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

Table of Notes

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page |< < (102) of 300 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div213" type="section" level="1" n="137">
          <p>
            <s xml:id="echoid-s10154" xml:space="preserve">
              <pb o="102" file="0122" n="126" rhead="De Mundi Fabrica,"/>
            ſupra diximus Vrbem eſſe Syenem, cui Sol Cancri tropicum percurrens fit verticalis. </s>
            <s xml:id="echoid-s10155" xml:space="preserve">in tali enim loco cir-
              <lb/>
            cumcirca per 300. </s>
            <s xml:id="echoid-s10156" xml:space="preserve">ſtadia, quę efficiunt milliaria ferè 37. </s>
            <s xml:id="echoid-s10157" xml:space="preserve">corpora nullas proijciunt vmbras. </s>
            <s xml:id="echoid-s10158" xml:space="preserve">quod manifeſtum
              <lb/>
            ſignum eſt Solem maiorum eſſe prædicto tractu milliar. </s>
            <s xml:id="echoid-s10159" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10160" xml:space="preserve">cum enim Sol vti oſtenſum eſt, valde ſublimis ſit,
              <lb/>
            & </s>
            <s xml:id="echoid-s10161" xml:space="preserve">vnumquodq; </s>
            <s xml:id="echoid-s10162" xml:space="preserve">illorum corporum vndique adeo colluſtret, vt nulla relinquatur vmbra, neceſſario ſequitur
              <lb/>
              <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="80">
                <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-01"/>
              </figure>
            extrema illius tractus corpora, veluti turres, habere ſupra ſuum verticem partẽ aliquam ſola-
              <lb/>
            ris corporis: </s>
            <s xml:id="echoid-s10163" xml:space="preserve">quare neceſtario cogimur aſſerere Solis magnitudinem eſſe ſaltem milliar. </s>
            <s xml:id="echoid-s10164" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10165" xml:space="preserve">ſit
              <lb/>
            enim figura tractus terræ A B. </s>
            <s xml:id="echoid-s10166" xml:space="preserve">in quo extremæ turres A D. </s>
            <s xml:id="echoid-s10167" xml:space="preserve">B E. </s>
            <s xml:id="echoid-s10168" xml:space="preserve">nullam efficiant vmbram.
              <lb/>
            </s>
            <s xml:id="echoid-s10169" xml:space="preserve">ergo ſi intelligamus duo illa corpora recta ſurſum produci, tandem Solem vtrinque contin-
              <lb/>
            gent: </s>
            <s xml:id="echoid-s10170" xml:space="preserve">quod ſi ita producantur vt A D. </s>
            <s xml:id="echoid-s10171" xml:space="preserve">contineat ſemidiametros terræ 1, 182, quot ſcilicet à
              <lb/>
            terra diſtat Sol, quando eſt ſupra Syenem, tunc enim eſt in tropico Cancri, ac propterea apo-
              <lb/>
            gæus diſtat ſemid. </s>
            <s xml:id="echoid-s10172" xml:space="preserve">1, 182,. </s>
            <s xml:id="echoid-s10173" xml:space="preserve">(vti ſupra demonſtratum eſt:) </s>
            <s xml:id="echoid-s10174" xml:space="preserve">ijs igitur productis ducatnr linea
              <lb/>
            eorum ſummas extremitates coniungens, qualis eſſet linea D E. </s>
            <s xml:id="echoid-s10175" xml:space="preserve">hæc enim erit diameter So-
              <lb/>
            lis, habebitq; </s>
            <s xml:id="echoid-s10176" xml:space="preserve">veram proportionem ad terrę diametrum A F. </s>
            <s xml:id="echoid-s10177" xml:space="preserve">quam vera diameter Solis habet
              <lb/>
            ad veram terræ diametrum. </s>
            <s xml:id="echoid-s10178" xml:space="preserve">vnde vera Solis magnitudo non latebit, vt paulo poſt explicabimus.</s>
            <s xml:id="echoid-s10179" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10180" xml:space="preserve">2 Dico olem eſſe Luna maiorem, quod inde patere poteſt, quia vt ſupra oſtenſum eſt, Sol eſt Luna mul
              <lb/>
            to ſublimior, & </s>
            <s xml:id="echoid-s10181" xml:space="preserve">tamen videtur eſſe eiuſdem cum ea magnitudinis; </s>
            <s xml:id="echoid-s10182" xml:space="preserve">at quæ ſunt remotiora minora ſemper, cę-
              <lb/>
