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-div57" type="section" level="1" n="39">
          <p>
            <s xml:id="echoid-s2973" xml:space="preserve">
              <pb o="30" file="0046" n="46" rhead="De Mundi Fabrica."/>
            titas; </s>
            <s xml:id="echoid-s2974" xml:space="preserve">ducta igitur ſemidiametro 2. </s>
            <s xml:id="echoid-s2975" xml:space="preserve">cum ſex vndecimis in 8. </s>
            <s xml:id="echoid-s2976" xml:space="preserve">ſemicircumferentiam, producitur 20 cum qua-
              <lb/>
            tuor vndecimis pro circuli area. </s>
            <s xml:id="echoid-s2977" xml:space="preserve">id clarè perſpicitur conſtructo rectangulo ex ſemidiametro, & </s>
            <s xml:id="echoid-s2978" xml:space="preserve">ſemicircũ-
              <lb/>
            ferentia, vti vides in figura, ſic enim ſemidiameter ducitur in circumſerentiam; </s>
            <s xml:id="echoid-s2979" xml:space="preserve">in eo rectangulo vides
              <lb/>
            contineri 16. </s>
            <s xml:id="echoid-s2980" xml:space="preserve">parua quadrata, & </s>
            <s xml:id="echoid-s2981" xml:space="preserve">alia 8. </s>
            <s xml:id="echoid-s2982" xml:space="preserve">rectangula, quadratis minora, quę tamen æqualia ſunt 4. </s>
            <s xml:id="echoid-s2983" xml:space="preserve">& </s>
            <s xml:id="echoid-s2984" xml:space="preserve">quatuor
              <lb/>
            vndecimis quadratis, quibus circulus quadratum ſuperat. </s>
            <s xml:id="echoid-s2985" xml:space="preserve">hæc praxis probatur à P. </s>
            <s xml:id="echoid-s2986" xml:space="preserve">Clauio in Geom. </s>
            <s xml:id="echoid-s2987" xml:space="preserve">practi-
              <lb/>
            ca lib. </s>
            <s xml:id="echoid-s2988" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2989" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s2990" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">& </s>
            <s xml:id="echoid-s2992" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s2993" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2994" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2995" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2996" xml:space="preserve">idem aliqua ex parte experiri poteris, ſi enim prædi ctus circulus diuidatur
              <lb/>
            in parua quadrata prædictis æqualia, apparebit eum multa plura ex ijs continere quam 16. </s>
            <s xml:id="echoid-s2997" xml:space="preserve">vti videre eſt in
              <lb/>
            circulo P. </s>
            <s xml:id="echoid-s2998" xml:space="preserve">pr
              <unsure/>
            iori æquali, vnde patet circulum eſſe trium harum figurarum Iſoperimetrarũ capaciſſimum,
              <lb/>
            idemque accidet in omnibus alijs figuris: </s>
            <s xml:id="echoid-s2999" xml:space="preserve">vbi obſeruandum eſt illam ſemper eſſe capaciorem, quæ ro-
              <lb/>
            tundior eſt.</s>
            <s xml:id="echoid-s3000" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3001" xml:space="preserve">Ex demonſtratis è contrario patet, eandem ſuperficiem minori ambitu contineri, quo ambitus fuerit
              <lb/>
            rotundior. </s>
            <s xml:id="echoid-s3002" xml:space="preserve">Præterea manifeſtum eſt eos hallucinari poſſe, qui vrbes, aut regiones Iſoperimetr as æqua-
              <lb/>
            les eſſe exiſtimant; </s>
            <s xml:id="echoid-s3003" xml:space="preserve">aut eas eſſe maiores, quæ maiori ambitu ambiuntur; </s>
            <s xml:id="echoid-s3004" xml:space="preserve">cũ eadem area ſub minori, & </s>
            <s xml:id="echoid-s3005" xml:space="preserve">ma-
              <lb/>
            iori ambitu coarctari poſſit. </s>
            <s xml:id="echoid-s3006" xml:space="preserve">vide Pappum Alexandrinum lib. </s>
            <s xml:id="echoid-s3007" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3008" xml:space="preserve">collectionum, aut Clauium lib. </s>
            <s xml:id="echoid-s3009" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3010" xml:space="preserve">Geom.
