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-div615" type="section" level="1" n="431">
          <p>
            <s xml:id="echoid-s22207" xml:space="preserve">
              <pb o="23" file="0277" n="282" rhead="DEHOROLOGIIS."/>
            in ea ſcribo productum. </s>
            <s xml:id="echoid-s22208" xml:space="preserve">poſtea eadem ratione propter tertiam figuram 9. </s>
            <s xml:id="echoid-s22209" xml:space="preserve">tranſeribo eundem produ-
              <lb/>
            ctum ſine noua multiplicatione deinde propter quartam figuram o.</s>
            <s xml:id="echoid-s22210" xml:space="preserve">accipio tabellam o. </s>
            <s xml:id="echoid-s22211" xml:space="preserve">iam cifris no-
              <lb/>
            tatam, eamque præcedentibus ſuppono. </s>
            <s xml:id="echoid-s22212" xml:space="preserve">tandem ob vltimam 9. </s>
            <s xml:id="echoid-s22213" xml:space="preserve">aliam tabellam 9. </s>
            <s xml:id="echoid-s22214" xml:space="preserve">inſcribo eodem
              <lb/>
            producto, quo aliæ duæ 9. </s>
            <s xml:id="echoid-s22215" xml:space="preserve">eamque ſuo loco cæteris appono. </s>
            <s xml:id="echoid-s22216" xml:space="preserve">ex quibus omnibus fit ſumma cum pro-
              <lb/>
            batione per 9. </s>
            <s xml:id="echoid-s22217" xml:space="preserve">quę ſumma diuiditur vt ſupra per 100,000, abiectis quinq; </s>
            <s xml:id="echoid-s22218" xml:space="preserve">figuris dexteris, & </s>
            <s xml:id="echoid-s22219" xml:space="preserve">Quotiens
              <lb/>
            hinc proueniens detractus ex ſinu recto altit. </s>
            <s xml:id="echoid-s22220" xml:space="preserve">meridianę relinquat ſinum rectũ altitudinis hor. </s>
            <s xml:id="echoid-s22221" xml:space="preserve">22. </s>
            <s xml:id="echoid-s22222" xml:space="preserve">cui
              <lb/>
            in Tabula finuum dantur gra. </s>
            <s xml:id="echoid-s22223" xml:space="preserve">19. </s>
            <s xml:id="echoid-s22224" xml:space="preserve">40′. </s>
            <s xml:id="echoid-s22225" xml:space="preserve">quos ideo ſcribo è regione horæ 22. </s>
            <s xml:id="echoid-s22226" xml:space="preserve">in Apparatu. </s>
            <s xml:id="echoid-s22227" xml:space="preserve">tabellas ve-
              <lb/>
            rò ſeorſum repono. </s>
            <s xml:id="echoid-s22228" xml:space="preserve">Quotientem hunc ſeruare non eſſe opus ex dictis ſuperius.</s>
            <s xml:id="echoid-s22229" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22230" xml:space="preserve">4 Iam multiplicandus eſt ſinus verſus horæ 21,. </s>
            <s xml:id="echoid-s22231" xml:space="preserve">in eandem ſemiſsem. </s>
            <s xml:id="echoid-s22232" xml:space="preserve">eius prima figura multipli-
              <lb/>
              <note position="right" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">Calculas
                <lb/>
              horæ 21.</note>
            cans eſt 4. </s>
            <s xml:id="echoid-s22233" xml:space="preserve">ſed quia tabella 4. </s>
            <s xml:id="echoid-s22234" xml:space="preserve">eſt inſcripta, eam ſine vllollabore multiplicationis pono ſub numeris
              <lb/>
            multiplicandis, deinde propter ſecundam figuram 2. </s>
            <s xml:id="echoid-s22235" xml:space="preserve">cuius tabella adhuc vacua eſt multiplico ſemiſ-
              <lb/>
            ſe per 2. </s>
            <s xml:id="echoid-s22236" xml:space="preserve">excipiendo in tabella 2. </s>
            <s xml:id="echoid-s22237" xml:space="preserve">productum ſimiliter facio cum duabus figuris duabus 5, 5,. </s>
            <s xml:id="echoid-s22238" xml:space="preserve">& </s>
            <s xml:id="echoid-s22239" xml:space="preserve">dua-
              <lb/>
            bus tabellis 5, 5,. </s>
            <s xml:id="echoid-s22240" xml:space="preserve">& </s>
            <s xml:id="echoid-s22241" xml:space="preserve">idem cum ſigura 6,. </s>
            <s xml:id="echoid-s22242" xml:space="preserve">ſcribendo in tabula 6. </s>
            <s xml:id="echoid-s22243" xml:space="preserve">&</s>
            <s xml:id="echoid-s22244" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22245" xml:space="preserve">facta poſtea ſumma, eaque diuiſa
              <lb/>
            per ſinum totum, & </s>
            <s xml:id="echoid-s22246" xml:space="preserve">quotiente demptio ex ſinu altitudinis meridie, reliquus ſinus ex hibebit in tabula
              <lb/>
            ſinuum altitudinem horæ 21. </s>
            <s xml:id="echoid-s22247" xml:space="preserve">ſcilicet gr. </s>
            <s xml:id="echoid-s22248" xml:space="preserve">30. </s>
            <s xml:id="echoid-s22249" xml:space="preserve">18,. </s>
            <s xml:id="echoid-s22250" xml:space="preserve">quos è directo horæ 21. </s>
            <s xml:id="echoid-s22251" xml:space="preserve">in apparatu ſcribo, neque eſt
              <lb/>
            opus ſeruare hunc quotientem.</s>
            <s xml:id="echoid-s22252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22253" xml:space="preserve">5 Iam per multiplicationem ſinus verſi horæ 20. </s>
            <s xml:id="echoid-s22254" xml:space="preserve">nihil ferè laborandum eſt, cum omnes eius figu-
              <lb/>
