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-div85" type="section" level="1" n="59">
          <p>
            <s xml:id="echoid-s4566" xml:space="preserve">
              <pb o="46" file="0066" n="70" rhead="De Mundi Fabrica."/>
            bus; </s>
            <s xml:id="echoid-s4567" xml:space="preserve">ſi enim radix quadrata huius ſummæ per Arithmetices præcepta extrahatur, erit ipſa linea A C. </s>
            <s xml:id="echoid-s4568" xml:space="preserve">ide@,
              <lb/>
            numerus paſſuum radicis extractæ, erit idem ac numerus paſſuum in linea A C. </s>
            <s xml:id="echoid-s4569" xml:space="preserve">contentorum. </s>
            <s xml:id="echoid-s4570" xml:space="preserve">quoniam ve-
              <lb/>
            ro A C. </s>
            <s xml:id="echoid-s4571" xml:space="preserve">tangit circulum in C. </s>
            <s xml:id="echoid-s4572" xml:space="preserve">erit per penult. </s>
            <s xml:id="echoid-s4573" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4574" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s4575" xml:space="preserve">quadratum eius ęquale rectangulo contento ſub linei
              <unsure/>
            s
              <lb/>
            A G. </s>
            <s xml:id="echoid-s4576" xml:space="preserve">A B. </s>
            <s xml:id="echoid-s4577" xml:space="preserve">quale in figura eſt rectangulum A G E F. </s>
            <s xml:id="echoid-s4578" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s4579" xml:space="preserve">ipſum cognitum. </s>
            <s xml:id="echoid-s4580" xml:space="preserve">ſi ergo numerus quadratus,
              <lb/>
            qui numero rectanguli huius eſt æqualis, diuidatur per numerum lineæ A F. </s>
            <s xml:id="echoid-s4581" xml:space="preserve">alterum latus A G. </s>
            <s xml:id="echoid-s4582" xml:space="preserve">cognoſcetur
              <lb/>
            in paſſibus; </s>
            <s xml:id="echoid-s4583" xml:space="preserve">ex numero autem lateris A G. </s>
            <s xml:id="echoid-s4584" xml:space="preserve">detracta montis altitudine A B. </s>
            <s xml:id="echoid-s4585" xml:space="preserve">reliqua B G. </s>
            <s xml:id="echoid-s4586" xml:space="preserve">erit terræ diameter
              <lb/>
            quæſita. </s>
            <s xml:id="echoid-s4587" xml:space="preserve">hic eſt modus Maurolyci, quem in praxim non videtur deduxiſſe, cum inde nullam aſſerat ſemidia-
              <lb/>
            metri quantitatem, neq; </s>
            <s xml:id="echoid-s4588" xml:space="preserve">vllam montis altitudinem certam ponat. </s>
            <s xml:id="echoid-s4589" xml:space="preserve">Cum tamen ipſe dicat lineam B C. </s>
            <s xml:id="echoid-s4590" xml:space="preserve">eſſe
              <lb/>
            plus quam ducenta milliaria, ponatur, breuitatis gratia C A, ipſi ſenſibiliter æqualis, eritq; </s>
            <s xml:id="echoid-s4591" xml:space="preserve">quadratum eius
              <lb/>
            40.</s>
            <s xml:id="echoid-s4592" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4593" xml:space="preserve">quod æquale eſt rectangulo A E. </s>
            <s xml:id="echoid-s4594" xml:space="preserve">ponamus etiam montis altitudinem A B. </s>
            <s xml:id="echoid-s4595" xml:space="preserve">ad ſummum eſſe duorum
              <lb/>
            milliariorum, diuidatur igitur rectangulum 40.</s>
            <s xml:id="echoid-s4596" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4597" xml:space="preserve">per 2. </s>
            <s xml:id="echoid-s4598" xml:space="preserve">& </s>
            <s xml:id="echoid-s4599" xml:space="preserve">erit quoties num. </s>
            <s xml:id="echoid-s4600" xml:space="preserve">20.</s>
            <s xml:id="echoid-s4601" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4602" xml:space="preserve">pro tota A G. </s>
