml:space="preserve">eſſe paralellas Ean-
              <lb/>
            dem peccaret fallaciam qui demonſtrationem aliquam citaret, quę
              <lb/>
            ex demonſtranda penderet, ſeu ſequeretur, vt ſi quis probaret 10.
              <lb/>
            </s>
            <s xml:id="echoid-s18586" xml:space="preserve">p. </s>
            <s xml:id="echoid-s18587" xml:space="preserve">per 32. </s>
            <s xml:id="echoid-s18588" xml:space="preserve">primi.</s>
            <s xml:id="echoid-s18589" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18590" xml:space="preserve">Octaua, aliquando Tyrones dum demonſtrat@ones Euclidis repetunt falluntur ob ſimilitudinem </s>
          </p>
        </div>
      </text>
    </echo>
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