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-div85" type="section" level="1" n="59">
          <p>
            <s xml:id="echoid-s4247" xml:space="preserve">
              <pb o="43" file="0063" n="67" rhead="Liber Quartus."/>
            quantitatem conſiderare Geometræ ſolet; </s>
            <s xml:id="echoid-s4248" xml:space="preserve">diametrum videlicet eius, peripherlam elus eirculi maximi, ſu-
              <lb/>
            perficiem conuexam, vltimo ſoliditatem. </s>
            <s xml:id="echoid-s4249" xml:space="preserve">ſed priuſquam prædictas terræ quantitates indagemus, aut me-
              <lb/>
            tiamu r, de menſuris ipſis nonnulla præmittere oportet.</s>
            <s xml:id="echoid-s4250" xml:space="preserve"/>
          </p>
          <figure number="35">
            <image file="0063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0063-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s4251" xml:space="preserve">Pes Romanus erat duplo maior quam linea A B. </s>
            <s xml:id="echoid-s4252" xml:space="preserve">in margine adſcripta, quem ex P. </s>
            <s xml:id="echoid-s4253" xml:space="preserve">Vilalpando
              <lb/>
            de Templo Salom. </s>
            <s xml:id="echoid-s4254" xml:space="preserve">deſumpſimus. </s>
            <s xml:id="echoid-s4255" xml:space="preserve">Pes autem continet digitos 16.</s>
            <s xml:id="echoid-s4256" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4257" xml:space="preserve">Paſſus Geometricus continebat pedes quinque. </s>
            <s xml:id="echoid-s4258" xml:space="preserve">eſt autem interuallum intus eiuſdem pedis ve-
              <lb/>
            ſtigia duo ambulamus. </s>
            <s xml:id="echoid-s4259" xml:space="preserve">ideſt, ab eleuatione eiuſdem incluſiuè plantæ vſque ad eiuſdem poſitionem
              <lb/>
            excluſiue.</s>
            <s xml:id="echoid-s4260" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4261" xml:space="preserve">Stadium continet paſſus Geometricos 125. </s>
            <s xml:id="echoid-s4262" xml:space="preserve">vel pedes 625.</s>
            <s xml:id="echoid-s4263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4264" xml:space="preserve">Milliaria ſiue milliare continet 8. </s>
            <s xml:id="echoid-s4265" xml:space="preserve">ſtadia; </s>
            <s xml:id="echoid-s4266" xml:space="preserve">ſed paſſus Geometricos mille, vnde & </s>
            <s xml:id="echoid-s4267" xml:space="preserve">milliarium de-
              <lb/>
            nominatur.</s>
            <s xml:id="echoid-s4268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4269" xml:space="preserve">Leuca Gallica, & </s>
            <s xml:id="echoid-s4270" xml:space="preserve">Hiſpanica continet ſeſquimilliarium, ideſt vnum cum dimidio.</s>
            <s xml:id="echoid-s4271" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4272" xml:space="preserve">Leuca Germanica communis conſtat milliar. </s>
            <s xml:id="echoid-s4273" xml:space="preserve">4.</s>
            <s xml:id="echoid-s4274" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4275" xml:space="preserve">Valor autem harum menſurarum ſumitur penes longitudinem, ac propterea terreſtres longi-
              <lb/>
            tudine veluti itinere, per eas metimur. </s>
            <s xml:id="echoid-s4276" xml:space="preserve">ſolent præterea hæ menſuræ ſumi etiam ſecundum latitu-
              <lb/>
            dinem, ideſt, ſecundum ſuperficiem, in qua acceptione euadunt ſuperficies quadratæ, ſiue qua-
              <lb/>
            drata; </s>
            <s xml:id="echoid-s4277" xml:space="preserve">ſic pes quadratus, paſſus quadratus; </s>
            <s xml:id="echoid-s4278" xml:space="preserve">ſtadium quadratum, milliare quadratum, ſunt quadratæ
              <lb/>
            ſuperficies, quarum quatuor latera ſunt æqualia quatuor pedibus linearibus; </s>
            <s xml:id="echoid-s4279" xml:space="preserve">vel quatuor paſſibus,
              <lb/>
            ſtadijs, aut milliarijs linearibus. </s>
            <s xml:id="echoid-s4280" xml:space="preserve">in qua acceptione non habent inuicem eaſdem proportiones quas
              <lb/>
            habent latera eorum, ſiue quas habent quando vti lineæ ſumuntur. </s>
            <s xml:id="echoid-s4281" xml:space="preserve">hiſce autem quadratis ſuperfi-
