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-div85" type="section" level="1" n="59">
          <p>
            <s xml:id="echoid-s4449" xml:space="preserve">
              <pb o="45" file="0065" n="69" rhead="Liber Quartus."/>
            mus accuratè ſtellis omnibus numeros, & </s>
            <s xml:id="echoid-s4450" xml:space="preserve">nomina fecit, maiorum vijs inſiſtens. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">affirmauit terræ ambitum
              <lb/>
            continere ſtadia 277, 000, quæ efficiunt milliaria 34. </s>
            <s xml:id="echoid-s4452" xml:space="preserve">625.</s>
            <s xml:id="echoid-s4453" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4454" xml:space="preserve">Prolemæus deinde Aſtronomorum princeps, ijſdem modis terreſtri peripheriæ ſtadia 180’ 000. </s>
            <s xml:id="echoid-s4455" xml:space="preserve">ſeu mil-
              <lb/>
            liaria 22. </s>
            <s xml:id="echoid-s4456" xml:space="preserve">500, attribuit.</s>
            <s xml:id="echoid-s4457" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4458" xml:space="preserve">Cum deinde litteræ ac præcipue Aſtronomica ſtudia apud Arabes florerent, extitit Almamon rex Ara-
              <lb/>
            bum regalibus hiſce ſtudijs oblectatus, cuius præcepto, vti narrat Abifeldea pariter Arabs initio ſuæ Geo-
              <lb/>
            graphiæ, nonnulli ablegati fuerunt, qui in Campis Singar, & </s>
            <s xml:id="echoid-s4459" xml:space="preserve">vicinis maribus iuxta rectum iter, & </s>
            <s xml:id="echoid-s4460" xml:space="preserve">poli ſi-
              <lb/>
            tum, obſeruarunt quot milliaria reſponderent vni gradui cæleſti, & </s>
            <s xml:id="echoid-s4461" xml:space="preserve">depræhenſum fuiſſe ab illis in vno gra-
              <lb/>
            du conficiendo milliaria 56. </s>
            <s xml:id="echoid-s4462" xml:space="preserve">& </s>
            <s xml:id="echoid-s4463" xml:space="preserve">duo tertia per tranſiri, ac proinde totum terræ ambitum conſtare millia-
              <lb/>
            ribus 20.</s>
            <s xml:id="echoid-s4464" xml:space="preserve">400. </s>
            <s xml:id="echoid-s4465" xml:space="preserve">quam magnitudindem cæteri
              <unsure/>
            Arabes, Alfraganus, Thebitus, &</s>
            <s xml:id="echoid-s4466" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4467" xml:space="preserve">complexi ſunt.</s>
            <s xml:id="echoid-s4468" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4469" xml:space="preserve">Neque vero in præclara adeo inquiſitione deceſſe tandem aliqua experientia debuit; </s>
            <s xml:id="echoid-s4470" xml:space="preserve">recentiores enim
              <lb/>
            Argonautæ rerum Aſtronomicarum ſatis gnari, qui iam ſæpius totum Oceanum magno ac fælici auſu cir-
              <lb/>
            cumnauigarunt, quantum ipſi experiri potuerunt, exiſtimant totum terreni Globi circuitum complecti
              <lb/>
            milliaria 19′080. </s>
            <s xml:id="echoid-s4471" xml:space="preserve">ſic autem vni gradui cedunt milliaria 53.</s>
            <s xml:id="echoid-s4472" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4473" xml:space="preserve">Omnes porrò prædicti indagatores primo terræ ambitum præueſtigarunt, vnde poſtea cæteras quantita-
              <lb/>
            tes habere poſſent; </s>
            <s xml:id="echoid-s4474" xml:space="preserve">vt paulo poſt oſtendam.</s>
            <s xml:id="echoid-s4475" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4476" xml:space="preserve">Illud tandem conſideratione dignum videtur, quanto videlicet antiquiores ſunt prædicti obſeruatores,
              <lb/>
            eo facere terræ ambitum maiorem, ita vt ſemper a priſcis illis, vſq; </s>
