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

Table of Notes

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    <echo version="1.0RC">
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        <div xml:id="echoid-div91" type="section" level="1" n="61">
          <p>
            <s xml:id="echoid-s4838" xml:space="preserve">
              <pb o="48" file="0068" n="72" rhead="De Mundi Fabrica."/>
            in ratione ſubdupla, habebunt inuicem rationem eam, quam habebunt numeri 1,8. </s>
            <s xml:id="echoid-s4839" xml:space="preserve">ideſt, ea cuius diameter
              <lb/>
            erat diametro alterius dupla, eam octies continebit.</s>
            <s xml:id="echoid-s4840" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4841" xml:space="preserve">Hiſce ita præmiſſis, cum diametri harum ſphęrarum, grani papaueris, ſphæræ digitalis, ſphæræ milliariæ,
              <lb/>
            ſphæræ globi terreſtris, & </s>
            <s xml:id="echoid-s4842" xml:space="preserve">tandem totius mundi ſint notæ, neque latere poterunt earumdem ſphærarum
              <lb/>
            mutuæ proportiones; </s>
            <s xml:id="echoid-s4843" xml:space="preserve">quare notum erit quoties quælibet maior minorem contineat. </s>
            <s xml:id="echoid-s4844" xml:space="preserve">verum per ſingulas
              <lb/>
            ratiocinemur.</s>
            <s xml:id="echoid-s4845" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4846" xml:space="preserve">Quoniam igitur diameter grani papaueris, ad diametrum ſphæræ digitalis habet rationem, quæ eſt in-
              <lb/>
            ter 1. </s>
            <s xml:id="echoid-s4847" xml:space="preserve">& </s>
            <s xml:id="echoid-s4848" xml:space="preserve">40. </s>
            <s xml:id="echoid-s4849" xml:space="preserve">habebunt iſtæ ſphæræ huius triplicatam rationem; </s>
            <s xml:id="echoid-s4850" xml:space="preserve">ſi autem illa triplicentur exhibebit hos nu-
              <lb/>
            meros. </s>
            <s xml:id="echoid-s4851" xml:space="preserve">1, 40, 16, 00, 64, 000. </s>
            <s xml:id="echoid-s4852" xml:space="preserve">igitur inter extremos numeros 1. </s>
            <s xml:id="echoid-s4853" xml:space="preserve">& </s>
            <s xml:id="echoid-s4854" xml:space="preserve">64.</s>
            <s xml:id="echoid-s4855" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4856" xml:space="preserve">eſt ratio triplicata quæſita, quam
              <lb/>
            ſpæræ inuicem habent: </s>
            <s xml:id="echoid-s4857" xml:space="preserve">hoc eſt ſphæra digitalis continent grana papaueris. </s>
            <s xml:id="echoid-s4858" xml:space="preserve">64,000. </s>
            <s xml:id="echoid-s4859" xml:space="preserve">quia vero granum vnum
              <lb/>
            pap. </s>
            <s xml:id="echoid-s4860" xml:space="preserve">continet arenulas 100. </s>
            <s xml:id="echoid-s4861" xml:space="preserve">ſequitur ſphæram digitalem continere arenulas, 6,400,000. </s>
            <s xml:id="echoid-s4862" xml:space="preserve">qui numerus pro-
              <lb/>
            ducitur multiplicando 100. </s>
            <s xml:id="echoid-s4863" xml:space="preserve">in 64, 000.</s>
            <s xml:id="echoid-s4864" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4865" xml:space="preserve">Rurſus quoniam diameter ſphæræ digitalis ad diametrum ſphæræ milliariæ, habet rationem, quam ha-
              <lb/>
            bent 1, 80, 000. </s>
            <s xml:id="echoid-s4866" xml:space="preserve">quæ ratio triplicata dat hoſce terminos; </s>
            <s xml:id="echoid-s4867" xml:space="preserve">1, 80, 000, 6, 400, 000, 000, 512, 000, 000, 000, 000.
