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

List of thumbnails

< >
71
71 (47) 		72
72 (48)
73
73 (49) 		74
74 (50)
75
75 (51) 		76
76 (52)
77
77 (53) 		78
78 (54)
79
79 (55) 		80
80 (56)
< >
page |< < (47) of 300 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div89" type="section" level="1" n="60">
          <p>
            <s xml:id="echoid-s4734" xml:space="preserve">
              <pb o="47" file="0067" n="71" rhead="Liber Quarius."/>
              <figure xlink:label="fig-0067-01" xlink:href="fig-0067-01a" number="39">
                <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01"/>
              </figure>
            patet ex Appar. </s>
            <s xml:id="echoid-s4735" xml:space="preserve">Ego Parmæ
              <lb/>
            exiſtens montẽ Baldũ totius
              <lb/>
            Lombardiæ altiſſimũ in agro
              <lb/>
            Veronenſi ſitum, diſtantemq:
              <lb/>
            </s>
            <s xml:id="echoid-s4736" xml:space="preserve">Parma milliar. </s>
            <s xml:id="echoid-s4737" xml:space="preserve">70. </s>
            <s xml:id="echoid-s4738" xml:space="preserve">menſuraui
              <lb/>
            per quadratum, reperique la-
              <lb/>
            tus B D. </s>
            <s xml:id="echoid-s4739" xml:space="preserve">parui trianguli con-
              <lb/>
            tineri ferè octuagies ſepties
              <lb/>
            in latere A B. </s>
            <s xml:id="echoid-s4740" xml:space="preserve">quare concluſi
              <lb/>
            altitudinem eius perpendicu-
              <lb/>
            larem contineri in diſtantia
              <lb/>
            ctiam octuagies ſepties; </s>
            <s xml:id="echoid-s4741" xml:space="preserve">di-
              <lb/>
            ſtantia autem eſt paſſuum 70. </s>
            <s xml:id="echoid-s4742" xml:space="preserve">
              <lb/>
            000. </s>
            <s xml:id="echoid-s4743" xml:space="preserve">quæ diuiſa per 87. </s>
            <s xml:id="echoid-s4744" xml:space="preserve">exhi-
              <lb/>
            bet quotientem 804. </s>
            <s xml:id="echoid-s4745" xml:space="preserve">altitudi-
              <lb/>
            nem nempe quęſitam. </s>
            <s xml:id="echoid-s4746" xml:space="preserve">Si ve-
              <lb/>
            ro d ſtantia ſit ignota, eam ſic
              <lb/>
            dignoſcunt à loco A. </s>
            <s xml:id="echoid-s4747" xml:space="preserve">intelli-
              <lb/>
            gitur duas lineas, vnam ipſam diſtantiam A F. </s>
            <s xml:id="echoid-s4748" xml:space="preserve">alteram vero, quam ipſi ambulando ducunt à loco A. </s>
            <s xml:id="echoid-s4749" xml:space="preserve">priori
              <lb/>
            lineæ perpendicularem, cuius longitudinem paſſibus ambulantes obſeruant recedũt, v. </s>
            <s xml:id="echoid-s4750" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4751" xml:space="preserve">ab eo loco per 40. </s>
            <s xml:id="echoid-s4752" xml:space="preserve">
              <lb/>
            vel 50. </s>
            <s xml:id="echoid-s4753" xml:space="preserve">paſſus per lineam A H. </s>
            <s xml:id="echoid-s4754" xml:space="preserve">poſtea ex loco H. </s>
            <s xml:id="echoid-s4755" xml:space="preserve">verſus montis medium deſignant tertiam lineam H F. </s>
            <s xml:id="echoid-s4756" xml:space="preserve">huic
              <lb/>
            ergo triangulo magno A F H. </s>
            <s xml:id="echoid-s4757" xml:space="preserve">conſtruunt triangulum proportionale, iuxto Appar. </s>
            <s xml:id="echoid-s4758" xml:space="preserve">doctrinam, ducta ſcili-
              <lb/>
            cet linea I K. </s>
            <s xml:id="echoid-s4759" xml:space="preserve">perpendiculari ad A H. </s>
            <s xml:id="echoid-s4760" xml:space="preserve">ſic enim triangulum H I K. </s>
            <s xml:id="echoid-s4761" xml:space="preserve">æquiangulum, & </s>
            <s xml:id="echoid-s4762" xml:space="preserve">proportionale erit ma-
              <lb/>
            gno triangulo H A F. </s>
            <s xml:id="echoid-s4763" xml:space="preserve">& </s>
            <s xml:id="echoid-s4764" xml:space="preserve">quoties H I. </s>
            <s xml:id="echoid-s4765" xml:space="preserve">continebitur in I K. </s>
            <s xml:id="echoid-s4766" xml:space="preserve">toties A H. </s>