            <s xml:id="echoid-s4603" xml:space="preserve">ex qua
              <lb/>
            detracta A B. </s>
            <s xml:id="echoid-s4604" xml:space="preserve">quæ eſt 2. </s>
            <s xml:id="echoid-s4605" xml:space="preserve">remanet 19, 998. </s>
            <s xml:id="echoid-s4606" xml:space="preserve">pro terrena diametro, quæ a ſuperiorum Aſtronomorum quan-
              <lb/>
            titatibus, parum diſcrepat, quare ſequitur lineam B C. </s>
            <s xml:id="echoid-s4607" xml:space="preserve">eſſe tot milliariorum ferè, quot a Maurolyco aſ-
              <lb/>
            ſumitur.</s>
            <s xml:id="echoid-s4608" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4609" xml:space="preserve">Quoniam verò milliare Aſtronomum, de quo ſupra egimus, idoneum eſt rebus Aſtronomicis menſuran-
              <lb/>
            dis, proinde ſi eo vti libuerit, erunt in toto telluris circuitu milliaria 21, 600. </s>
            <s xml:id="echoid-s4610" xml:space="preserve">ſiquidem vni 60. </s>
            <s xml:id="echoid-s4611" xml:space="preserve">competunt;
              <lb/>
            </s>
            <s xml:id="echoid-s4612" xml:space="preserve">quæ inter Ptolemæi, & </s>
            <s xml:id="echoid-s4613" xml:space="preserve">recentiorum quantitates, quæ cæteris veriſimiliores ſunt, media eſt.</s>
            <s xml:id="echoid-s4614" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4615" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s4616" xml:space="preserve">hæc ſunt, vt cum Plinio loquamur, quæ de terra circuitu digna memoratu putem, magna ſubtilita-
              <lb/>
            te, atq; </s>
            <s xml:id="echoid-s4617" xml:space="preserve">ingeniorum ſolertia literis prodita; </s>
            <s xml:id="echoid-s4618" xml:space="preserve">improbum equidem auſum, verum ita ſubtili argumentatione
              <lb/>
            comprehenſum, vt pudeat non credere.</s>
            <s xml:id="echoid-s4619" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4620" xml:space="preserve">Perſpecto igitur telluris gyro in Aſtron. </s>
            <s xml:id="echoid-s4621" xml:space="preserve">milliar. </s>
            <s xml:id="echoid-s4622" xml:space="preserve">reliquas iam quantitates, ex ijs, quæ Archimedes partim
              <lb/>
            de circulo, partim de ſphæra, & </s>
            <s xml:id="echoid-s4623" xml:space="preserve">cylindro demonſtrauit, facilè obtinere poterimus; </s>
            <s xml:id="echoid-s4624" xml:space="preserve">cum enim (per ipſum)
              <lb/>
            circuli peripheria ad ſuum diametrum eam habeant ferè rationem, quam 22. </s>
            <s xml:id="echoid-s4625" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s4626" xml:space="preserve">(quod etiam experientia
              <lb/>
            probari poteſt) ſi per auream Arithmeticorũ regula fiat, vt 22. </s>
            <s xml:id="echoid-s4627" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s4628" xml:space="preserve">ita 21, 600. </s>
            <s xml:id="echoid-s4629" xml:space="preserve">milliaria peripherie
              <unsure/>
            ad aliud,
              <lb/>
            procreabitur numerus 6,873. </s>
            <s xml:id="echoid-s4630" xml:space="preserve">milliariorum totius diametri terreſtris. </s>
            <s xml:id="echoid-s4631" xml:space="preserve">cuius dimidium 3. </s>
            <s xml:id="echoid-s4632" xml:space="preserve">43 6 {1/2}. </s>
            <s xml:id="echoid-s4633" xml:space="preserve">erit eiuſdem
              <lb/>
            ſemidiameter, diſtantia videlicet a terræ ſuperficie vſque ad eius centrum; </s>
            <s xml:id="echoid-s4634" xml:space="preserve">qui locus profundiſſima abyſſus
              <lb/>
            dicitur. </s>