            <s xml:id="echoid-s4477" xml:space="preserve">ad noſtra tempora hic ambitus decreue-
              <lb/>
            rit. </s>
            <s xml:id="echoid-s4478" xml:space="preserve">quod non niſi ex rudioribus obſeruationibus, quæ quotidie exactiores euadunt, vel ex ſtadiorum, aut mil
              <lb/>
            liariorum varietate accidiſſe exiſtimo: </s>
            <s xml:id="echoid-s4479" xml:space="preserve">videmus enim, quod ad hanc varietatem attinet, ſingulas nationes,
              <lb/>
            imo etiam prouincias ab inuicem valde diſcrepare. </s>
            <s xml:id="echoid-s4480" xml:space="preserve">qua propter vt hæc varietas, ac proinde veritatis obum-
              <lb/>
            bratio tollatur, libenter Aſtronomis auctor eſſe velim, vt deinceps omnes pro vno milliario intelligãt vnius
              <lb/>
            terreſtris gradus partem ſexageſimam. </s>
            <s xml:id="echoid-s4481" xml:space="preserve">quamuis enim talis pars nondum ſit determinata, nec ſatis cognita,
              <lb/>
            facile tamen eſt eam cognoſcere; </s>
            <s xml:id="echoid-s4482" xml:space="preserve">quidni enim Princeps quiſpiam nobiliſſimo hoc ſtudio delectatus, ceu al-
              <lb/>
            ter Almamon poterit exquiſitè gradum vnum in planitie quapiam, vel in ora maritima explorare; </s>
            <s xml:id="echoid-s4483" xml:space="preserve">ac pro-
              <lb/>
            inde eius ſexageſimam partem accuratè metiri; </s>
            <s xml:id="echoid-s4484" xml:space="preserve">quam poſtea milliarium aſtronomicum in poſterum ſtatuat,
              <lb/>
            atq; </s>
            <s xml:id="echoid-s4485" xml:space="preserve">determinet. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">quod quidem valde conueniens eſſet, tum quia nonnulli iam ex antiquis vni gradui millia-
              <lb/>
            ria 60. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">attribuerunt, cum alij plura alij pauciora attribuerent: </s>
            <s xml:id="echoid-s4488" xml:space="preserve">quapropter erit hoc milliare Aſtronomicum
              <lb/>
            idem fere ac milliare commune, tũ etiam quia ſexagenarius numerus ob varias ſui ipſius commoditates val-
              <lb/>
            de familiaris eſt Aſtronomis.</s>
            <s xml:id="echoid-s4489" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4490" xml:space="preserve">Poſtremus omnium ſuperiori ſeculo Franciſcus Maurolycus Abbas Syracuſanus, acutiſſimam rationem
              <lb/>
            adinuenit, qua primo, non ambitus, vt à
              <unsure/>
            cæteris factum eſt, ſed diameter terreni orbis explorari poſſit: </s>
            <s xml:id="echoid-s4491" xml:space="preserve">Eli-
              <lb/>
            gendus eſt (inquit in ſua Coſmographia) in primis mons editiſſimus, vnde maris proſpectus longè pateat;
              <lb/>
            </s>
            <s xml:id="echoid-s4492" xml:space="preserve">exiſtimo Aethnam montem huic negotio aptiſſimum, nam ex eius apice per plura quam ducenta paſſuum
              <lb/>
            millia in pelago viſus pro@enditur. </s>
            <s xml:id="echoid-s4493" xml:space="preserve">Oportet igitur vt montis altitudo perpendicularis ab eius vertice, vſq; </s>
            <s xml:id="echoid-s4494" xml:space="preserve">
              <lb/>
            ad maris æquilibrium (ideſt, vſq; </s>
            <s xml:id="echoid-s4495" xml:space="preserve">ad maris ſuperficiem, quæ fi extenderetur ſub monte eſſet) nota ſit in paſ
              <lb/>
            ſibus. </s>
            <s xml:id="echoid-s4496" xml:space="preserve">(qua vero ratione hæ montium altitudines menſurentur, in ſequenti appendice oſtendemus) deinde
              <lb/>
            ex ipſius vertice metiemur interuallum vſq; </s>
