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

Page concordance

< >
Scan Original
101 75
102 76
103 77
104 78
105 79
106 78
107 79
108 80
109 85
110 86
111 87
112 88
113 89
114 90
115 91
116 92
117 93
118 94
119 95
120 96
121 97
122 98
123 99
124 100
125 101
126 102
127 103
128 104
129 105
130 106
< >
page |< < (75) of 300 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div154" type="section" level="1" n="97">
          <p>
            <s xml:id="echoid-s7478" xml:space="preserve">
              <pb o="75" file="0097" n="101" rhead="Liber Nonus."/>
            recta vmbræ ſectio, in loco tranſitus Lunæ; </s>
            <s xml:id="echoid-s7479" xml:space="preserve">ita vt diameter eius B C. </s>
            <s xml:id="echoid-s7480" xml:space="preserve">refe-
              <lb/>
              <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a" number="69">
                <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-01"/>
              </figure>
            ram craſſitiem illam vmbræ. </s>
            <s xml:id="echoid-s7481" xml:space="preserve">linea autem D A E. </s>
            <s xml:id="echoid-s7482" xml:space="preserve">referat eclypticam. </s>
            <s xml:id="echoid-s7483" xml:space="preserve">fit Lu-
              <lb/>
            na vbi B. </s>
            <s xml:id="echoid-s7484" xml:space="preserve">vſque ad dimidium eclypſata. </s>
            <s xml:id="echoid-s7485" xml:space="preserve">quia igitur Lunæ latitudo nota eſt,
              <lb/>
            nota erit linea A B. </s>
            <s xml:id="echoid-s7486" xml:space="preserve">quæ ipſam refert; </s>
            <s xml:id="echoid-s7487" xml:space="preserve">& </s>
            <s xml:id="echoid-s7488" xml:space="preserve">conſequenter nota erit vmbræ ſe-
              <lb/>
            midiameter B A. </s>
            <s xml:id="echoid-s7489" xml:space="preserve">ſi igitur latitudo Lunæ fuiſſet 43. </s>
            <s xml:id="echoid-s7490" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7491" xml:space="preserve">totidem eſſet ſemi-
              <lb/>
            diameter B A. </s>
            <s xml:id="echoid-s7492" xml:space="preserve">tota autem diameter B C. </s>
            <s xml:id="echoid-s7493" xml:space="preserve">86. </s>
            <s xml:id="echoid-s7494" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7495" xml:space="preserve">ſemid. </s>
            <s xml:id="echoid-s7496" xml:space="preserve">vmbræ minima in
              <lb/>
            loco Lunæ eſt 45. </s>
            <s xml:id="echoid-s7497" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7498" xml:space="preserve">maxima eſt 47. </s>
            <s xml:id="echoid-s7499" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7500" xml:space="preserve">ex Tich. </s>
            <s xml:id="echoid-s7501" xml:space="preserve">Inuenta hac ratione
              <lb/>
            craſſitie vmbræ, aliam poſtea eclypſim notant, in qua ſint eædem diſtantiæ
              <lb/>
            Solis, & </s>
            <s xml:id="echoid-s7502" xml:space="preserve">Lunæ à terra. </s>
            <s xml:id="echoid-s7503" xml:space="preserve">ac per eam ſic Lunę diametrum apparentem ſcrutan-
              <lb/>
            tur, ſit v.</s>
            <s xml:id="echoid-s7504" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7505" xml:space="preserve">in eadem figura Luna F. </s>
            <s xml:id="echoid-s7506" xml:space="preserve">cuius quarta pars C @. </s>
            <s xml:id="echoid-s7507" xml:space="preserve">ſit obſcurata. </s>
            <s xml:id="echoid-s7508" xml:space="preserve">lati
              <unsure/>
            -
              <lb/>
            tudinem etiam Lunæ compertam habent, v. </s>
            <s xml:id="echoid-s7509" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7510" xml:space="preserve">51. </s>
            <s xml:id="echoid-s7511" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7512" xml:space="preserve">quæ eſt linea A F.
