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-div368" type="section" level="1" n="264">
          <pb o="182" file="0204" n="209" rhead="De Mundi Fabrica,"/>
        </div>
        <div xml:id="echoid-div369" type="section" level="1" n="265">
          <head xml:id="echoid-head282" style="it" xml:space="preserve">Magnitudines affixarum. Cap. XIIII.</head>
          <p>
            <s xml:id="echoid-s15839" xml:space="preserve">QVemadmodum in cæter is aſtris duo neceſſaria fuerunt ad eorum veras magnitudines indagandas, ita
              <lb/>
            etiam in affixis, diſtantia videlicet earum a
              <unsure/>
            medio Mundi; </s>
            <s xml:id="echoid-s15840" xml:space="preserve">necnon earum apparens diameter. </s>
            <s xml:id="echoid-s15841" xml:space="preserve">Porrò
              <lb/>
            veteres Aſtrologiæ cultores, Hipparchus, & </s>
            <s xml:id="echoid-s15842" xml:space="preserve">Ptolemæus hanc partem veluti abſtruſam, & </s>
            <s xml:id="echoid-s15843" xml:space="preserve">altam,
              <lb/>
            attingere non ſunt auſi. </s>
            <s xml:id="echoid-s15844" xml:space="preserve">Albategnius tamen vir Arabs improbo auxu affixarum etiam magnitudines ſubti-
              <lb/>
            liter admodum aggreſſus eſt; </s>
            <s xml:id="echoid-s15845" xml:space="preserve">quas poſtea recentiores multo adhuc certius depræhenderunt: </s>
            <s xml:id="echoid-s15846" xml:space="preserve">vt igitur vtro-
              <lb/>
            rumq; </s>
            <s xml:id="echoid-s15847" xml:space="preserve">ſubtiliſſimas indagationes explicemus, præmittenda prius ſunt illa duo, quæ modo commemoraui.
              <lb/>
            </s>
            <s xml:id="echoid-s15848" xml:space="preserve">Ac primo de earum diſtantia à medio ſic ſtatuendum; </s>
            <s xml:id="echoid-s15849" xml:space="preserve">cum oſtenſum ſit ex Tychone ſupremos Saturni cir-
              <lb/>
            cuitus à medio attolli ſemidiametris terræ 12′900′. </s>
            <s xml:id="echoid-s15850" xml:space="preserve">conueniens eſſe putandum eſt, affixas paulò altius collo-
              <lb/>
            catas eſie. </s>
            <s xml:id="echoid-s15851" xml:space="preserve">præterea cùm craſſities firmamenti incerta ſit, ac proinde incertnm an omnes affixæ ſint in eadem
              <lb/>
            altitudine, vtaliquid medio loco ſtatuamus, ſtatuemus cum recentioribus affixas à centro terræ ſemidiam. </s>
            <s xml:id="echoid-s15852" xml:space="preserve">
              <lb/>
            terræ 14′000′. </s>
            <s xml:id="echoid-s15853" xml:space="preserve">plus minus attolli. </s>
            <s xml:id="echoid-s15854" xml:space="preserve">Secundo de earum apparenti diametro: </s>
            <s xml:id="echoid-s15855" xml:space="preserve">diligenti inſpectatione habita
              <lb/>
            depræhenſa eſt diameter apparens ſtellarum primæ magnitudinis minuta 2′. </s>
            <s xml:id="echoid-s15856" xml:space="preserve">adimplere. </s>
            <s xml:id="echoid-s15857" xml:space="preserve">talibus præmiſſis
              <lb/>
            hanc Albategnius in libro de ſcientia Stellarum inibat rationem. </s>
            <s xml:id="echoid-s15858" xml:space="preserve">imaginabatur triangulum vti præſens, in
              <lb/>
            quo E C. </s>
            <s xml:id="echoid-s15859" xml:space="preserve">referret mediocrem Solis à terra diſtantiam, quæ eſt 1142. </s>
            <s xml:id="echoid-s15860" xml:space="preserve">ſemid. </s>
            <s xml:id="echoid-s15861" xml:space="preserve">terra. </s>
            <s xml:id="echoid-s15862" xml:space="preserve">C D. </s>
            <s xml:id="echoid-s15863" xml:space="preserve">referret ſemidiame-
              <lb/>
              <figure xlink:label="fig-0204-01" xlink:href="fig-0204-01a" number="110">
                <image file="0204-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0204-01"/>
              </figure>
            trum Solis apparentem, min.