            <s xml:id="echoid-s4635" xml:space="preserve">hæc porrò cognitio adeò abſtruſa, ac recondita eſt, vt nihil magis; </s>
            <s xml:id="echoid-s4636" xml:space="preserve">vnde & </s>
            <s xml:id="echoid-s4637" xml:space="preserve">ſacrę litteræ merito quaſi
              <lb/>
            mirabundæ dicant, profunditatem abyſſi quis dimenſus eſt? </s>
            <s xml:id="echoid-s4638" xml:space="preserve">vide lib. </s>
            <s xml:id="echoid-s4639" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4640" xml:space="preserve">Geomet. </s>
            <s xml:id="echoid-s4641" xml:space="preserve">pract. </s>
            <s xml:id="echoid-s4642" xml:space="preserve">P. </s>
            <s xml:id="echoid-s4643" xml:space="preserve">Clauij.</s>
            <s xml:id="echoid-s4644" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4645" xml:space="preserve">Superficiem verò conuexam totius orbis terræ, ac maris ſimul ſic habebimus; </s>
            <s xml:id="echoid-s4646" xml:space="preserve">multiplicentur inuicem cir-
              <lb/>
            cumferentia, & </s>
            <s xml:id="echoid-s4647" xml:space="preserve">diameter, productus enim erit numerus quadratorum milliariorũ, quæ totam terræ, & </s>
            <s xml:id="echoid-s4648" xml:space="preserve">quæ
              <lb/>
            faciem conſtituunt; </s>
            <s xml:id="echoid-s4649" xml:space="preserve">is autem eſt 148, 456, 800. </s>
            <s xml:id="echoid-s4650" xml:space="preserve">vide lib. </s>
            <s xml:id="echoid-s4651" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4652" xml:space="preserve">Geom. </s>
            <s xml:id="echoid-s4653" xml:space="preserve">pract. </s>
            <s xml:id="echoid-s4654" xml:space="preserve">P. </s>
            <s xml:id="echoid-s4655" xml:space="preserve">Clauij.</s>
            <s xml:id="echoid-s4656" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4657" xml:space="preserve">Demum globi terreſtris ſoliditas ſic conſtabit: </s>
            <s xml:id="echoid-s4658" xml:space="preserve">ducantur inuicem ſemidiameter terræ, videlicet 3. </s>
            <s xml:id="echoid-s4659" xml:space="preserve">436 {1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s4660" xml:space="preserve">& </s>
            <s xml:id="echoid-s4661" xml:space="preserve">tertia pars ſuperficialis circumferentiæ modò inuẽtæ, quæ eſt 49, 485, 600. </s>
            <s xml:id="echoid-s4662" xml:space="preserve">nam producetur numerus h@c
              <lb/>
            170, 032, 521, 600. </s>
            <s xml:id="echoid-s4663" xml:space="preserve">milliariorum cubicorum, quæ totam terræ craſſitiem conflarent. </s>
            <s xml:id="echoid-s4664" xml:space="preserve">vide lib. </s>
            <s xml:id="echoid-s4665" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4666" xml:space="preserve">Geometricæ
              <lb/>
            pract. </s>
            <s xml:id="echoid-s4667" xml:space="preserve">P. </s>
            <s xml:id="echoid-s4668" xml:space="preserve">Clauij. </s>
            <s xml:id="echoid-s4669" xml:space="preserve">ſi verò quis addubitet hanc terrę corporeitatem iuſto minorem eſſe, propterca quod in hanc
              <lb/>
            computationem colles ac montes non venerint, is oculos Mari obuertat, quod loco montium, & </s>
            <s xml:id="echoid-s4670" xml:space="preserve">collium
              <lb/>
            ſubſtituimus; </s>
            <s xml:id="echoid-s4671" xml:space="preserve">neque equidem abſque ratione, quandoquidem vt infra patebit, veriſimile eſt montium, & </s>
            <s xml:id="echoid-s4672" xml:space="preserve">
              <lb/>
            maris corporeitates eſſe æquales.</s>
            <s xml:id="echoid-s4673" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div89" type="section" level="1" n="60">