            teris paribus apparent, quam propiora, vt opticorum obſeruationes docent, quare ſi Sol deſcenderet a d Lu-
              <lb/>
            næ locum multo maior quam Luna appareret. </s>
            <s xml:id="echoid-s10183" xml:space="preserve">Idem perſpicuè colligitur ex ſolari illa eclypſi, in qua Luna
              <lb/>
            totum Solem adæquate nobis occultat; </s>
            <s xml:id="echoid-s10184" xml:space="preserve">tunc enim videmus Lunam, & </s>
            <s xml:id="echoid-s10185" xml:space="preserve">Solem ſub eodem angulo, vt ſupra ina
              <lb/>
            figura cap. </s>
            <s xml:id="echoid-s10186" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10187" xml:space="preserve">videre eſt, in qua ſub eodem angulo A K C. </s>
            <s xml:id="echoid-s10188" xml:space="preserve">vtruinq; </s>
            <s xml:id="echoid-s10189" xml:space="preserve">luminare compræhenditur, ac proptere
              <lb/>
            Solibi Lunam magnitudine valde ſuperat.</s>
            <s xml:id="echoid-s10190" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10191" xml:space="preserve">3 Aſſero Solem eſſe terreſtri ſphæra maiorem: </s>
            <s xml:id="echoid-s10192" xml:space="preserve">quod manifeſte conuincitur ex vmbra terræ, quæ à Sole
              <lb/>
            procedit; </s>
            <s xml:id="echoid-s10193" xml:space="preserve">ea enim, vt ſupra oſtenſum eſt, conica ſeu acuminata eſt, atq; </s>
            <s xml:id="echoid-s10194" xml:space="preserve">in nihilum deſineſis; </s>
            <s xml:id="echoid-s10195" xml:space="preserve">quod nullo mo-
              <lb/>
            do fieri poſſet, niſi Sol illuminans, tota terra illuminata, amplior eſſet, quæ ratio optimè demonſtrat ſi ea re-
              <lb/>
            petantur, quæ de lumine, & </s>
            <s xml:id="echoid-s10196" xml:space="preserve">vmbra ſuperius in tractatu de mundo præmiſſa ſunt.</s>
            <s xml:id="echoid-s10197" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10198" xml:space="preserve">4 Aio Solem eſſe adeo magnum vt terram centies, & </s>
            <s xml:id="echoid-s10199" xml:space="preserve">quadragies contineat. </s>
            <s xml:id="echoid-s10200" xml:space="preserve">quæ propoſitio eſt probatiſ-
              <lb/>
            ſimi Aſtronomi Tychonis, quam hiſce rationibus euidenter oſtendemus. </s>
            <s xml:id="echoid-s10201" xml:space="preserve">Primo quidem ex conſtructione
              <lb/>
            figuræ quam cap. </s>
            <s xml:id="echoid-s10202" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10203" xml:space="preserve">huius tractatus num. </s>
            <s xml:id="echoid-s10204" xml:space="preserve">4. </s>
            <s xml:id="echoid-s10205" xml:space="preserve">pro Solis diſtantia inuenienda adumbrauimus; </s>
            <s xml:id="echoid-s10206" xml:space="preserve">ſi enim illa figura
              <lb/>
            cum ſuis veris proportionibus accuratè conſtruatur, vt factum eſt in figura pag 38. </s>
            <s xml:id="echoid-s10207" xml:space="preserve">num. </s>
            <s xml:id="echoid-s10208" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10209" xml:space="preserve">ſtatim in ea appa-
              <lb/>
            rebit, quam rationem habeat dimetiens A C. </s>
            <s xml:id="echoid-s10210" xml:space="preserve">Solis ad dimetientem G E. </s>
            <s xml:id="echoid-s10211" xml:space="preserve">terræ; </s>
            <s xml:id="echoid-s10212" xml:space="preserve">quæ ferè erit vt 5 {1/5}. </s>
            <s xml:id="echoid-s10213" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s10214" xml:space="preserve">hoc
              <lb/>
            eſt diameter Solis continet terræ diametrum quinquies, & </s>
            <s xml:id="echoid-s10215" xml:space="preserve">præ erea quintam eiuſdem partem qua propor-
              <lb/>
            tione habita facilè eſt ſphærarum quoque ipſarum mutuam habitudinam cognoſcere. </s>
            <s xml:id="echoid-s10216" xml:space="preserve">Primo mechanicè, ſi
              <lb/>
            enim fiant duo globi ex eadem materia, vti ex plumbo, habentes ſuos diametros æquales diametris A C. </s>
            <s xml:id="echoid-s10217" xml:space="preserve">G E.
