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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        <div xml:id="echoid-div456" type="section" level="1" n="344">
          <pb o="213" file="0235" n="240" rhead="AD MATHEMATICAS."/>
        </div>
        <div xml:id="echoid-div457" type="section" level="1" n="345">
          <head xml:id="echoid-head363" style="it" xml:space="preserve">Methodus ad Aſtronomiam, & partes eius.</head>
          <p>
            <s xml:id="echoid-s18200" xml:space="preserve">QVoniam Aſtronomiam, vt rectè Plato aduertit, duabus veluti alis Geometria, & </s>
            <s xml:id="echoid-s18201" xml:space="preserve">Arithmetica in cæ-
              <lb/>
            lum euolat, ideo primo neceſſaria eſt totius Euclidis præcognitio, necnon Arithmeticæ vulgaris, il-
              <lb/>
            lius præſertim, quæ de Aſtronomicis fractionibus agit, quibus præmiſſis aggredi poteris Autho-
              <lb/>
            res ſuper recenſitos, eodem ordine ſeruato.</s>
            <s xml:id="echoid-s18202" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div458" type="section" level="1" n="346">
          <head xml:id="echoid-head364" style="it" xml:space="preserve">Pro Gnomonica.</head>
          <p>
            <s xml:id="echoid-s18203" xml:space="preserve">ADres Gnomonicas facilè, & </s>
            <s xml:id="echoid-s18204" xml:space="preserve">rectè percipiendas plurimum confert conſtructio Sphæræ Gnomonicæ.
              <lb/>
            </s>
            <s xml:id="echoid-s18205" xml:space="preserve">appello Sphæram Gnomonicam eam in cuius ſuperficie deſcripti ſunt pimò Tropici, Aequator, & </s>
            <s xml:id="echoid-s18206" xml:space="preserve">duo
              <lb/>
            paralelli horizontem tangentes, vnus maximus apparentium, alter occultorum maximus. </s>
            <s xml:id="echoid-s18207" xml:space="preserve">deinde omnes cir-
              <lb/>
            culi horarij, tam hi qui indicant horas Aſtronomicas à meridie inchoatas, quique tranſeunt per polos mun-
              <lb/>
            di, & </s>
            <s xml:id="echoid-s18208" xml:space="preserve">quorum vnus eſt meridianus; </s>
            <s xml:id="echoid-s18209" xml:space="preserve">quam ij, qui indicant horas ab ortu, vel occaſu numeratas, quorum vnus
              <lb/>
            eſt horizon, & </s>
            <s xml:id="echoid-s18210" xml:space="preserve">tangunt duos circulos æquatori paralellos, quorum vnus eſt maximus ſemper apparentium,
              <lb/>
            altet maximus ſemper latentium. </s>
            <s xml:id="echoid-s18211" xml:space="preserve">Conſtructio hæc innuitur a P. </s>
            <s xml:id="echoid-s18212" xml:space="preserve">Clauio in Gnomonica lib. </s>
            <s xml:id="echoid-s18213" xml:space="preserve">1. </s>
            <s xml:id="echoid-s18214" xml:space="preserve">propoſitione 9. </s>
            <s xml:id="echoid-s18215" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s18216" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18217" xml:space="preserve">& </s>
            <s xml:id="echoid-s18218" xml:space="preserve">inde elici poteſt. </s>
            <s xml:id="echoid-s18219" xml:space="preserve">in hac pila ſumma iucunditate, vti expertus ſum, licebit intueri omnes horum cir-
              <lb/>
            culorum poſitus, & </s>
            <s xml:id="echoid-s18220" xml:space="preserve">interſectiones; </s>
            <s xml:id="echoid-s18221" xml:space="preserve">& </s>
            <s xml:id="echoid-s18222" xml:space="preserve">in quibus diurnis circulis omnes tres ſe mutuo ſecent; </s>
            <s xml:id="echoid-s18223" xml:space="preserve">vt in arcubus
              <lb/>
            diurnis horarum 14. </s>
            <s xml:id="echoid-s18224" xml:space="preserve">& </s>
            <s xml:id="echoid-s18225" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18226" xml:space="preserve">& </s>
            <s xml:id="echoid-s18227" xml:space="preserve">in quibus duo tantum; </s>
            <s xml:id="echoid-s18228" xml:space="preserve">& </s>
            <s xml:id="echoid-s18229" xml:space="preserve">alia omnia quæ alioquin obſcuriſſima ſunt, quęq; </s>
            <s xml:id="echoid-s18230" xml:space="preserve">Cla-
              <lb/>
            uius prolixo tædio ad propoſitionem 20. </s>
            <s xml:id="echoid-s18231" xml:space="preserve">explicat. </s>
            <s xml:id="echoid-s18232" xml:space="preserve">hæc porrò Sphæræ conſtructio fieri debet ad datam poli
              <lb/>
            cleuationem, vnica enim nequit eſſe vniuerſalis. </s>
            <s xml:id="echoid-s18233" xml:space="preserve">Reliquæ Aſtronomiæ partes non alia indigent directio-
              <lb/>
            ne præter eam, quam ſupra in Auth. </s>
            <s xml:id="echoid-s18234" xml:space="preserve">Biblioth. </s>
            <s xml:id="echoid-s18235" xml:space="preserve">innuimus.</s>
            <s xml:id="echoid-s18236" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div459" type="section" level="1" n="347">
          <head xml:id="echoid-head365" style="it" xml:space="preserve">Methodus vniuerſalis ad totius Matheſos curriculum ineundum.</head>
          <p>
            <s xml:id="echoid-s18237" xml:space="preserve">SIomnes aut præcipuè Authores ſingularum Mathematicarum, quos ſupra in Bibliotheca recenſuimus,