            <s xml:id="echoid-s4767" xml:space="preserve">40. </s>
            <s xml:id="echoid-s4768" xml:space="preserve">paſſuum continebitur in diſtantia
              <lb/>
            A F. </s>
            <s xml:id="echoid-s4769" xml:space="preserve">eamq; </s>
            <s xml:id="echoid-s4770" xml:space="preserve">propterea cognitam reddet. </s>
            <s xml:id="echoid-s4771" xml:space="preserve">vide tractationem noſtram de altitudine montis Caucaſi, in lib. </s>
            <s xml:id="echoid-s4772" xml:space="preserve">
              <lb/>
            noſtro de locis Mathematicis apud Ariſt. </s>
            <s xml:id="echoid-s4773" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4774" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4775" xml:space="preserve">Meteorum, ad num. </s>
            <s xml:id="echoid-s4776" xml:space="preserve">184. </s>
            <s xml:id="echoid-s4777" xml:space="preserve">marginalem, vbi plura de montium
              <lb/>
            altitudine ſcitu digniſſima, & </s>
            <s xml:id="echoid-s4778" xml:space="preserve">iucundiſſima reperies.</s>
            <s xml:id="echoid-s4779" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div91" type="section" level="1" n="61">
          <head xml:id="echoid-head64" style="it" xml:space="preserve">Corollarium de Arenæ numero. Cap. VII.</head>
          <p>
            <s xml:id="echoid-s4780" xml:space="preserve">NOn alienum ab inſtituto videtur acutiſſimam Archimedis de arenæ numero diſputationem huc acco@
              <lb/>
            modare, cum arenæ ipſæ telluris particulæ ſint, earumque multitudo indaganda proponatur. </s>
            <s xml:id="echoid-s4781" xml:space="preserve">Qua
              <lb/>
            igitur tempeſtate rex Gelon Siciliæ regnum adminiſtrabat, Philoſophi complures, inter quos, ille ingenio-
              <lb/>
            rum phœnix Archimedes, verſabatur, Regis aulam frequentabant. </s>
            <s xml:id="echoid-s4782" xml:space="preserve">cumque varijs eorum diſſertationibus
              <lb/>
            Rex ille ſæpius oblectaretur, factum eſt aliquando vt inter eos de numero arenæ maris oriretur diſputatio;
              <lb/>
            </s>
            <s xml:id="echoid-s4783" xml:space="preserve">quod ipſemet refert Archimedes. </s>
            <s xml:id="echoid-s4784" xml:space="preserve">eorum igitur nõnulli arenæ numerum, non ſolum eius quæ toto orbe, ſed
              <lb/>
            cius etiam, quæ littoribus tantum Syracuſanis contineretur, infinitum eſſe arbitrabantur: </s>
            <s xml:id="echoid-s4785" xml:space="preserve">alij vero è contra,
              <lb/>
            cum infinitum eſſe negantes, propterea quod infinitum omnem tollerent, aiebant tamen nullum poſſe re-
              <lb/>
            periri determinatum numerum, qui illius arenæ multitudini explicandæ par eſſet, ita vt quamuis quiſpiam
              <lb/>
            per mille annos continenter proferret milliones millionum millionum, & </s>
            <s xml:id="echoid-s4786" xml:space="preserve">numquam, tamen ſatis magnum
              <lb/>
            numerum prolatũ haberet. </s>
            <s xml:id="echoid-s4787" xml:space="preserve">diu iam proceſſerat diſputatio, nec tamen certi quidquam ſtatui videbatur: </s>
            <s xml:id="echoid-s4788" xml:space="preserve">cum
              <lb/>
            rex Archimedis rogauit ſententiam, cui ſic ille reſpondit: </s>
            <s xml:id="echoid-s4789" xml:space="preserve">Sapientiſſime rex, quæſtio hæc Mathematicis ra-
              <lb/>
            tionibus diſsolui poteſt, ijs enim oſtendi poteſt, non ſolum inueniri poſſe numerum, qui totam totius orbis
              <lb/>
            terræ arenam complectatur, verum etiamſi totus mundus, quantus quantus eſt, minutiſſimis arenulis com-
              <lb/>
            pleretur, eandem multitudinem numero definiri poſſe contendimus, quod quidem, & </s>
            <s xml:id="echoid-s4790" xml:space="preserve">Regi, Philoſophiſ-
              <lb/>
            que illis omni admiratione ac fide maius videbatur: </s>
            <s xml:id="echoid-s4791" xml:space="preserve">apud quos in hunc ferè modum ratiocinatus eſt. </s>
            <s xml:id="echoid-s4792" xml:space="preserve">vt pro-
              <lb/>
            poſitæ quæſtioni ſatis a me fieri poſſit, neceſſe habeo nonnulla præmittere.</s>
            <s xml:id="echoid-s4793" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4794" xml:space="preserve">1 Primum iſtud ſit; </s>