              <lb/>
            </s>
            <s xml:id="echoid-s7513" xml:space="preserve">nota eſt etiam ex præcedenti obſeruatione linea A C. </s>
            <s xml:id="echoid-s7514" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7515" xml:space="preserve">42. </s>
            <s xml:id="echoid-s7516" xml:space="preserve">igitur detra-
              <lb/>
            cta A C. </s>
            <s xml:id="echoid-s7517" xml:space="preserve">ab A F. </s>
            <s xml:id="echoid-s7518" xml:space="preserve">remanebit C F. </s>
            <s xml:id="echoid-s7519" xml:space="preserve">nota min. </s>
            <s xml:id="echoid-s7520" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7521" xml:space="preserve">quę eſt quarta pars diametri Lu-
              <lb/>
            @æ, ergo tota diameter erit 32. </s>
            <s xml:id="echoid-s7522" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7523" xml:space="preserve">in minima diſtantia Lunæ, quæ eſt ſemid. </s>
            <s xml:id="echoid-s7524" xml:space="preserve">T. </s>
            <s xml:id="echoid-s7525" xml:space="preserve">52. </s>
            <s xml:id="echoid-s7526" xml:space="preserve">apparens eius diam. </s>
            <s xml:id="echoid-s7527" xml:space="preserve">eſt
              <lb/>
            36′. </s>
            <s xml:id="echoid-s7528" xml:space="preserve">in maxima diſtantia quæ eſt ſemid. </s>
            <s xml:id="echoid-s7529" xml:space="preserve">T. </s>
            <s xml:id="echoid-s7530" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7531" xml:space="preserve">apparens diam. </s>
            <s xml:id="echoid-s7532" xml:space="preserve">eſt 33′. </s>
            <s xml:id="echoid-s7533" xml:space="preserve">ex Tychone. </s>
            <s xml:id="echoid-s7534" xml:space="preserve">Obiter notandum, quod
              <lb/>
            habita diam. </s>
            <s xml:id="echoid-s7535" xml:space="preserve">vm-
              <lb/>
              <figure xlink:label="fig-0097-02" xlink:href="fig-0097-02a" number="70">
                <image file="0097-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-02"/>
              </figure>
            bræ apparente in
              <lb/>
            tranſitu Lunę, poſ
              <lb/>
            ſumus vmbrã ter-
              <lb/>
            ræ delincare, de-
              <lb/>
            ſcribẽdo figuram,
              <lb/>
            quæ veras habeat
              <lb/>
            proportiones, hoc modo, accepta terrę ſemid. </s>
            <s xml:id="echoid-s7536" xml:space="preserve">A E. </s>
            <s xml:id="echoid-s7537" xml:space="preserve">cuiuſuis magnitudinis ducantur ab A. </s>
            <s xml:id="echoid-s7538" xml:space="preserve">centro terrę binæ
              <lb/>
            lineę conſtituentes angulum tot min. </s>
            <s xml:id="echoid-s7539" xml:space="preserve">quot ſunt in vmbra apparente, vt in figura angulus B A C. </s>
            <s xml:id="echoid-s7540" xml:space="preserve">fit 40′. </s>
            <s xml:id="echoid-s7541" xml:space="preserve">min.
              <lb/>
            </s>
            <s xml:id="echoid-s7542" xml:space="preserve">linea vero A B, vel A C. </s>
            <s xml:id="echoid-s7543" xml:space="preserve">contineat aſſumptus ſemid. </s>
            <s xml:id="echoid-s7544" xml:space="preserve">terrę A E. </s>
            <s xml:id="echoid-s7545" xml:space="preserve">v.</s>
            <s xml:id="echoid-s7546" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7547" xml:space="preserve">52′. </s>
            <s xml:id="echoid-s7548" xml:space="preserve">& </s>
            <s xml:id="echoid-s7549" xml:space="preserve">earum extremitas ſit vbi B C. </s>
            <s xml:id="echoid-s7550" xml:space="preserve">du-
              <lb/>
            ctis iam duabus lineis E B D. </s>
            <s xml:id="echoid-s7551" xml:space="preserve">F C D. </s>
            <s xml:id="echoid-s7552" xml:space="preserve">vmbram terrę repręſentabunt, vt ex ſe pater.</s>
            <s xml:id="echoid-s7553" xml:space="preserve"/>
          </p>
          <figure number="71">
            <image file="0097-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-03"/>
          </figure>
          <p>
            <s xml:id="echoid-s7554" xml:space="preserve">Modus 4. </s>
            <s xml:id="echoid-s7555" xml:space="preserve">pręrequirit diſtantiã Solis à
              <unsure/>
            terra, necnõ proportionem
              <lb/>
            corporis ſolaris ad terrã, quibus habitis conſtruenda eſt figura
              <lb/>
            vera proportionalis, quam ſupra pag. </s>
