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-div452" type="section" level="1" n="340">
          <p>
            <s xml:id="echoid-s18111" xml:space="preserve">
              <pb o="212" file="0234" n="239" rhead="APPARATVS"/>
            perfectius, & </s>
            <s xml:id="echoid-s18112" xml:space="preserve">ſecundum Logicæ præcepta percipitur ipſa Geometria. </s>
            <s xml:id="echoid-s18113" xml:space="preserve">Secunda regula: </s>
            <s xml:id="echoid-s18114" xml:space="preserve">In difficilioribus
              <lb/>
            demonſtrationibus aliquando augetur difficultas. </s>
            <s xml:id="echoid-s18115" xml:space="preserve">propterea quod in ijs percipiendis neceſſe eſt fatigari ima-
              <lb/>
            ginationem circa plures figuras quæ ibi ſupponuntur, & </s>
            <s xml:id="echoid-s18116" xml:space="preserve">deſiderantur concipiendas, ac retinendas, vt intel-
              <lb/>
            lectus circa eas poſſit diſcurrere, quod primo accidit in 12. </s>
            <s xml:id="echoid-s18117" xml:space="preserve">ſecundi Elem. </s>
            <s xml:id="echoid-s18118" xml:space="preserve">in qua dicitur, quadratum|lateris
              <lb/>
            A C. </s>
            <s xml:id="echoid-s18119" xml:space="preserve">maius eſſe quadratis laterum A B. </s>
            <s xml:id="echoid-s18120" xml:space="preserve">B C. </s>
            <s xml:id="echoid-s18121" xml:space="preserve">rectangulo bis compræhenſo ſub C C. </s>
            <s xml:id="echoid-s18122" xml:space="preserve">B D. </s>
            <s xml:id="echoid-s18123" xml:space="preserve">quę tamen quadra-
              <lb/>
            ta, & </s>
            <s xml:id="echoid-s18124" xml:space="preserve">rectangula, & </s>
            <s xml:id="echoid-s18125" xml:space="preserve">aliæ figuræ ibi deſiderantur: </s>
            <s xml:id="echoid-s18126" xml:space="preserve">vnde difficilis euadit intelligentia illius: </s>
            <s xml:id="echoid-s18127" xml:space="preserve">facilis tamen red-
              <lb/>
            ditur ſi prædictæ figuræ ibi vtcunque addantur, eo modo, quo citantur. </s>
            <s xml:id="echoid-s18128" xml:space="preserve">Tertſa regula aliquando obſcuritas
              <lb/>
            oritur ex longo diſcurſu per plures æqualitates, quæ ſubinde variantur addendo, demendo, transferendo,
              <lb/>
            commutando, quo caſu vtile eſt rem ad calculum redigere, ideſt, in pagella notare membra æqualitatis hinc
              <lb/>
            inde ſe poſita, ideſt, figuras æquales contradiſtinctas, eaſque ſecundum diſcurſus exigentiam addere, deme-
              <lb/>
            re, transferre, commutare, &</s>
            <s xml:id="echoid-s18129" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18130" xml:space="preserve">hac enim calculatione iuuatur imaginatio, & </s>
            <s xml:id="echoid-s18131" xml:space="preserve">diſcurſus, vt poſſit vſq; </s>
            <s xml:id="echoid-s18132" xml:space="preserve">ad fi-
              <lb/>
            nem peruenire, alioquin in medio ſæpè curſu frangitur, & </s>
            <s xml:id="echoid-s18133" xml:space="preserve">coincidit. </s>
            <s xml:id="echoid-s18134" xml:space="preserve">hoc etiam vſu venit in 12. </s>
            <s xml:id="echoid-s18135" xml:space="preserve">& </s>
            <s xml:id="echoid-s18136" xml:space="preserve">13. </s>
            <s xml:id="echoid-s18137" xml:space="preserve">ſecun-
              <lb/>
            di Elementorum.</s>
            <s xml:id="echoid-s18138" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18139" xml:space="preserve">Secundò tandem ſciat lector neminem poſſe euadere perfectum Geometram ſine Arith. </s>
            <s xml:id="echoid-s18140" xml:space="preserve">neq; </s>
            <s xml:id="echoid-s18141" xml:space="preserve">perfectum
              <lb/>
            Arithm. </s>
            <s xml:id="echoid-s18142" xml:space="preserve">ſine Geometria; </s>
            <s xml:id="echoid-s18143" xml:space="preserve">ſunt enim hæ duæ ſcientiæ veluti duæ ſorores, vt ait Eutocius, quæ ſibi mutuas tra-
              <lb/>
            dunt operas. </s>
            <s xml:id="echoid-s18144" xml:space="preserve">hac de cauſa Euclides ſapientiſſimè tres Arithm. </s>
            <s xml:id="echoid-s18145" xml:space="preserve">libros inter ſua Geometrica Elem. </s>
            <s xml:id="echoid-s18146" xml:space="preserve">@inſeruit.