              <lb/>
            </s>
            <s xml:id="echoid-s15864" xml:space="preserve">15 {1/2}. </s>
            <s xml:id="echoid-s15865" xml:space="preserve">E A, referret diſtantiam
              <lb/>
            affixarum prædictam, ideſt,
              <lb/>
            ſemidiam. </s>
            <s xml:id="echoid-s15866" xml:space="preserve">14′000′. </s>
            <s xml:id="echoid-s15867" xml:space="preserve">A B. </s>
            <s xml:id="echoid-s15868" xml:space="preserve">refer-
              <lb/>
            ret ſemidiametrum Solis ap-
              <lb/>
            parentem in firmamento, vbi
              <lb/>
            ſunt aſſixæ, ſiue interuallum
              <lb/>
            illud, quodapparẽs ſemidiam. </s>
            <s xml:id="echoid-s15869" xml:space="preserve">
              <lb/>
            Solis in firmamento occupare
              <lb/>
            videtur. </s>
            <s xml:id="echoid-s15870" xml:space="preserve">quoniam vero diame-
              <lb/>
            ter apparens Stellæ primi ordinis eſt min. </s>
            <s xml:id="echoid-s15871" xml:space="preserve">2′. </s>
            <s xml:id="echoid-s15872" xml:space="preserve">ideo erit ferè pars octaua totius A B. </s>
            <s xml:id="echoid-s15873" xml:space="preserve">repræſentetur igitur in
              <lb/>
            A F. </s>
            <s xml:id="echoid-s15874" xml:space="preserve">parte octaua totius A B. </s>
            <s xml:id="echoid-s15875" xml:space="preserve">quoniam igitur ſunt duo triangula ſimilia E C D. </s>
            <s xml:id="echoid-s15876" xml:space="preserve">E A B. </s>
            <s xml:id="echoid-s15877" xml:space="preserve">erit vt E C. </s>
            <s xml:id="echoid-s15878" xml:space="preserve">ad C D. </s>
            <s xml:id="echoid-s15879" xml:space="preserve">
              <lb/>
            ita E A. </s>
            <s xml:id="echoid-s15880" xml:space="preserve">ad A B. </s>
            <s xml:id="echoid-s15881" xml:space="preserve">ideſt, erit vt 1142. </s>
            <s xml:id="echoid-s15882" xml:space="preserve">ad min. </s>
            <s xml:id="echoid-s15883" xml:space="preserve">15 {1/2}. </s>
            <s xml:id="echoid-s15884" xml:space="preserve">ita 14′000′. </s>
            <s xml:id="echoid-s15885" xml:space="preserve">ad 190. </s>
            <s xml:id="echoid-s15886" xml:space="preserve">ferè per auream regulã. </s>
            <s xml:id="echoid-s15887" xml:space="preserve">qui numerus 190. </s>
            <s xml:id="echoid-s15888" xml:space="preserve">
              <lb/>
            ſignificat in interuallo A B. </s>
            <s xml:id="echoid-s15889" xml:space="preserve">contineri min. </s>
            <s xml:id="echoid-s15890" xml:space="preserve">190. </s>
            <s xml:id="echoid-s15891" xml:space="preserve">ex ijs, ſiue eiuſdem magnitudinis cum min. </s>
            <s xml:id="echoid-s15892" xml:space="preserve">15 {1/2} quæ ſunt in
              <lb/>
            C D. </s>
            <s xml:id="echoid-s15893" xml:space="preserve">quia verò A F. </s>
            <s xml:id="echoid-s15894" xml:space="preserve">eſt pars ferè octaua totius A B. </s>
            <s xml:id="echoid-s15895" xml:space="preserve">ſiue min. </s>
            <s xml:id="echoid-s15896" xml:space="preserve">190. </s>
            <s xml:id="echoid-s15897" xml:space="preserve">erit A F. </s>
            <s xml:id="echoid-s15898" xml:space="preserve">min. </s>
            <s xml:id="echoid-s15899" xml:space="preserve">circiter 24′. </s>
            <s xml:id="echoid-s15900" xml:space="preserve">ex ijs, quorum
              <lb/>
            15 {1/2}. </s>
            <s xml:id="echoid-s15901" xml:space="preserve">conflant ſemidiam. </s>
            <s xml:id="echoid-s15902" xml:space="preserve">Solis. </s>
            <s xml:id="echoid-s15903" xml:space="preserve">31′. </s>
            <s xml:id="echoid-s15904" xml:space="preserve">verò totam diametrum Solis. </s>
            <s xml:id="echoid-s15905" xml:space="preserve">quare proportio diametri Stellæ ad diame-
              <lb/>
            trum Solis, erit vt 24. </s>
            <s xml:id="echoid-s15906" xml:space="preserve">ad 31. </s>
            <s xml:id="echoid-s15907" xml:space="preserve">ſiue fere vt 4. </s>
            <s xml:id="echoid-s15908" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s15909" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s15910" xml:space="preserve">proportio ſphærarum erit ferè ſubdupla, ideſt, vna ex
              <lb/>
            dictis Stellis erit quaſi dimidia Solis, porrò cum Sol ad terram ſit vt 140. </s>
            <s xml:id="echoid-s15911" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s15912" xml:space="preserve">Stella, quæ eſt Solis medietas