              <lb/>
            </s>
            <s xml:id="echoid-s10218" xml:space="preserve">quos deinde vel pondere, vel menſura expendamus, videbimus maiorcm ad minorem eſſe vt 140. </s>
            <s xml:id="echoid-s10219" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s10220" xml:space="preserve">idem
              <lb/>
            Geometricè aſſequemur, eadem omnino ratione, qua vſi ſumus in Lunæ magnitudine inquirenda, ideſt,
              <lb/>
            ex eo, quod ſphæræ habent triplicatam proportionem ſuarum diametrorum. </s>
            <s xml:id="echoid-s10221" xml:space="preserve">cum igitur diameter Solis ad
              <lb/>
            diam. </s>
            <s xml:id="echoid-s10222" xml:space="preserve">terræ, ſit vt 5 {1/5}. </s>
            <s xml:id="echoid-s10223" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s10224" xml:space="preserve">ſiue vt 26. </s>
            <s xml:id="echoid-s10225" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s10226" xml:space="preserve">ſi accipiantur quatuornumeri, ſicuti etiam in Luna, in continua ea-
              <lb/>
            rum ratione, quales ſunt hi 303. </s>
            <s xml:id="echoid-s10227" xml:space="preserve">135 {1/5}. </s>
            <s xml:id="echoid-s10228" xml:space="preserve">26. </s>
            <s xml:id="echoid-s10229" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10230" xml:space="preserve">erit ratio primi 703. </s>
            <s xml:id="echoid-s10231" xml:space="preserve">ad vltimum 5. </s>
            <s xml:id="echoid-s10232" xml:space="preserve">eadem quæ Solis ad terram. </s>
            <s xml:id="echoid-s10233" xml:space="preserve">
              <lb/>
            continet autem ille numerus hunc centies, & </s>
            <s xml:id="echoid-s10234" xml:space="preserve">quadrigies, vt patet diuidendo 703. </s>
            <s xml:id="echoid-s10235" xml:space="preserve">per 5. </s>
            <s xml:id="echoid-s10236" xml:space="preserve">quotiens enim eſt
              <lb/>
            140 {3/5}. </s>
            <s xml:id="echoid-s10237" xml:space="preserve">Sol igitur terra maior eſt, ita vt ipſam toties compræhendat, vti propoſuimus.</s>
            <s xml:id="echoid-s10238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10239" xml:space="preserve">Hinc facilè etiam licet colligere quanto maior ſit quam Luna, cum enim terra Lunam contineat quadra-
              <lb/>
            gies; </s>
            <s xml:id="echoid-s10240" xml:space="preserve">Sol vero terrã centies, & </s>
            <s xml:id="echoid-s10241" xml:space="preserve">quadragies, ſi numeri 40. </s>
            <s xml:id="echoid-s10242" xml:space="preserve">& </s>
            <s xml:id="echoid-s10243" xml:space="preserve">140. </s>
            <s xml:id="echoid-s10244" xml:space="preserve">inuicem multiplicentur, prodibit num. </s>
            <s xml:id="echoid-s10245" xml:space="preserve">5, 600.