              <lb/>
            </s>
            <s xml:id="echoid-s4868" xml:space="preserve">propterea ratio primi ad vltimum eſt proportio ſpærarum: </s>
            <s xml:id="echoid-s4869" xml:space="preserve">quare ſphæra milliaria continet tot ſphæras di-
              <lb/>
            gitales, quot quartus numerus continet vnitates, & </s>
            <s xml:id="echoid-s4870" xml:space="preserve">quia ſphæra digitalis continet arenulas 6. </s>
            <s xml:id="echoid-s4871" xml:space="preserve">400.</s>
            <s xml:id="echoid-s4872" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4873" xml:space="preserve">ſi hic
              <lb/>
            numerus in quartum prædictum multiplicetur, producetur numerus 3, 276, 800, 000, 000, 000, 000, 000. </s>
            <s xml:id="echoid-s4874" xml:space="preserve">nu-
              <lb/>
            merus videlicet arenularum in milliario globo contentarum.</s>
            <s xml:id="echoid-s4875" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4876" xml:space="preserve">Præterea quia diameter terreſtris ſphæræ continet 7, 000. </s>
            <s xml:id="echoid-s4877" xml:space="preserve">erit eius habitudo ad diametrum globi millia-
              <lb/>
            rij, quæ 1. </s>
            <s xml:id="echoid-s4878" xml:space="preserve">ad 7, 000. </s>
            <s xml:id="echoid-s4879" xml:space="preserve">cuius triplicata eſt in his numeris 1, 7, 000, 49, 000, 000, 343, 000, 000, 000. </s>
            <s xml:id="echoid-s4880" xml:space="preserve">Tota igitur
              <lb/>
            terra ad ſphæram milliariam collata eſt ſicuti quartus num. </s>
            <s xml:id="echoid-s4881" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4882" xml:space="preserve">Iam vero ſi num. </s>
            <s xml:id="echoid-s4883" xml:space="preserve">arenularum vnius giobi mil-
              <lb/>
            liarij, quem ante inuenimus, ducatur in hũc quartum numerum, productus numerus indicabit arenulas om-
              <lb/>
            nes in tota terræ mole contentas: </s>
            <s xml:id="echoid-s4884" xml:space="preserve">is autem eſt hic; </s>
            <s xml:id="echoid-s4885" xml:space="preserve">1, 123, 942, 400, 000, 000, 000, 000, 000, 000, 000, 000.
              <lb/>
            </s>
            <s xml:id="echoid-s4886" xml:space="preserve">vnde iam ſatis patere poteſt, illorum Philoſophorum opinionũ minimè ſubſiſtere, qui arenarum omnium
              <lb/>
            per maria diſperſarum adeò magnum eſſe numerum opinabantur, vt nullo pacto ſcribi, aut proferri poſſet. </s>
            <s xml:id="echoid-s4887" xml:space="preserve">
              <lb/>
            atque hæc ſatis in præſentia videri poſſent, cum tractationem quantitatis terræ ſapiant, eamque minime
              <lb/>
            excedant.</s>
            <s xml:id="echoid-s4888" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4889" xml:space="preserve">Verumtamen ne Archimedis diſcurſus ſubtiliſſimus obtruncetur, pauca quæ ſuperſunt afferam. </s>
            <s xml:id="echoid-s4890" xml:space="preserve">ſtatutum
              <lb/>
            eſt ſupra diametrum terræ ad diametrum mundi eſſe ficut 1. </s>
            <s xml:id="echoid-s4891" xml:space="preserve">ad 14,000. </s>
            <s xml:id="echoid-s4892" xml:space="preserve">quæ analogia ſi triplicetur dabit ho-
              <lb/>
            ſce numeros, 1,14,000. </s>
            <s xml:id="echoid-s4893" xml:space="preserve">196,000,000. </s>
            <s xml:id="echoid-s4894" xml:space="preserve">2,744,000,000,000. </s>
            <s xml:id="echoid-s4895" xml:space="preserve">terra igitur ad totam mundi ſphæram eſt ſicut 1. </s>
            <s xml:id="echoid-s4896" xml:space="preserve">ad
              <lb/>
            quartum numerum. </s>
            <s xml:id="echoid-s4897" xml:space="preserve">& </s>
            <s xml:id="echoid-s4898" xml:space="preserve">quoniam numerus arenularum totius globi terreſtri paulò ante repertus eſt, ſi is du-
              <lb/>