              <lb/>
            erit vt 70 ad terram, ideſt, terram ſeptuagies adæquabit.</s>
            <s xml:id="echoid-s15913" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15914" xml:space="preserve">Aliter ex ijſdem præmiſſis ex Tychone ſic; </s>
            <s xml:id="echoid-s15915" xml:space="preserve">cum habeamus ſemidiametrum firmamenti cognitam in ſe-
              <lb/>
            midiametris terræ, habebimus etiam eiuſdem ſemicircumferentiam in ijſdem ſemidiametris, eſt enim ſe-
              <lb/>
            midiameter ad circumferentiam vt 7. </s>
            <s xml:id="echoid-s15916" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s15917" xml:space="preserve">igitur per auream regulam, erit vt 7. </s>
            <s xml:id="echoid-s15918" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s15919" xml:space="preserve">ita 14′000′. </s>
            <s xml:id="echoid-s15920" xml:space="preserve">ad
              <lb/>
            44′000′. </s>
            <s xml:id="echoid-s15921" xml:space="preserve">ſemicirculum firmamenti. </s>
            <s xml:id="echoid-s15922" xml:space="preserve">videndum nunc eſt, vnum minutum firmamenti quot ſemid ametros
              <lb/>
            contineat. </s>
            <s xml:id="echoid-s15923" xml:space="preserve">diuidantur ergo 44′000′. </s>
            <s xml:id="echoid-s15924" xml:space="preserve">vel breuitatis cauſa 22000. </s>
            <s xml:id="echoid-s15925" xml:space="preserve">ſemidiametri per gradus 90. </s>
            <s xml:id="echoid-s15926" xml:space="preserve">ideſt, per mi-
              <lb/>
            nuta 5400. </s>
            <s xml:id="echoid-s15927" xml:space="preserve">ſic enim diuidetur quadrans per quadrantem; </s>
            <s xml:id="echoid-s15928" xml:space="preserve">erit autem quotiens 4 {1/15} ferè. </s>
            <s xml:id="echoid-s15929" xml:space="preserve">quare vnum minu-
              <lb/>
            tum firmamenti continet ſemidiam. </s>
            <s xml:id="echoid-s15930" xml:space="preserve">4 {1/13}. </s>
            <s xml:id="echoid-s15931" xml:space="preserve">Et quia diameter apparens Stellæ eſt min. </s>
            <s xml:id="echoid-s15932" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15933" xml:space="preserve">ideo apparens Stellæ
              <lb/>
            diameter continebit 8 {2/13}. </s>
            <s xml:id="echoid-s15934" xml:space="preserve">ſemidiam. </s>
            <s xml:id="echoid-s15935" xml:space="preserve">terræ, ideſt, diametros terra 4 {1/3}. </s>
            <s xml:id="echoid-s15936" xml:space="preserve">cum ergo nota ſit proportio diametro-
              <lb/>
            rum, nota quoq; </s>
            <s xml:id="echoid-s15937" xml:space="preserve">euadet proportio ſphærarum, eadem ferè quæ ſupra, vt 70. </s>
            <s xml:id="echoid-s15938" xml:space="preserve">ad 1.</s>
            <s xml:id="echoid-s15939" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15940" xml:space="preserve">Aliter tandem practicè ex conſtructione trianguli iſoſcelis, cuius latera contineant ſemidiam. </s>
            <s xml:id="echoid-s15941" xml:space="preserve">terræ 1400
              <lb/>
            baſis vero contineat min. </s>
            <s xml:id="echoid-s15942" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15943" xml:space="preserve">vt in planetis fecimus.</s>
            <s xml:id="echoid-s15944" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15945" xml:space="preserve">Eadem methodo reperit Tycho Stel@as ſecundæ claſſis terræ molem continere vicies, & </s>
            <s xml:id="echoid-s15946" xml:space="preserve">octies, ideſt, eas
              <lb/>
            eſſe ad terram, vt 28. </s>
            <s xml:id="echoid-s15947" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s15948" xml:space="preserve">Stellas tertij ordinis eſſe ad terram, vt 11. </s>
            <s xml:id="echoid-s15949" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s15950" xml:space="preserve">quarti honoris eſſe ad terram vt 27.
              <lb/>
            </s>
            <s xml:id="echoid-s15951" xml:space="preserve">ad 8. </s>
            <s xml:id="echoid-s15952" xml:space="preserve">quinti paulo terram ſuperare. </s>
            <s xml:id="echoid-s15953" xml:space="preserve">ſexti paulo a terra ſuperari. </s>
            <s xml:id="echoid-s15954" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s15955" xml:space="preserve">hæc de affixis iam inde ab origine mun-
              <lb/>
            di cognitis ſufficiant, nunc ad nuper cognitas, ac mortalibus noua tranſeamus.</s>
            <s xml:id="echoid-s15956" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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