              <lb/>
            </s>
            <s xml:id="echoid-s18147" xml:space="preserve">hinc videmus multa in 10. </s>
            <s xml:id="echoid-s18148" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18149" xml:space="preserve">ſecundum numerorum rationes demonſtrari; </s>
            <s xml:id="echoid-s18150" xml:space="preserve">ſic omnia ferè quæ à Geometris
              <lb/>
            demonſtrantur etiam per numeros, ſiue rationales, ſiue irrationales, ſumma iucunditate peraguntur, atq; </s>
            <s xml:id="echoid-s18151" xml:space="preserve">ob
              <lb/>
            oculos ponuntur, v. </s>
            <s xml:id="echoid-s18152" xml:space="preserve">g. </s>
            <s xml:id="echoid-s18153" xml:space="preserve">demonſtratio 47. </s>
            <s xml:id="echoid-s18154" xml:space="preserve">primi, oſtendit quadratum illud lateris angulum rectum ſubtenden-
              <lb/>
            tis, eſſe ęquales quadratis reliquorum duorum laterum; </s>
            <s xml:id="echoid-s18155" xml:space="preserve">hoc idem numeris exequi poſſumus, ſi enim fiat trian
              <lb/>
            gulum rectangulum cuius baſis ſit linea quinque vnciarum, alterum latus ſit quatuor vnciarum, tertium ſit
              <lb/>
            @rium vnciarum, & </s>
            <s xml:id="echoid-s18156" xml:space="preserve">quadrati horum numerorum ſumantur, erit quadratus num. </s>
            <s xml:id="echoid-s18157" xml:space="preserve">quinque nimirum 25. </s>
            <s xml:id="echoid-s18158" xml:space="preserve">æqua-
              <lb/>
            lis duc
              <unsure/>
            bus quadratis reliquorum, nam quadratus numeri 4. </s>
            <s xml:id="echoid-s18159" xml:space="preserve">eſt 16. </s>
            <s xml:id="echoid-s18160" xml:space="preserve">quadratus numeri 3. </s>
            <s xml:id="echoid-s18161" xml:space="preserve">eſt 9. </s>
            <s xml:id="echoid-s18162" xml:space="preserve">qui duo quadra-
              <lb/>
            ti ſimul conficiunt 25. </s>
            <s xml:id="echoid-s18163" xml:space="preserve">Sed hoc magis manifeſtum eſt in Algebra, quæ quamuis Arithmet. </s>
            <s xml:id="echoid-s18164" xml:space="preserve">fit, vtitur ta-
              <lb/>
            men Geometricis demonſtrationibus, & </s>
            <s xml:id="echoid-s18165" xml:space="preserve">problemata Geometrica præſertim 10. </s>
            <s xml:id="echoid-s18166" xml:space="preserve">Element. </s>
            <s xml:id="echoid-s18167" xml:space="preserve">per numeros
              <lb/>
            reſoluit.</s>
            <s xml:id="echoid-s18168" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18169" xml:space="preserve">Tertio poſtquam quis probè in Elementis Euclidianis verſatus fuerit, alios Geometras aggrediatur, eo
              <lb/>
            ordine quo ſuper in Bibliotheca recenſiti ſunt.</s>
            <s xml:id="echoid-s18170" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div453" type="section" level="1" n="341">
          <head xml:id="echoid-head359" style="it" xml:space="preserve">Methodus ad Arithmeticam.</head>
          <p>
            <s xml:id="echoid-s18171" xml:space="preserve">OB affinitatem, & </s>
            <s xml:id="echoid-s18172" xml:space="preserve">connexionem quæ inter Geometriam’
              <unsure/>
            , & </s>
            <s xml:id="echoid-s18173" xml:space="preserve">Arithmeticam intercedit, nulla ratione
              <lb/>
            merebitur quiſpiam Arithmetici cognomen; </s>
            <s xml:id="echoid-s18174" xml:space="preserve">quin Element. </s>
            <s xml:id="echoid-s18175" xml:space="preserve">ſaltem Euclidis probè percipiat, quibus
              <lb/>
            perceptis debet poſtea operam Arithm. </s>
            <s xml:id="echoid-s18176" xml:space="preserve">illis impendere, quos ſuper recenſuimus, atque ex eodem ordine
              <lb/>