            <s xml:id="echoid-s4497" xml:space="preserve">ad extremam horizontis periphæriam, quod quidem non ſolũ
              <lb/>
            Geometricè, vt ipſe Maurolycus ſupponit oſtendemus, verum etiam Mechanicè prædictum interuallum. </s>
            <s xml:id="echoid-s4498" xml:space="preserve">
              <lb/>
            vſq; </s>
            <s xml:id="echoid-s4499" xml:space="preserve">ad aliquod vltimum in horizonte viſum, menſurabimus, videlicet per decempedam, qua practici men-
              <lb/>
            ſores vtuntur. </s>
            <s xml:id="echoid-s4500" xml:space="preserve">quibus paratis intelligantur iam hæc in præſenti figura; </s>
            <s xml:id="echoid-s4501" xml:space="preserve">ſit circulus terræ C B. </s>
            <s xml:id="echoid-s4502" xml:space="preserve">ex centro D. </s>
            <s xml:id="echoid-s4503" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0065-01" xlink:href="fig-0065-01a" number="38">
                <image file="0065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0065-01"/>
              </figure>
            deſcriptus: </s>
            <s xml:id="echoid-s4504" xml:space="preserve">linea A B. </s>
            <s xml:id="echoid-s4505" xml:space="preserve">ſit pro altitudine montis perpendiculari, quę extendantur vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s4506" xml:space="preserve">ad centrum terræ D. </s>
            <s xml:id="echoid-s4507" xml:space="preserve">linea A C. </s>
            <s xml:id="echoid-s4508" xml:space="preserve">ſit radius viſiuus ad vltimum vſq; </s>
            <s xml:id="echoid-s4509" xml:space="preserve">horizontem C. </s>
            <s xml:id="echoid-s4510" xml:space="preserve">de-
              <lb/>
            ſinens, ac proinde tangens terram in puncto C. </s>
            <s xml:id="echoid-s4511" xml:space="preserve">ducanturque C D. </s>
            <s xml:id="echoid-s4512" xml:space="preserve">& </s>
            <s xml:id="echoid-s4513" xml:space="preserve">C B. </s>
            <s xml:id="echoid-s4514" xml:space="preserve">propoſitum
              <lb/>
            eſt igitur ex prænotatis cognoſcere lineam B D. </s>
            <s xml:id="echoid-s4515" xml:space="preserve">ſemidiametrũ videlicet terræ. </s>
            <s xml:id="echoid-s4516" xml:space="preserve">con-
              <lb/>
            ſidero igitur triangulum A C D. </s>
            <s xml:id="echoid-s4517" xml:space="preserve">in quo ex præmiſſis cognitum eſt latus C C. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">ad ſen-
              <lb/>
            ſum enim æquale eſt ipſi C B. </s>
            <s xml:id="echoid-s4519" xml:space="preserve">iam in paſſibus cognito. </s>
            <s xml:id="echoid-s4520" xml:space="preserve">duo præterea anguli manife-
              <lb/>
            ſti ſunt, angulus enim ad C. </s>
            <s xml:id="echoid-s4521" xml:space="preserve">eſt rectus per 18. </s>
            <s xml:id="echoid-s4522" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4523" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4524" xml:space="preserve">Elementi. </s>
            <s xml:id="echoid-s4525" xml:space="preserve">Angulus vero ad
              <lb/>
            A. </s>
            <s xml:id="echoid-s4526" xml:space="preserve">cognoſcitur ex inſtrumento, veluti ex quadrante noſtro, per cuius dioptram ex A. </s>
            <s xml:id="echoid-s4527" xml:space="preserve">
              <lb/>
            collimandum eſt in C. </s>
            <s xml:id="echoid-s4528" xml:space="preserve">per 5. </s>
            <s xml:id="echoid-s4529" xml:space="preserve">igitur Appar. </s>
            <s xml:id="echoid-s4530" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4531" xml:space="preserve">conſtruatur in papyro triangulum
              <lb/>
            ſimile triangulo huic A C D. </s>