              <lb/>
            </s>
            <s xml:id="echoid-s10246" xml:space="preserve">qui indicat Solem continere Lunam quinquies millies, ac ſexcenties. </s>
            <s xml:id="echoid-s10247" xml:space="preserve">Rurſus eandem proportionem com-
              <lb/>
            probamus ex angulo, ſub quo Sol videtur, ſiue ex diametro eius apparenti, vna cũ diſtantia eius a centro vni-
              <lb/>
              <figure xlink:label="fig-0122-02" xlink:href="fig-0122-02a" number="81">
                <image file="0122-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-02"/>
              </figure>
            uerſi, quam ſupra indagauimus. </s>
            <s xml:id="echoid-s10248" xml:space="preserve">diametrum autem eius apparentem ſic olim Hippar-
              <lb/>
            chus inquirebat. </s>
            <s xml:id="echoid-s10249" xml:space="preserve">huius enim rei gratia dioptram quandam excogitauit, cuius imagi-
              <lb/>
            nem exhibuimus pag. </s>
            <s xml:id="echoid-s10250" xml:space="preserve">74. </s>
            <s xml:id="echoid-s10251" xml:space="preserve">vbi de Lunæ magnitudine egimus; </s>
            <s xml:id="echoid-s10252" xml:space="preserve">per eam ſic diametrum
              <lb/>
            apparentem capiebat; </s>
            <s xml:id="echoid-s10253" xml:space="preserve">ea namque in ſolem obuerſa alteroque oculo foramini D. </s>
            <s xml:id="echoid-s10254" xml:space="preserve">ap-
              <lb/>
            plicato, ita tabellam E F. </s>
            <s xml:id="echoid-s10255" xml:space="preserve">vltro citroq; </s>
            <s xml:id="echoid-s10256" xml:space="preserve">commouebat, vt ocuius per D. </s>
            <s xml:id="echoid-s10257" xml:space="preserve">ac ſimul per
              <lb/>
            duo foramina E F. </s>
            <s xml:id="echoid-s10258" xml:space="preserve">inſpiciens Solis limbum, ſeu oram, viſus leuiter perſtringeret:
              <lb/>
            </s>
            <s xml:id="echoid-s10259" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s10260" xml:space="preserve">in ea diſtantia obfirmata tabella E F. </s>
            <s xml:id="echoid-s10261" xml:space="preserve">angul. </s>
            <s xml:id="echoid-s10262" xml:space="preserve">contipiebat F D E. </s>
            <s xml:id="echoid-s10263" xml:space="preserve">eumq; </s>
            <s xml:id="echoid-s10264" xml:space="preserve">quantus eſ-
              <lb/>
            ſet expendebat: </s>
            <s xml:id="echoid-s10265" xml:space="preserve">vt in prop. </s>
            <s xml:id="echoid-s10266" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10267" xml:space="preserve">Appar. </s>
            <s xml:id="echoid-s10268" xml:space="preserve">dictum eſt. </s>
            <s xml:id="echoid-s10269" xml:space="preserve">reperitq; </s>
            <s xml:id="echoid-s10270" xml:space="preserve">hic angulum in mediocri
              <lb/>
            Solis a terra diſtantia continere min. </s>
            <s xml:id="echoid-s10271" xml:space="preserve">31. </s>
            <s xml:id="echoid-s10272" xml:space="preserve">ſiue diametrum Solis apparentem ſub ten-
              <lb/>
            dere 31@.</s>
            <s xml:id="echoid-s10273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10274" xml:space="preserve">Eadem Dioptra alij aliter vtuntur, nam pro viſiuis radijs excipiunt per foramina
              <lb/>
            E F. </s>
            <s xml:id="echoid-s10275" xml:space="preserve">Solis radios tabellamque E F. </s>
            <s xml:id="echoid-s10276" xml:space="preserve">tandium mouent donec binæ Solis illuminationes
              <lb/>
            per foramina E F. </s>
            <s xml:id="echoid-s10277" xml:space="preserve">illapſæ, atque in oppoſita tabella R D. </s>
            <s xml:id="echoid-s10278" xml:space="preserve">exceptę, ſe mutuo ad D. </s>
            <s xml:id="echoid-s10279" xml:space="preserve">con-
              <lb/>
            tingant; </s>
            <s xml:id="echoid-s10280" xml:space="preserve">tunc enim angulus E D F. </s>
            <s xml:id="echoid-s10281" xml:space="preserve">comprehendit diametrum Solis viſibilem; </s>
            <s xml:id="echoid-s10282" xml:space="preserve">vt in
              <lb/>
            figura binæ illuminationes per foramina E F. </s>
            <s xml:id="echoid-s10283" xml:space="preserve">ad punctum D. </s>
            <s xml:id="echoid-s10284" xml:space="preserve">concurant, ita vt duo
              <lb/>
            luminoſi circelli ſe mutuo in D. </s>
            <s xml:id="echoid-s10285" xml:space="preserve">contingant, eritque angulus E D F. </s>
            <s xml:id="echoid-s10286" xml:space="preserve">angulus ſub quo
              <lb/>
            Solis diameter ſpectatur. </s>
            <s xml:id="echoid-s10287" xml:space="preserve">imo ex vnica illuminatione eundem angulum obtinebimus,
              <lb/>
            angulus enim R E D. </s>
            <s xml:id="echoid-s10288" xml:space="preserve">eſt angulus, ſub quo ſol apparet; </s>
            <s xml:id="echoid-s10289" xml:space="preserve">ſi enim duo radij R E D. </s>
            <s xml:id="echoid-s10290" xml:space="preserve">pro-
              <lb/>
            ducantur verſus Solem, eum tandem hinc inde attinget, eruntque anguli ad </s>
          </p>
        </div>
      </text>
    </echo>
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