            catur in hunc quartum numerum, producetur numerus ille admirabilis omnium arenularum, quæ totam
              <lb/>
            mundi ſphęram complerent, is autem eſt huiuſmodi, 3,084,097,945,6000,000,000,000,000,000,000,000,000,
              <lb/>
            000,000,000. </s>
            <s xml:id="echoid-s4899" xml:space="preserve">qui numerus conſtat tantummodo figuris quadraginta ſex, qui tamen multo maior iuſto fit,
              <lb/>
            neceſſe eſt, cùm multa aduerſarijs dederimus, vt illuſtrior, ac admirabilior noſtra euaderet diſputatio.</s>
            <s xml:id="echoid-s4900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4901" xml:space="preserve">Atque hæc eſt illa Archimedis de arenæ numero mira perueſtigatio, quam ſummopere tota antiqui-
              <lb/>
            tas ſimul, ac poſteritas admirata eſt.</s>
            <s xml:id="echoid-s4902" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div92" type="section" level="1" n="62">
          <head xml:id="echoid-head65" xml:space="preserve">LIBER QVINTVS</head>
          <head xml:id="echoid-head66" xml:space="preserve">De Aqua Elementari, ſiue de Mari.</head>
          <head xml:id="echoid-head67" style="it" xml:space="preserve">De loco Aque Mariſuè. Cap. I.</head>
          <p>
            <s xml:id="echoid-s4903" xml:space="preserve">QVem locum Mare in ordine Elementorum occupet, ſenſu manifeſtum eſt, videmus enim
              <lb/>
            ipſum proximè ſupra terram collocatum eſſe, non tamen ita, vt totam ambiat, ſed dimidiã
              <unsure/>
              <lb/>
            ferè ſuperficiem, tantum contingat. </s>
            <s xml:id="echoid-s4904" xml:space="preserve">quod factum eſt, quia terra non eſt perſectè rotunda,
              <lb/>
            ſed habet plurimas, ac magnas cauitates, in quas omnis aquarum copia receſſit: </s>
            <s xml:id="echoid-s4905" xml:space="preserve">ibiq; </s>
            <s xml:id="echoid-s4906" xml:space="preserve">ſubſi-
              <lb/>
            det: </s>
            <s xml:id="echoid-s4907" xml:space="preserve">ſi enim eſſet perfectè rotũda deberent aquæ iuxta naturalem earum ſtatum ſupra vni-
              <lb/>
            uerſam terræ faciem circunfundi, eamque complecti, cum elementum aquæ ſit elemento
              <lb/>
            terræ leuius. </s>
            <s xml:id="echoid-s4908" xml:space="preserve">vnde nonnulli magnę auctoritatis Theologi, terram initio mundi à Deo om-
              <lb/>
            nino rotundam, ſiue vllis cauitatibus, aut eminentijs factam, ac proinde totam aquis circumfuſam fuiſſe exi-
              <lb/>
            ſtimant. </s>
            <s xml:id="echoid-s4909" xml:space="preserve">Cùm vero Deus dixit; </s>
            <s xml:id="echoid-s4910" xml:space="preserve">congregentur aquæ in locum vnum, vt appareat arida; </s>
            <s xml:id="echoid-s4911" xml:space="preserve">ob animantium ſci-
              <lb/>
            licet terreſtrium vitam, tũc diuino iuſſu cauitates latè patentes in terras factas eſſe, in quas omnem aquarum
              <lb/>
            vim ſua naturali propenſione, qua ad decliuiora loca deſcendunt, tanquam in ſuas congregationes conceſ-
              <lb/>
            ſiſſe, ſicq; </s>
            <s xml:id="echoid-s4912" xml:space="preserve">varia maria in diuerſis terræ partibus exorta eſſe porrò ex partibus illis terrę inde extractis, mon-
              <lb/>
            tes eſſe conſtructos veriſimile eſſe parires opinantur. </s>
            <s xml:id="echoid-s4913" xml:space="preserve">quod inde colligunt, quia quanta eſt montium altitu-
              <lb/>
            do, tanta eſt etiam maris profunditas, vt de mari nautæ; </s>
            <s xml:id="echoid-s4914" xml:space="preserve">de montibus vero Geometræ obſeruarunt.</s>
            <s xml:id="echoid-s4915" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4916" xml:space="preserve">Pręterea rationi conſentaneũ eſt, vt aqua ſecundum à terra locum obtineat, cùm ſit proximè leuior </s>
          </p>
        </div>
      </text>
    </echo>
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