              <lb/>
            </s>
            <s xml:id="echoid-s3011" xml:space="preserve">pract. </s>
            <s xml:id="echoid-s3012" xml:space="preserve">ſed iam ad ſolida tranſeamus.</s>
            <s xml:id="echoid-s3013" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3014" xml:space="preserve">Exponantur igitur, ex. </s>
            <s xml:id="echoid-s3015" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3016" xml:space="preserve">tria ſolida Iſoperimetra, Paralellepipedum, Cubus, Sphæra. </s>
            <s xml:id="echoid-s3017" xml:space="preserve">quorũ ambien-
              <lb/>
            tes ſuperficies conſtent ex 24. </s>
            <s xml:id="echoid-s3018" xml:space="preserve">æqualibus quadratis, quorum modulus ſit quadratum M. </s>
            <s xml:id="echoid-s3019" xml:space="preserve">Paralellepipedum
              <lb/>
              <figure xlink:label="fig-0046-01" xlink:href="fig-0046-01a" number="23">
                <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-01"/>
              </figure>
            corpus quadratum oblungum inſtar trabis, cuius oppoſita
              <lb/>
            facies ſunt paralellæ. </s>
            <s xml:id="echoid-s3020" xml:space="preserve">quod autem in figura exponitur am-
              <lb/>
            bitu 6. </s>
            <s xml:id="echoid-s3021" xml:space="preserve">faciebus, ſeu planis, quorum 4. </s>
            <s xml:id="echoid-s3022" xml:space="preserve">lõgiora, ſingula con-
              <lb/>
            tinent 5. </s>
            <s xml:id="echoid-s3023" xml:space="preserve">quadrata cum dimidio: </s>
            <s xml:id="echoid-s3024" xml:space="preserve">extrema verò duo vnum
              <lb/>
            tantum. </s>
            <s xml:id="echoid-s3025" xml:space="preserve">Cubus verò tetminatur 6. </s>
            <s xml:id="echoid-s3026" xml:space="preserve">quadratis ſaciebus, in
              <lb/>
            quibus ſingulis ſunt 4. </s>
            <s xml:id="echoid-s3027" xml:space="preserve">quadrata. </s>
            <s xml:id="echoid-s3028" xml:space="preserve">Sphæra autem debet, & </s>
            <s xml:id="echoid-s3029" xml:space="preserve">
              <lb/>
            ipſa ſphærica ſuperficie ambiri, quæ 24. </s>
            <s xml:id="echoid-s3030" xml:space="preserve">ex ijſdem quadra-
              <lb/>
            tis æqualis ſit. </s>
            <s xml:id="echoid-s3031" xml:space="preserve">conſtruitur autem ſphæra prædicto cubo Iſoperimetra hoc modo. </s>
            <s xml:id="echoid-s3032" xml:space="preserve">Accipitur quarta pars
              <lb/>
            ſuperficiei eam ambituræ, ideſt, parua 6. </s>
            <s xml:id="echoid-s3033" xml:space="preserve">quadrata ex ijs, quæ cubum ambiunt, in circulum redi guntur (vti
              <lb/>
            docet Clauius in fine lib. </s>
            <s xml:id="echoid-s3034" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3035" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3036" xml:space="preserve">Euclidis, aut in Geom. </s>
            <s xml:id="echoid-s3037" xml:space="preserve">pract. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3039" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3040" xml:space="preserve">num. </s>
            <s xml:id="echoid-s3041" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3042" xml:space="preserve">appendicis) erit enim is circu-
              <lb/>
            lus, circulus maximus futuræ ſphæræ, ac proinde diameter eius eiuſdem ſphæræ diameter erit; </s>
            <s xml:id="echoid-s3043" xml:space="preserve">habita igi-
              <lb/>
            tur diametro, habebitur etiam ſphæra, ſicque tria aderunt Iſoperimetra, quæ etiam Mechanicè, diligenti
              <lb/>
            tamen opera, ex aliqua ductili materia, veluti ex cera, confici poſſunt, quòd Lectoris induſtr@æ relinquo.