            <s xml:id="echoid-s7556" xml:space="preserve">38. </s>
            <s xml:id="echoid-s7557" xml:space="preserve">exhibuimus, in qua
              <lb/>
            vera vmbræ craſſitie practicè accipi poteſt in loco trãſitus Lu
              <lb/>
            næ, qui locus etiam cognitus eſt, quia cognita eſt diſtantia Lu-
              <lb/>
            næ a terra, vti ſupra patuit. </s>
            <s xml:id="echoid-s7558" xml:space="preserve">Idem per auream proportionum
              <lb/>
            regulam, & </s>
            <s xml:id="echoid-s7559" xml:space="preserve">triangulorum ſimilium aſſequemur hoc pacto; </s>
            <s xml:id="echoid-s7560" xml:space="preserve">fit vmbra terræ A B C. </s>
            <s xml:id="echoid-s7561" xml:space="preserve">tranſi@us Lunæ E D. </s>
            <s xml:id="echoid-s7562" xml:space="preserve">ſunt
              <lb/>
            igitur duo triangula, æquiangula videlicet A B C. </s>
            <s xml:id="echoid-s7563" xml:space="preserve">E B D. </s>
            <s xml:id="echoid-s7564" xml:space="preserve">erit ergo vt A B. </s>
            <s xml:id="echoid-s7565" xml:space="preserve">ad E B. </s>
            <s xml:id="echoid-s7566" xml:space="preserve">ad E B. </s>
            <s xml:id="echoid-s7567" xml:space="preserve">quę nota ſunt, ita
              <lb/>
            A C. </s>
            <s xml:id="echoid-s7568" xml:space="preserve">diameter terræ nota ad aliud, quod per regulam auream prodibit, eritq; </s>
            <s xml:id="echoid-s7569" xml:space="preserve">vmbræ diameter. </s>
            <s xml:id="echoid-s7570" xml:space="preserve">Eadem por-
              <lb/>
            rò opera manifeſta eſt proportio diametri terræ ad diametrum vmbræ. </s>
            <s xml:id="echoid-s7571" xml:space="preserve">Hiſce præcognitis.</s>
            <s xml:id="echoid-s7572" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7573" xml:space="preserve">4 Aſſero Lunam eſſe adeò terra minorem, vt ſit eius pars quadrageſima; </s>
            <s xml:id="echoid-s7574" xml:space="preserve">quod patere poteſt. </s>
            <s xml:id="echoid-s7575" xml:space="preserve">Pri
              <unsure/>
            mo ſic;
              <lb/>
            </s>
            <s xml:id="echoid-s7576" xml:space="preserve">habita proportione diametri terræ ad diametrum vmbrę, necnon diametri vmbræ ad diametrum Lunæ; </s>
            <s xml:id="echoid-s7577" xml:space="preserve">ha-
              <lb/>
            bebitur quoque proportio diametri terræ ad diametrum Lunæ. </s>
            <s xml:id="echoid-s7578" xml:space="preserve">habit
              <unsure/>
            a autem proportione diametrorum
              <lb/>
            duarum ſphærarum, inde quoque elicitur earundem ſphærarum proportio, vt paulo poſt explicabo. </s>
            <s xml:id="echoid-s7579" xml:space="preserve">Secun-
              <lb/>
            do ſic, ex diſtantia Lunæ a terra duplicata conflatur tota diameter cæli Lunæ; </s>
            <s xml:id="echoid-s7580" xml:space="preserve">deinde ex hac diametro elici-
              <lb/>
            tur tota cæli peripheria in terræ ſemidiametris; </s>
            <s xml:id="echoid-s7581" xml:space="preserve">quia nota eſt ratio peripheriæ ad ſuam diametrum, quæ eſt
              <lb/>
            ferè ſicuti 22. </s>
            <s xml:id="echoid-s7582" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s7583" xml:space="preserve">vti ſuperius ſatis explicauimus. </s>
            <s xml:id="echoid-s7584" xml:space="preserve">& </s>
            <s xml:id="echoid-s7585" xml:space="preserve">quia nota eſt apparens Lunæ diameter,
              <unsure/>
            ideſt, eſt notum
              <lb/>
            eſt quot minuta in cælo ſubt
              <unsure/>
            endat; </s>
            <s xml:id="echoid-s7586" xml:space="preserve">& </s>
            <s xml:id="echoid-s7587" xml:space="preserve">pariter notũſit quot min@ta, aut gradus vna terræ diameter contineat,
              <lb/>
            aut ſubtendat. </s>
            <s xml:id="echoid-s7588" xml:space="preserve">hinc harum diametrorum ratio cognoſcetur. </s>
            <s xml:id="echoid-s7589" xml:space="preserve">Exempli gratia, diſtet Luna à terra ſemid. </s>
            <s xml:id="echoid-s7590" xml:space="preserve">52. </s>
            <s xml:id="echoid-s7591" xml:space="preserve">
              <lb/>
            quibus duplicatis erit diameter huius lunaris gyri 104. </s>
            <s xml:id="echoid-s7592" xml:space="preserve">ſemidiametri terræ, fiat ergo vt 7. </s>
            <s xml:id="echoid-s7593" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s7594" xml:space="preserve">ita 104. </s>