            <s xml:id="echoid-s4532" xml:space="preserve">cx quo per 6. </s>
            <s xml:id="echoid-s4533" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4534" xml:space="preserve">eiuſdem Appar. </s>
            <s xml:id="echoid-s4535" xml:space="preserve">veniemus in co-
              <lb/>
            gnitione proportionis, quæ eſt inter latera C A. </s>
            <s xml:id="echoid-s4536" xml:space="preserve">C D. </s>
            <s xml:id="echoid-s4537" xml:space="preserve">ideſt, in@oteſcet quoties C A. </s>
            <s xml:id="echoid-s4538" xml:space="preserve">
              <lb/>
            contineatur in C D. </s>
            <s xml:id="echoid-s4539" xml:space="preserve">cum autem C A. </s>
            <s xml:id="echoid-s4540" xml:space="preserve">cognita ſit in paſſionis, neceſſario ipſa quoque
              <lb/>
            C D. </s>
            <s xml:id="echoid-s4541" xml:space="preserve">terræ ſemidiameter in paſſibus manifeſta erit. </s>
            <s xml:id="echoid-s4542" xml:space="preserve">quod porrò attinet ad interuallum C B. </s>
            <s xml:id="echoid-s4543" xml:space="preserve">menſurandum,
              <lb/>
            ſatius fortaſſe eſſet illud non ex montis apice A. </s>
            <s xml:id="echoid-s4544" xml:space="preserve">verum ex C. </s>
            <s xml:id="echoid-s4545" xml:space="preserve">prænotare. </s>
            <s xml:id="echoid-s4546" xml:space="preserve">eſt autem C. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">primo horizontis pun
              <lb/>
            ctum, ex quo Aethnæ vertex igniuomus primo ſpectatur: </s>
            <s xml:id="echoid-s4548" xml:space="preserve">quare eſſet id Nautis admodum facilè, quibus no-
              <lb/>
            ctu is vertex, cũ ſit igniuomus, ac ſplendidus in mari a longe conſpicuus eſt; </s>
            <s xml:id="echoid-s4549" xml:space="preserve">a loco enim in quo primus con-
              <lb/>
            ſpicitur, menſurandum eſſet vſque ad montis perpendiculum. </s>
            <s xml:id="echoid-s4550" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s4551" xml:space="preserve">hic eſto modus iuxta noſtram demon-
              <lb/>
            ſtrandi methodum. </s>
            <s xml:id="echoid-s4552" xml:space="preserve">magis vero geometricè cum ipſo Maurolyco in hunc modum; </s>
            <s xml:id="echoid-s4553" xml:space="preserve">in eadẽ figura linea C B. </s>
            <s xml:id="echoid-s4554" xml:space="preserve">
              <lb/>
            quamuis re vera ſit curua, ſi tamen pro recta capiatur, in tam pauca circuli terreſtris portione, nihil erroris
              <lb/>
            ſenſibus ingeret. </s>
            <s xml:id="echoid-s4555" xml:space="preserve">Cũ igitur in triangulo A B C. </s>
            <s xml:id="echoid-s4556" xml:space="preserve">angulus ad B. </s>
            <s xml:id="echoid-s4557" xml:space="preserve">ſit rectus, & </s>
            <s xml:id="echoid-s4558" xml:space="preserve">rectæ C B. </s>
            <s xml:id="echoid-s4559" xml:space="preserve">B A. </s>
            <s xml:id="echoid-s4560" xml:space="preserve">notæ ſint ex men-
              <lb/>
            ſuratione; </s>
            <s xml:id="echoid-s4561" xml:space="preserve">eorum quadrata capiantur, ideſt, numeri, paſſuum earum in ſeipſos ducãtur; </s>
            <s xml:id="echoid-s4562" xml:space="preserve">horum numerorum
              <lb/>
            quadra@orum ſumma æqualis erit quadrato lineæ A C. </s>
            <s xml:id="echoid-s4563" xml:space="preserve">per 47. </s>
            <s xml:id="echoid-s4564" xml:space="preserve">primi Elem. </s>
            <s xml:id="echoid-s4565" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s4566" xml:space="preserve">ipſa nota erit in </s>
          </p>
        </div>
      </text>
    </echo>
Impressum