              <lb/>
            </s>
            <s xml:id="echoid-s3044" xml:space="preserve">Prædicta igitur tria Iſoperimetra iam menſuranda ſunt, ideſt, earum capacitates inueſtigandæ: </s>
            <s xml:id="echoid-s3045" xml:space="preserve">porrò li-
              <lb/>
            neas lineis, & </s>
            <s xml:id="echoid-s3046" xml:space="preserve">ſuperficies quadratis ſuperficiebus menſuramus, ita etiam corpora corporibus, cub@s videli-
              <lb/>
            cet metimur, quia teſte Ariſtotele, menſura debet eſſe eiuſdem generis, cum re menſurata. </s>
            <s xml:id="echoid-s3047" xml:space="preserve">Primo igitur
              <lb/>
            ex lib. </s>
            <s xml:id="echoid-s3048" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3049" xml:space="preserve">Geom. </s>
            <s xml:id="echoid-s3050" xml:space="preserve">pract. </s>
            <s xml:id="echoid-s3051" xml:space="preserve">Clauij, Paralellepipedum capit paruos cubos 5 {1/2}. </s>
            <s xml:id="echoid-s3052" xml:space="preserve">vt etiam ex ſolo figuræ aſpectu pa-
              <lb/>
            tet. </s>
            <s xml:id="echoid-s3053" xml:space="preserve">Cubus autem capit paruos 8. </s>
            <s xml:id="echoid-s3054" xml:space="preserve">cubos ex ijſdem, quare ſuperat Paralellepipedum cubis 2 {1/2}. </s>
            <s xml:id="echoid-s3055" xml:space="preserve">ſphæram ſic
              <lb/>
            menſurabis, per circinum diligenter, accipe diametrũ circuli maximi datæ ſphæræ, quem ſupra diximus
              <lb/>
            continere parua 6. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">quadrata ex ibi aſſumptis; </s>
            <s xml:id="echoid-s3057" xml:space="preserve">eam diametrum inuenies cõtinere paulo plus quam 2. </s>
            <s xml:id="echoid-s3058" xml:space="preserve">& </s>
            <s xml:id="echoid-s3059" xml:space="preserve">duas
              <lb/>
            tertias ex lineolis, ſeu lateribus quadratorum prædictorum; </s>
            <s xml:id="echoid-s3060" xml:space="preserve">hanc etiam diametrum ſic reperies, quoniam
              <lb/>
            area circuli ad quadratum ſuæ diametri habet proportionem ſicuti ferè 11. </s>
            <s xml:id="echoid-s3061" xml:space="preserve">ad 14. </s>
            <s xml:id="echoid-s3062" xml:space="preserve">ex prop @. </s>
            <s xml:id="echoid-s3063" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3064" xml:space="preserve">lib 4. </s>
            <s xml:id="echoid-s3065" xml:space="preserve">Geom-
              <lb/>
            pract. </s>
            <s xml:id="echoid-s3066" xml:space="preserve">Clauij, ſi per auream regulam fiat, vt 11. </s>
            <s xml:id="echoid-s3067" xml:space="preserve">ad 14. </s>
            <s xml:id="echoid-s3068" xml:space="preserve">ita 6. </s>
            <s xml:id="echoid-s3069" xml:space="preserve">area circuli, ad aliud, inuenies 7. </s>
            <s xml:id="echoid-s3070" xml:space="preserve">cum ſeptem vn-
              <lb/>
            decimis pro quadrato diametri: </s>
            <s xml:id="echoid-s3071" xml:space="preserve">huius quadrati radix, erit etiam circuli diameter; </s>
            <s xml:id="echoid-s3072" xml:space="preserve">ea autem radix ſit linea
              <lb/>
            2. </s>
            <s xml:id="echoid-s3073" xml:space="preserve">& </s>
            <s xml:id="echoid-s3074" xml:space="preserve">duo tertia, quamuis ſit vera radice minor: </s>
            <s xml:id="echoid-s3075" xml:space="preserve">hic igitur radix ſi multiplicetur in ſextam partem ſuperfi-
              <lb/>
            ciei ambientis ſphærã, ideſt, in 4. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">productus numerus erit ſphæræ ſoliditas, ex propoſ. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3078" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3079" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3080" xml:space="preserve">Geom. </s>
            <s xml:id="echoid-s3081" xml:space="preserve">pract. </s>
            <s xml:id="echoid-s3082" xml:space="preserve">
              <lb/>
            Clauij, productus autẽ numerus ex ductu 2. </s>
            <s xml:id="echoid-s3083" xml:space="preserve">& </s>