            quo ſunt recenſiti. </s>
            <s xml:id="echoid-s18177" xml:space="preserve">occurrentibus vero difficultatibus. </s>
            <s xml:id="echoid-s18178" xml:space="preserve">Primum ſit remedium adhibere paruos numeros pro
              <lb/>
            magnis, atque in illis prius experiri veritatem anteqnam aggrediaris, aut ſuperes totam oblatam demon-
              <lb/>
            ſtrationem. </s>
            <s xml:id="echoid-s18179" xml:space="preserve">Secundum ſit, in numeris irrationalibus, & </s>
            <s xml:id="echoid-s18180" xml:space="preserve">radicalibus Algebræ, quando occurrunt obſcuri-
              <lb/>
            tates, pro eis ſupponantur prius facilitatis gratia numeri rationales, & </s>
            <s xml:id="echoid-s18181" xml:space="preserve">communes, ijque parui; </s>
            <s xml:id="echoid-s18182" xml:space="preserve">in iſtis
              <lb/>
            enim apparet etiam veritas illa, quæ de Algebraticis proponitur, ſicque intellectus illuminatur, vt Alge
              <unsure/>
              <lb/>
            braticas tenebras diſijcere queat.</s>
            <s xml:id="echoid-s18183" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div454" type="section" level="1" n="342">
          <head xml:id="echoid-head360" style="it" xml:space="preserve">Methodus ad Opticam.</head>
          <p>
            <s xml:id="echoid-s18184" xml:space="preserve">QVoniam Optica Geometriæ ſubalternatur, ideo ad eam rectè capeſſendam neceſſario præcedere de-
              <lb/>
            bent ſaltem ſex primi libri Euclidis: </s>
            <s xml:id="echoid-s18185" xml:space="preserve">poſtea ſtudium impendatur Authoribus Opticæ ſupra recenſitis,
              <lb/>
            atque eodem ordine. </s>
            <s xml:id="echoid-s18186" xml:space="preserve">proderit autem multum ea experiri præſertim in ſpeculis, & </s>
            <s xml:id="echoid-s18187" xml:space="preserve">vitris, & </s>
            <s xml:id="echoid-s18188" xml:space="preserve">pili@
              <lb/>
            vitreis, & </s>
            <s xml:id="echoid-s18189" xml:space="preserve">chriſtallinis, nam experientia rerum magiſtra.</s>
            <s xml:id="echoid-s18190" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div455" type="section" level="1" n="343">
          <head xml:id="echoid-head361" style="it" xml:space="preserve">Methodus ad Mechanicam.</head>
          <p>
            <s xml:id="echoid-s18191" xml:space="preserve">QVoniam Mechanici Geometricè demonſtrant, ideo neceſſaria eſt hic quoque ſaltem ſex primorum
              <lb/>
            Euclidis pręcognitio, poſt quam ſequatur ſtudium Authorum ſupra numeratorum, atq; </s>
            <s xml:id="echoid-s18192" xml:space="preserve">eodem ordine.</s>
            <s xml:id="echoid-s18193" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div456" type="section" level="1" n="344">
          <head xml:id="echoid-head362" style="it" xml:space="preserve">Methodus ad Muſicam.</head>
          <p>
            <s xml:id="echoid-s18194" xml:space="preserve">HÆc Arithmeticè demonſtrat, ideo neceſſe eſt præcedat cognitio mediocris Arithmeticæ,|præſertim
              <lb/>
            proportionum Arithmeticarum quas ad 5. </s>
            <s xml:id="echoid-s18195" xml:space="preserve">Fuclidis P. </s>
            <s xml:id="echoid-s18196" xml:space="preserve">Clauius fusè exponit, necnõ ad finem 9. </s>
            <s xml:id="echoid-s18197" xml:space="preserve">Euclidis,
              <lb/>
            vtitur etiam aliquando figuris Geometricis, vnde primorum ſex elementorum Euclidis aliqua præcognitio
              <lb/>
            neceſſaria eſt: </s>
            <s xml:id="echoid-s18198" xml:space="preserve">deinde ſuperiores Authores eo ordine, adhibito ſtudio legantur, quo enumerati ſunt.</s>
            <s xml:id="echoid-s18199" xml:space="preserve"/>
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