          <head xml:id="echoid-head63" style="it" xml:space="preserve">De altitudine Montium. Cap. VI.</head>
          <p>
            <s xml:id="echoid-s4674" xml:space="preserve">VT tractatio de terræ quautitate omnibus numeris abſoluta euadat, minimè omittenda videtur mõtium
              <lb/>
            altitudo, quandoquidem, & </s>
            <s xml:id="echoid-s4675" xml:space="preserve">ipſi altiores terræ ſunt partes, & </s>
            <s xml:id="echoid-s4676" xml:space="preserve">eius perſcrutatio ſubtilis æque, ac iucunda
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s4677" xml:space="preserve">litteris igitur proditum eſt, inquit Plin. </s>
            <s xml:id="echoid-s4678" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4679" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4680" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s4681" xml:space="preserve">67. </s>
            <s xml:id="echoid-s4682" xml:space="preserve">Dicearchum Siculum Ariſtotelis diſcipulum, pri-
              <lb/>
            mum perpendicularem montium altitudinem dimenſum eſſe, altiffimumq; </s>
            <s xml:id="echoid-s4683" xml:space="preserve">prodidiſſe Pelion, eiuſque per-
              <lb/>
            pendiculum aſſeruiſſe 1, 250. </s>
            <s xml:id="echoid-s4684" xml:space="preserve">paſſus; </s>
            <s xml:id="echoid-s4685" xml:space="preserve">vnde concludere licet montium altitudinem multo minorem eſſe ſeſ-
              <lb/>
            quimilliari. </s>
            <s xml:id="echoid-s4686" xml:space="preserve">Notandum vero montium altitudines quotidie magis decreſcere, vti manifeſtè probauimus
              <lb/>
            ſupra in Corollario de permutatione rotunditatis terræ, Geometrę autem hoc modo altitudinem hanc me-
              <lb/>
            tiuntur: </s>
            <s xml:id="echoid-s4687" xml:space="preserve">in plano quopiam mõti proximo, ſupra quod mons attollitur, quadratum quod vltima Appar, pro-
              <lb/>
            poſitione conſtruximus, ita in cultrum ſtatuunt, vt latus A B. </s>
            <s xml:id="echoid-s4688" xml:space="preserve">horizonti æquidiſtet; </s>
            <s xml:id="echoid-s4689" xml:space="preserve">latus vero B E. </s>
            <s xml:id="echoid-s4690" xml:space="preserve">ad mon-
              <lb/>
            tem reſpiciat; </s>
            <s xml:id="echoid-s4691" xml:space="preserve">perpendiculum autem C I. </s>
            <s xml:id="echoid-s4692" xml:space="preserve">lateri, C A. </s>
            <s xml:id="echoid-s4693" xml:space="preserve">appenſum debet ſuæ lineæ reſpondere exactè; </s>
            <s xml:id="echoid-s4694" xml:space="preserve">ho c
              <lb/>
            enim modo inſtrumentum erit in cultrum poſitum, ſiue horizonti perpendiculare. </s>
            <s xml:id="echoid-s4695" xml:space="preserve">deinde menſor inſpi-
              <lb/>
            ciens per pinnulas dioptræ verſus apicem montis, eam ſuſque deque eleuet, donec exactè ipſius apicem per
              <lb/>
            rimulas pinnularum inſpiciat; </s>
            <s xml:id="echoid-s4696" xml:space="preserve">in quo ſitu dioptram ſiſtat; </s>
            <s xml:id="echoid-s4697" xml:space="preserve">& </s>
            <s xml:id="echoid-s4698" xml:space="preserve">conſideret triangulum in inſtrumento factum,
              <lb/>
            v. </s>
            <s xml:id="echoid-s4699" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4700" xml:space="preserve">ſit altitudo alicuius montis perpendicularis E F. </s>
            <s xml:id="echoid-s4701" xml:space="preserve">menſuranda, & </s>
            <s xml:id="echoid-s4702" xml:space="preserve">quadratũ cum dioptra ad apicem mon-
              <lb/>
            tis ſit directa, vt apparet in figura ſequenti, in qua conſidera duo triangula ſimilia, primum, & </s>
            <s xml:id="echoid-s4703" xml:space="preserve">maius A E F.