            <s xml:id="echoid-s4795" xml:space="preserve">aſſumo pro fundamento omnium, quæ dicturus ſum, granum papaueris, ſiue ſphæ-
              <lb/>
            rulam illi æqualem cõtinere arenulas 100. </s>
            <s xml:id="echoid-s4796" xml:space="preserve">eſt autem granum papaueris hoc (ſimulque illud oſcendebat) quod
              <lb/>
            vix oculorum acies aſſequi valet: </s>
            <s xml:id="echoid-s4797" xml:space="preserve">quod cũ arenulas 100. </s>
            <s xml:id="echoid-s4798" xml:space="preserve">continere ponamus, conſequens eſt huiuſmodi are-
              <lb/>
            nulas eſſe minutiſſimi pulueris inſtar, minor@ſque quam vſpiam inueniri queant.</s>
            <s xml:id="echoid-s4799" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4800" xml:space="preserve">2 Suppono, grana papaueris 40. </s>
            <s xml:id="echoid-s4801" xml:space="preserve">in recta linea diſpoſita, ſeque inuicem tangentia, vnius digiti Geome-
              <lb/>
            trici longitudinem hane; </s>
            <s xml:id="echoid-s4802" xml:space="preserve">-- non ſuperare, quamuis eam re vera multum extendant.</s>
            <s xml:id="echoid-s4803" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4804" xml:space="preserve">3 Milliare vnum continere digitas 80.</s>
            <s xml:id="echoid-s4805" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4806" xml:space="preserve">pes enim cont net 16. </s>
            <s xml:id="echoid-s4807" xml:space="preserve">digitos; </s>
            <s xml:id="echoid-s4808" xml:space="preserve">paſſus vero pedes 5. </s>
            <s xml:id="echoid-s4809" xml:space="preserve">milliare
              <lb/>
            paſſus 1000. </s>
            <s xml:id="echoid-s4810" xml:space="preserve">ex quibus arithmetica multiplicatione patet, quod ſuppono.</s>
            <s xml:id="echoid-s4811" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4812" xml:space="preserve">4 Diametrum terræ continere milliaria 7.</s>
            <s xml:id="echoid-s4813" xml:space="preserve">000. </s>
            <s xml:id="echoid-s4814" xml:space="preserve">plura ſcilicet aliquanto, quã Aſtronomi communiter ſen
              <lb/>
            tiant; </s>
            <s xml:id="echoid-s4815" xml:space="preserve">diametrum vero totius mundi continere diamecios terræ 14.</s>
            <s xml:id="echoid-s4816" xml:space="preserve">000.</s>
            <s xml:id="echoid-s4817" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4818" xml:space="preserve">5 Tandem poſitio ſit; </s>
            <s xml:id="echoid-s4819" xml:space="preserve">iphæras habere inuicem triplicatam ſuarum diametrorum proportionem ex 18.
              <lb/>
            </s>
            <s xml:id="echoid-s4820" xml:space="preserve">propoſitione 12. </s>
            <s xml:id="echoid-s4821" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s4822" xml:space="preserve">v. </s>
            <s xml:id="echoid-s4823" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4824" xml:space="preserve">ſint duæ ſphæræ, quarum diainetrorum notæ ſint rationes, & </s>
            <s xml:id="echoid-s4825" xml:space="preserve">ſit, v. </s>
            <s xml:id="echoid-s4826" xml:space="preserve">g. </s>
            <s xml:id="echoid-s4827" xml:space="preserve">diame-
              <lb/>
            ter vnius diametri alterius dimidia, ideſt, ſint in ratione ſubdupla, quali eſt hæc 1. </s>
            <s xml:id="echoid-s4828" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4829" xml:space="preserve">iam ſi hæc ratio tripli-
              <lb/>
            cetur, ideſt, ſi accipiantur hi numeri, 1. </s>
            <s xml:id="echoid-s4830" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4831" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4832" xml:space="preserve">8. </s>
            <s xml:id="echoid-s4833" xml:space="preserve">inter quos eadem dupla ratio ter contineratur, erit inter pri-
              <lb/>
            mum numerum 1. </s>
            <s xml:id="echoid-s4834" xml:space="preserve">& </s>
            <s xml:id="echoid-s4835" xml:space="preserve">vltimum 8. </s>
            <s xml:id="echoid-s4836" xml:space="preserve">ratio triplicata rationis ſubduplæ: </s>
            <s xml:id="echoid-s4837" xml:space="preserve">& </s>
            <s xml:id="echoid-s4838" xml:space="preserve">ſphęrę pariter quarum diametri </s>
          </p>
        </div>
      </text>
    </echo>
Impressum