            <s xml:id="echoid-s3084" xml:space="preserve">duobus tertijs, ſeu octo tertijs, ideſt, 10 cũ duabus tert@js, igi-
              <lb/>
            tur cubi 10. </s>
            <s xml:id="echoid-s3085" xml:space="preserve">cum duabus tertijs paruis ex ijſdem, qui conflant Paralellepipedũ, & </s>
            <s xml:id="echoid-s3086" xml:space="preserve">cubum, cõſtituuntſphæ-
              <lb/>
            ræ ſoliditatem, ſeu aream ſolidam. </s>
            <s xml:id="echoid-s3087" xml:space="preserve">quæ quantitas quamuis ſit vera minor ob aſlumptas proportiones, ad-
              <lb/>
            huctamen ſuperat multo alia duo corpora Iſoperimetra, eſt enim ad Paralellepipedum ferè dupla, cubum
              <lb/>
            verò ſuperat paruis cub@s 2 {1/2}. </s>
            <s xml:id="echoid-s3088" xml:space="preserve">ad eum enim ſe habet, vt 10. </s>
            <s xml:id="echoid-s3089" xml:space="preserve">cum duabus tertijs, ad 8. </s>
            <s xml:id="echoid-s3090" xml:space="preserve">idem accidit omnibus
              <lb/>
            alijs @olidis ſphæræ Iſoperimetris. </s>
            <s xml:id="echoid-s3091" xml:space="preserve">patet igitur ſphæram eſſe omnium Iſoperimetrarum capaciſſimam. </s>
            <s xml:id="echoid-s3092" xml:space="preserve">
              <lb/>
            quod erat probandum.</s>
            <s xml:id="echoid-s3093" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3094" xml:space="preserve">Aliter eorum quantitates Mechanicè expendere poſſumus, ideſt, pondere examinare. </s>
            <s xml:id="echoid-s3095" xml:space="preserve">nam ſi paralel-
              <lb/>
            lepipedum pendit libras 5 {1/2}. </s>
            <s xml:id="echoid-s3096" xml:space="preserve">cubus pendet 8. </s>
            <s xml:id="echoid-s3097" xml:space="preserve">ſphæra, vero pluſquam 10. </s>
            <s xml:id="echoid-s3098" xml:space="preserve">cum duabus tertijs, debent autem
              <lb/>
            eſſe ex eadem materia, & </s>
            <s xml:id="echoid-s3099" xml:space="preserve">quidem in pondere homogena. </s>
            <s xml:id="echoid-s3100" xml:space="preserve">Hic etiam aduertendum eſt, corpus illud reli-
              <lb/>
            quis eſſe capacius, quod magis ad ſphæricitatem accedit; </s>
            <s xml:id="echoid-s3101" xml:space="preserve">quod eius anguli magis dilatentur. </s>
            <s xml:id="echoid-s3102" xml:space="preserve">Ex demon-
              <lb/>
            ſtratis etiam ſequitur, eandem materiam ſub figura ſphærica minori ſuperficie ambiri, quàm ſub quauis
              <lb/>
            alia figura: </s>
            <s xml:id="echoid-s3103" xml:space="preserve">quare eadem materia a ſphæricam ad cubicam translata figuram, maiori ambiente ſuperficie
              <lb/>
            indigeret. </s>
            <s xml:id="echoid-s3104" xml:space="preserve">Patet igitur circulum inter planas, ſphæram inter ſolidas, eſſe capaciſſimas. </s>
            <s xml:id="echoid-s3105" xml:space="preserve">Vide Clauium
              <lb/>
            de figuris Iſoperimetris in Geom. </s>
            <s xml:id="echoid-s3106" xml:space="preserve">pract.</s>
            <s xml:id="echoid-s3107" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3108" xml:space="preserve">3 Ratio, ſi mundus non eſſet ſphęr@cus, ſequeretur Deum, naturamuè fruſtra ſuperficiem aliquam fe-
              <lb/>
            ciſſe; </s>
            <s xml:id="echoid-s3109" xml:space="preserve">eadem enim mundi materia ſub alia quauis figura quam ſphęrica, ind@geret, vti ſupra annotauimus,
              <lb/>
            maiori ſuperficie ambiente: </s>
            <s xml:id="echoid-s3110" xml:space="preserve">quare cum poſſit exiſtere cum minori ſuperficie, ſi ſit ſphærica, cur ad aliam.
              <lb/>
            </s>
            <s xml:id="echoid-s3111" xml:space="preserve">figuram fuiſſe redigenda, quæ la xiori ambitu indueretur.</s>
            <s xml:id="echoid-s3112" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3113" xml:space="preserve">4 Apes, Veſpæ, Crabrones, ſuis cellulis capaciſſimam omnium figurarum replentium vacuum, </s>
          </p>
        </div>
      </text>
    </echo>
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