              <lb/>
            ciebus vtuntur ad alias ſuperficies menſurandas.</s>
            <s xml:id="echoid-s4282" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4283" xml:space="preserve">Sumuntur etiam pro ſolidis menſuris, qua ratione ſunt omnes Cubi, quorum ſex ſuperficies cos
              <lb/>
            terminantes, & </s>
            <s xml:id="echoid-s4284" xml:space="preserve">ambientes ſunt 6. </s>
            <s xml:id="echoid-s4285" xml:space="preserve">æqualia quadrata modo explicata: </s>
            <s xml:id="echoid-s4286" xml:space="preserve">ſic pes cubicus, paſſus cubicus,
              <lb/>
            milliare cubicum, &</s>
            <s xml:id="echoid-s4287" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4288" xml:space="preserve">ſunt cubi, quos 6. </s>
            <s xml:id="echoid-s4289" xml:space="preserve">pedes quadrati, vel 6. </s>
            <s xml:id="echoid-s4290" xml:space="preserve">paſſus quadrati, &</s>
            <s xml:id="echoid-s4291" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4292" xml:space="preserve">ambiunt. </s>
            <s xml:id="echoid-s4293" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s4294" xml:space="preserve">hi-
              <lb/>
            ſce cubis ſolida corpora menſurantur. </s>
            <s xml:id="echoid-s4295" xml:space="preserve">quare pes linearis menſurat alias lineas; </s>
            <s xml:id="echoid-s4296" xml:space="preserve">pes quadratus ſu-
              <lb/>
            perficialis, metitur ſuperficies: </s>
            <s xml:id="echoid-s4297" xml:space="preserve">Pes cubicus ſolidus, eſt ſolidarum menſura. </s>
            <s xml:id="echoid-s4298" xml:space="preserve">his prænotatis varios,
              <lb/>
            eoſque acutiſſimos modos explicemus, quibus Aſtronomi quadruplicem terræ quantitatem ſunt
              <lb/>
            perſcrutati.</s>
            <s xml:id="echoid-s4299" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4300" xml:space="preserve">Aſtronomorum veterrimi, vti Ptolemæus in Geographia tradit, hanc inibant rationem. </s>
            <s xml:id="echoid-s4301" xml:space="preserve">pri-
              <lb/>
            mo conſiderabant quod cum terra ſit rotunda, atque in medio ſirmamenti ſita, cumque ambitus
              <lb/>
            tam terræ, quam firmamenti maximus intelligatur ab Aſtronomis diuiſus in partes 360. </s>
            <s xml:id="echoid-s4302" xml:space="preserve">quas gra-
              <lb/>
            dus appellauimus, neceſſario ſequitur ſingulis cæli gradibus ſingulos terræ gradus reſpondere; </s>
            <s xml:id="echoid-s4303" xml:space="preserve">vt
              <lb/>
            in ſequenti figura, ſi inter duo loca in terra G H. </s>
            <s xml:id="echoid-s4304" xml:space="preserve">ſint duo, aut tres gradus, pariter in cælo in arcu
              <lb/>
            C S. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">illi reſpondebunt gradus duo, vel tres, &</s>
            <s xml:id="echoid-s4306" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4307" xml:space="preserve">duæ enim lineæ X C. </s>
            <s xml:id="echoid-s4308" xml:space="preserve">X S. </s>
            <s xml:id="echoid-s4309" xml:space="preserve">è centro ingredientes
              <lb/>
            intercipiunt arcus G H. </s>
            <s xml:id="echoid-s4310" xml:space="preserve">C S. </s>
            <s xml:id="echoid-s4311" xml:space="preserve">ſimiles, ſeu proportionales, ideſt, quota pars eſt arcus G H. </s>
            <s xml:id="echoid-s4312" xml:space="preserve">terreni
              <lb/>
            ambitus, tanta erit etiam arcus C S. </s>
            <s xml:id="echoid-s4313" xml:space="preserve">cæleſtis peripheriæ, vt propoſitione prima Appar. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">probaui-
              <lb/>
            mus, aſſumebant deinde duo loca ſub eodem meridiano poſita, v. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4316" xml:space="preserve">duo G H. </s>
            <s xml:id="echoid-s4317" xml:space="preserve">& </s>
            <s xml:id="echoid-s4318" xml:space="preserve">præterea duas
              <lb/>
            ſtellas fixas, quæ ijſdem locis eſſent verticales; </s>
            <s xml:id="echoid-s4319" xml:space="preserve">earum diſtantiam diligenter per quadrantem ob-
              <lb/>