              <lb/>
            eodem ordine percipiantur, res confecta erit. </s>
            <s xml:id="echoid-s18238" xml:space="preserve">Sed vtile imo neceſſarium puto ſeorſim ſingulis diſtinctè
              <lb/>
            dare operam. </s>
            <s xml:id="echoid-s18239" xml:space="preserve">Primo Geometriæ. </s>
            <s xml:id="echoid-s18240" xml:space="preserve">Secundo Arithmeticæ, & </s>
            <s xml:id="echoid-s18241" xml:space="preserve">ſic deinceps: </s>
            <s xml:id="echoid-s18242" xml:space="preserve">hac enim ratione tollitur omnis
              <lb/>
            confuſio, & </s>
            <s xml:id="echoid-s18243" xml:space="preserve">melius, ac clarius omnia intelliguntur, nam pluribus intentus minor eſt ad ſingula ſenſus.</s>
            <s xml:id="echoid-s18244" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div460" type="section" level="1" n="348">
          <head xml:id="echoid-head366" style="it" xml:space="preserve">Methodus ad Phyſicam, & Methaphyſicam, & Moralem.</head>
          <p>
            <s xml:id="echoid-s18245" xml:space="preserve">QVam neceſſariæ ſint Mathematicæ ad reliquas Philoſophiæ partes rectè capeſſendas, optimè Plato de-
              <lb/>
            clarauit, edicto illo pro foribus Gymnaſij propoſito, nullus ingrediatur ageometretos. </s>
            <s xml:id="echoid-s18246" xml:space="preserve">ſed melius re ip-
              <lb/>
            ſa id confirmabat, cum quotidie ſuis auditoribus problema aliquod Geometricum reſoluẽdum pro-
              <lb/>
            poneret. </s>
            <s xml:id="echoid-s18247" xml:space="preserve">idem etiam manifeſtum eſt ex opere noſtro de locis Mathematicis apud Ariſtotelem, in quo loca
              <lb/>
            num. </s>
            <s xml:id="echoid-s18248" xml:space="preserve">400. </s>
            <s xml:id="echoid-s18249" xml:space="preserve">expoſuimus, quæ abſq; </s>
            <s xml:id="echoid-s18250" xml:space="preserve">Mathematicis intelligi nequeunt. </s>
            <s xml:id="echoid-s18251" xml:space="preserve">Iacobus Zabarella fatetur ſe bis totum
              <lb/>
            Euclidem diligenter perlegiſſe, vt ad germanum Ariſt, ſenſum in libris Logicis penetraret. </s>
            <s xml:id="echoid-s18252" xml:space="preserve">quis libro de cę-
              <lb/>
            lo ſine Sphæra tractatu, quis Meteora, quis tractatum de Viſu, ſine Perſpectiua aſſequi poterit? </s>
            <s xml:id="echoid-s18253" xml:space="preserve">certè nullus.
              <lb/>
            </s>
            <s xml:id="echoid-s18254" xml:space="preserve">Quicunq; </s>
            <s xml:id="echoid-s18255" xml:space="preserve">igitur voluerit pro dignitate Philoſophiam profiteri, is nõ mediocrem Mathematis operam im-
              <lb/>
            pendat oportet, & </s>
            <s xml:id="echoid-s18256" xml:space="preserve">præterea opus noſtrum prædictum conetur intelligere, in eo enim omnia ferè quæ Pe-
              <lb/>
            ripateticis neceſſaria ſunt in vnum collecta, & </s>
            <s xml:id="echoid-s18257" xml:space="preserve">declarata reperiet.</s>
            <s xml:id="echoid-s18258" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div461" type="section" level="1" n="349">
          <head xml:id="echoid-head367" style="it" xml:space="preserve">Methodus ad Militiam.</head>
          <p>
            <s xml:id="echoid-s18259" xml:space="preserve">AD exercitum varijs modis, & </s>
            <s xml:id="echoid-s18260" xml:space="preserve">ordinibus diſponendum, neceſſaria eſt Arithmetica: </s>
            <s xml:id="echoid-s18261" xml:space="preserve">ad varias Machi-
              <lb/>
            nas tam ad oppugnationem, quam ad defenſionem neceſſarias, item ad aquas deducenda neceſſarias eſt
              <lb/>
            Mechanica; </s>
            <s xml:id="echoid-s18262" xml:space="preserve">ad menſurandas à longè per radium viſiuum tum altitudines, tum diſtantias, & </s>
            <s xml:id="echoid-s18263" xml:space="preserve">ad inacceſſarum
              <lb/>
            arcium deſcriptionem neceſſaria eſt Geometria practica. </s>
            <s xml:id="echoid-s18264" xml:space="preserve">miles igitur peritus, vt ſit dicaturque Ingegniero,
              <lb/>
            intelligat ſaltem ſex priores libros Euclidis, deinde Arithmeticam practicam, & </s>
            <s xml:id="echoid-s18265" xml:space="preserve">Geometriam practicam,
              <lb/>
            his enim inſtructus optimè ſtudere poterit libris militaribus, & </s>
            <s xml:id="echoid-s18266" xml:space="preserve">qui de Munitione ſiue, vt aiunt Fortificatio-
              <lb/>
            netractant.</s>
            <s xml:id="echoid-s18267" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18268" xml:space="preserve">Architectores, & </s>
            <s xml:id="echoid-s18269" xml:space="preserve">Pictores poſſim etiam Mathematicis indigent præſertim Perſpectiua. </s>
            <s xml:id="echoid-s18270" xml:space="preserve">Atque hi ſunt
              <lb/>
            præcipui fines quibus viſum eſt ſuas methodos indicare.</s>
            <s xml:id="echoid-s18271" xml:space="preserve"/>
          </p>
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