            <s xml:id="echoid-s7595" xml:space="preserve">ad fe-
              <lb/>
            rè 327. </s>
            <s xml:id="echoid-s7596" xml:space="preserve">ſemidiatros terræ, quæ gyrum Lunæ componunt. </s>
            <s xml:id="echoid-s7597" xml:space="preserve">In toto autẽ circuitu ſunt gr. </s>
            <s xml:id="echoid-s7598" xml:space="preserve">360. </s>
            <s xml:id="echoid-s7599" xml:space="preserve">ſiue min. </s>
            <s xml:id="echoid-s7600" xml:space="preserve">21600. </s>
            <s xml:id="echoid-s7601" xml:space="preserve">
              <lb/>
            quæ diuiſa per 327. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">producunt 66. </s>
            <s xml:id="echoid-s7603" xml:space="preserve">minuta, & </s>
            <s xml:id="echoid-s7604" xml:space="preserve">amplius. </s>
            <s xml:id="echoid-s7605" xml:space="preserve">Ergo vna terræ ſemidiameter occupat minuta ferè
              <lb/>
            66. </s>
            <s xml:id="echoid-s7606" xml:space="preserve">ac proinde tota diameter occupabit 132′. </s>
            <s xml:id="echoid-s7607" xml:space="preserve">At vero apparens Lunæ diameter occupat 36. </s>
            <s xml:id="echoid-s7608" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7609" xml:space="preserve">Eſt ergo
              <lb/>
            proportio diametri terræ ad diametrum Lunæ ſicuti 132. </s>
            <s xml:id="echoid-s7610" xml:space="preserve">ad 36. </s>
            <s xml:id="echoid-s7611" xml:space="preserve">hoc eſt quæ 3
              <emph style="super">2</emph>
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s7612" xml:space="preserve">ferè ad 1. </s>
            <s xml:id="echoid-s7613" xml:space="preserve">quare non latebit
              <lb/>
            ſphærarum proportio, vt mox dicam. </s>
            <s xml:id="echoid-s7614" xml:space="preserve">Tertio ſic, ac magis expeditè. </s>
            <s xml:id="echoid-s7615" xml:space="preserve">cognitis iam diſtantia Lunæ, necnon
              <lb/>
            diametro eius apparenti, conſtruatur trigonum Iſoſceles, cuius duo latera æqualia contineant angulum, ſub
              <lb/>
            quo diameter apparens apparet; </s>
            <s xml:id="echoid-s7616" xml:space="preserve">quæ duo latera ſint diuiſa in tot partes æquales, quot ſemidiametri terræ
              <lb/>
            confiant aſſumptam diſtantiam, v.</s>
            <s xml:id="echoid-s7617" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7618" xml:space="preserve">in partes 52. </s>
            <s xml:id="echoid-s7619" xml:space="preserve">ſit in figura trigonum A B. </s>
            <s xml:id="echoid-s7620" xml:space="preserve">cuius angulus A. </s>
            <s xml:id="echoid-s7621" xml:space="preserve">fit min. </s>
            <s xml:id="echoid-s7622" xml:space="preserve">36. </s>
            <s xml:id="echoid-s7623" xml:space="preserve">quot
              <lb/>
            nimirum continet diameter apparens. </s>
            <s xml:id="echoid-s7624" xml:space="preserve">latus A B. </s>
            <s xml:id="echoid-s7625" xml:space="preserve">vel A C. </s>
            <s xml:id="echoid-s7626" xml:space="preserve">contineat partes æquales 52. </s>
            <s xml:id="echoid-s7627" xml:space="preserve">quot nimirum conti-
              <lb/>
            net diſtantia Lunæ, cum talem exhibet diametrum, erit enim tale triangulum æquiangulum, ac proportio-
              <lb/>
            nale triangulo magno, quod ab oculo noſtro vſque ad Lunæ latera extrema exporrigitur. </s>
            <s xml:id="echoid-s7628" xml:space="preserve">Quapropter li-
              <lb/>
              <figure xlink:label="fig-0097-04" xlink:href="fig-0097-04a" number="72">
                <image file="0097-04" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-04"/>
              </figure>
            ce
              <unsure/>
            bit practicè accepta baſi B C. </s>
            <s xml:id="echoid-s7629" xml:space="preserve">quæ diametrum
              <lb/>
            refert per circinum, eam partibus conferre quæ
              <lb/>
            in latere A B. </s>
            <s xml:id="echoid-s7630" xml:space="preserve">referunt ſemidiametros terræ; </s>
            <s xml:id="echoid-s7631" xml:space="preserve">ac
              <lb/>
            perſpicere quam cum illis habeat rarionem. </s>
            <s xml:id="echoid-s7632" xml:space="preserve">fic-
              <lb/>
            que apparebit diametrum terræ continere dia-
              <lb/>
            metrum Lunæ ter, ac duas quintas, hoc eſt </s>
          </p>
        </div>
      </text>
    </echo>
Impressum