            ſeruabant, quot ſcilicet gradus in meridiano inter vtramq; </s>
            <s xml:id="echoid-s4320" xml:space="preserve">interciperentur, ſeu quantus eſſet ar-
              <lb/>
            cus meridiani inter vertices aſſumptorum locorum. </s>
            <s xml:id="echoid-s4321" xml:space="preserve">& </s>
            <s xml:id="echoid-s4322" xml:space="preserve">quamuis hæc obſeruatio ſieret in ſuperfi-
              <lb/>
            cie terræ, ob exiguam tamen eius paruitatem reſpectu firmamenti, perinde eſt, ac ſi in centro ha-
              <lb/>
            berentur. </s>
            <s xml:id="echoid-s4323" xml:space="preserve">eundem propterea arcum C S. </s>
            <s xml:id="echoid-s4324" xml:space="preserve">in cælo duo radij opſici, ſeu viſiui, ad ſenſum compræ-
              <lb/>
              <figure xlink:label="fig-0063-02" xlink:href="fig-0063-02a" number="36">
                <image file="0063-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0063-02"/>
              </figure>
            hendunt, ſiue ex G. </s>
            <s xml:id="echoid-s4325" xml:space="preserve">in ſuperficie, ſiue ex cen-
              <lb/>
            tro X. </s>
            <s xml:id="echoid-s4326" xml:space="preserve">egrediantur. </s>
            <s xml:id="echoid-s4327" xml:space="preserve">quot igitur gradus inar-
              <lb/>
            cu C S. </s>
            <s xml:id="echoid-s4328" xml:space="preserve">inueniebant, tot etiam in arcu terre-
              <lb/>
            ſtri G H. </s>
            <s xml:id="echoid-s4329" xml:space="preserve">contineri neceſſario concludebant;
              <lb/>
            </s>
            <s xml:id="echoid-s4330" xml:space="preserve">ponamus, v. </s>
            <s xml:id="echoid-s4331" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4332" xml:space="preserve">fuiſſe gr. </s>
            <s xml:id="echoid-s4333" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4334" xml:space="preserve">in arcu C S. </s>
            <s xml:id="echoid-s4335" xml:space="preserve">igitur
              <lb/>
            tres quoque in arcu G H. </s>
            <s xml:id="echoid-s4336" xml:space="preserve">terreſtri contine-
              <lb/>
            bantur: </s>
            <s xml:id="echoid-s4337" xml:space="preserve">quo in tres æquas partes diuiſo, gra-
              <lb/>
            dum etiam vnum in terra exploratũ habue-
              <lb/>
            runt. </s>
            <s xml:id="echoid-s4338" xml:space="preserve">hunc igitur ſic cognitum poſtea per ſta-
              <lb/>
            dia metiebantur: </s>
            <s xml:id="echoid-s4339" xml:space="preserve">ei quæ vni conuenere ſta-
              <lb/>
            dia ferè 1111. </s>
            <s xml:id="echoid-s4340" xml:space="preserve">milliaria verò prope 138. </s>
            <s xml:id="echoid-s4341" xml:space="preserve">quia
              <lb/>
            vero maximus terræ ambitus conſtat 360. </s>
            <s xml:id="echoid-s4342" xml:space="preserve">par
              <lb/>
            tibus, ideo prædictum numerum ſtadiorum
              <lb/>
            multiplicantes per 360. </s>
            <s xml:id="echoid-s4343" xml:space="preserve">totius terreni circuli
              <lb/>
            ambitum continere reperunt ſtadia 400,000. </s>
            <s xml:id="echoid-s4344" xml:space="preserve">
              <lb/>
            ideſt, quadringenta millia, quæ efficiunt mil-
              <lb/>
            liaria 50.</s>
            <s xml:id="echoid-s4345" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4346" xml:space="preserve">ideſt, quinquaginta millia; </s>
            <s xml:id="echoid-s4347" xml:space="preserve">vt
              <lb/>
            Ariſt. </s>
            <s xml:id="echoid-s4348" xml:space="preserve">ad finẽ 2. </s>
            <s xml:id="echoid-s4349" xml:space="preserve">de cælo ſic refert; </s>
            <s xml:id="echoid-s4350" xml:space="preserve">Mathema-
              <lb/>
            ticorum etiam, inquit, qui circumferentiæ
              <lb/>
            magnitudinem ratiocinari tentant ad 400. </s>
            <s xml:id="echoid-s4351" xml:space="preserve">
              <lb/>
            dicunt eſſe ſtadiorum millia.</s>
            <s xml:id="echoid-s4352" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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