              <lb/>
            </s>
            <s xml:id="echoid-s4704" xml:space="preserve">quod faciunt diſtantia A F. </s>
            <s xml:id="echoid-s4705" xml:space="preserve">altitudo F E. </s>
            <s xml:id="echoid-s4706" xml:space="preserve">& </s>
            <s xml:id="echoid-s4707" xml:space="preserve">radius viſiuus A E. </s>
            <s xml:id="echoid-s4708" xml:space="preserve">alternm minus eſt in inſtrumento triangulũ,
              <lb/>
            videlicet A B D. </s>
            <s xml:id="echoid-s4709" xml:space="preserve">quod æquiangulum eſt maiori; </s>
            <s xml:id="echoid-s4710" xml:space="preserve">nam anguli ad F. </s>
            <s xml:id="echoid-s4711" xml:space="preserve">& </s>
            <s xml:id="echoid-s4712" xml:space="preserve">F. </s>
            <s xml:id="echoid-s4713" xml:space="preserve">ſunt recti, angulus vero ad A. </s>
            <s xml:id="echoid-s4714" xml:space="preserve">eſt com-
              <lb/>
            munis igitur, & </s>
            <s xml:id="echoid-s4715" xml:space="preserve">reliqui anguli æquales erunt, ergo triangula erunt proportionalia, ideſt, erit vt latus A B. </s>
            <s xml:id="echoid-s4716" xml:space="preserve">
              <lb/>
            ad B D. </s>
            <s xml:id="echoid-s4717" xml:space="preserve">in paruo triangulo, ita in magno, diſtantia A F. </s>
            <s xml:id="echoid-s4718" xml:space="preserve">ad altitudinem F E. </s>
            <s xml:id="echoid-s4719" xml:space="preserve">ſi igitur diſtantia ſit nota in
              <lb/>
            paſſibus, vel milliarijs, facilè erit cognoſcere altitudinem F E. </s>
            <s xml:id="echoid-s4720" xml:space="preserve">quæ enim pars fuerit latus B D. </s>
            <s xml:id="echoid-s4721" xml:space="preserve">lateris A B. </s>
            <s xml:id="echoid-s4722" xml:space="preserve">
              <lb/>
            eadem pars erit altitudo F E. </s>
            <s xml:id="echoid-s4723" xml:space="preserve">diſtãtiæ A F. </s>
            <s xml:id="echoid-s4724" xml:space="preserve">v. </s>
            <s xml:id="echoid-s4725" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4726" xml:space="preserve">ſi B D. </s>
            <s xml:id="echoid-s4727" xml:space="preserve">fuerit pars decima, ipſius A B. </s>
            <s xml:id="echoid-s4728" xml:space="preserve">F E. </s>
            <s xml:id="echoid-s4729" xml:space="preserve">altitudo erit pars
              <lb/>
            10. </s>
            <s xml:id="echoid-s4730" xml:space="preserve">diſtantiæ A F. </s>
            <s xml:id="echoid-s4731" xml:space="preserve">quare ſi diſtantia A F. </s>
            <s xml:id="echoid-s4732" xml:space="preserve">eſſet milliaria 10. </s>
            <s xml:id="echoid-s4733" xml:space="preserve">eſſet F E. </s>
            <s xml:id="echoid-s4734" xml:space="preserve">milliare vnum, pars ſcilicet decima, </s>
          </p>
        </div>
      </text>
    </echo>
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