              <note position="right" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">Her@ 20.</note>
            ræ habeant ſuam multiplicationem in tabellis ſibi cognominibus. </s>
            <s xml:id="echoid-s22255" xml:space="preserve">ſolius figuræ 4. </s>
            <s xml:id="echoid-s22256" xml:space="preserve">erit bis repetenda
              <lb/>
            multiplicatio, quare eius ſuperior multiplicatio tranſcribenda erit in noua tabella 4. </s>
            <s xml:id="echoid-s22257" xml:space="preserve">atque hoc mo-
              <lb/>
            do procedendo habebis citò omnes multiplicationes in tabellis, vnde etiam earum ſummam, & </s>
            <s xml:id="echoid-s22258" xml:space="preserve">diui-
              <lb/>
            ſionem, & </s>
            <s xml:id="echoid-s22259" xml:space="preserve">quotientem nunc ſeruandum, & </s>
            <s xml:id="echoid-s22260" xml:space="preserve">detrahendum ex ſinu altitudinis meridianæ, atq; </s>
            <s xml:id="echoid-s22261" xml:space="preserve">hinc re-
              <lb/>
            liquum ſinum, qui in tabula ſinuum dabit altitudinem horæ 20. </s>
            <s xml:id="echoid-s22262" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s22263" xml:space="preserve">eodem modo agendum eſt in cæ-
              <lb/>
            teris horis.</s>
            <s xml:id="echoid-s22264" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22265" xml:space="preserve">Hic quotiens ſeruandus eſt, quoties oritur ex calculo alicuius horæ ♋. </s>
            <s xml:id="echoid-s22266" xml:space="preserve">vel alius paralelli, quæ ha-
              <lb/>
              <note position="right" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">Quando
                <lb/>
              quotiens
                <lb/>
              ſeruãdus
                <lb/>
              ſit.</note>
            beat eundem ſinum verſum cum hora oppoſiti paralelli, v.</s>
            <s xml:id="echoid-s22267" xml:space="preserve">g. </s>
            <s xml:id="echoid-s22268" xml:space="preserve">♑. </s>
            <s xml:id="echoid-s22269" xml:space="preserve">vti nunc eſt hora 20 ♋. </s>
            <s xml:id="echoid-s22270" xml:space="preserve">reſpectu ho-
              <lb/>
            ræ 16. </s>
            <s xml:id="echoid-s22271" xml:space="preserve">♑. </s>
            <s xml:id="echoid-s22272" xml:space="preserve">quia mihi quotientem inſeruiunt etiam pro horis oppoſiti paralelli, vti nunc ♑.</s>
            <s xml:id="echoid-s22273" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div623" type="section" level="1" n="432">
          <head xml:id="echoid-head457" style="it" xml:space="preserve">De Paralello oppoſito, qui est Capricorni.</head>
          <p>
            <s xml:id="echoid-s22274" xml:space="preserve">1 IAm pro oppoſito paralello ♑. </s>
            <s xml:id="echoid-s22275" xml:space="preserve">parum laboris ſupereſt; </s>
            <s xml:id="echoid-s22276" xml:space="preserve">ſunt enim omnia ferè huius paralelli com-
              <lb/>
              <note position="right" xlink:label="note-0277-04" xlink:href="note-0277-04a" xml:space="preserve">Portio
                <lb/>
              noctur-
                <lb/>
              na ♋,
                <lb/>
              æqualis
                <lb/>
              eſt diur-
                <lb/>
              nę oppo-
                <lb/>
              ſitipa-
                <lb/>
              ralelli
                <lb/>
              ♑, &c.
                <lb/>
              permu-
                <lb/>
              tatim.</note>
            munia cum paralello ♋. </s>
            <s xml:id="echoid-s22277" xml:space="preserve">ſed inuerſa, & </s>
            <s xml:id="echoid-s22278" xml:space="preserve">commutata. </s>
            <s xml:id="echoid-s22279" xml:space="preserve">ſic altitudo meridiana vnius eſt deprefſio
              <lb/>
            meridiana alterius, & </s>
            <s xml:id="echoid-s22280" xml:space="preserve">viceuerſa. </s>
            <s xml:id="echoid-s22281" xml:space="preserve">quare erit eadem ſemiſſis aggregati ex ſinubus earum, vt apparet in
              <lb/>
            apparatu. </s>
            <s xml:id="echoid-s22282" xml:space="preserve">ſim iliter tempus nocturnum illlus eſt diurnum huius, &</s>
            <s xml:id="echoid-s22283" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22284" xml:space="preserve">pręterea diſtantię horarum diur-
              <lb/>
            narum in ♑. </s>
            <s xml:id="echoid-s22285" xml:space="preserve">ſunt æquales totidem diſtantijs in ♋. </s>
            <s xml:id="echoid-s22286" xml:space="preserve">quod inde patet quia portio diurna ♑. </s>
            <s xml:id="echoid-s22287" xml:space="preserve">eſt æqualis
              <lb/>
            portioni nocturnæ ♋. </s>
            <s xml:id="echoid-s22288" xml:space="preserve">ſed media nox in ♋. </s>
            <s xml:id="echoid-s22289" xml:space="preserve">eſt hora 4. </s>
            <s xml:id="echoid-s22290" xml:space="preserve">21,. </s>
            <s xml:id="echoid-s22291" xml:space="preserve">meridies quoque in ♋. </s>
            <s xml:id="echoid-s22292" xml:space="preserve">eſt hora 16. </s>
            <s xml:id="echoid-s22293" xml:space="preserve">21,.
              <lb/>
            </s>
            <s xml:id="echoid-s22294" xml:space="preserve">quare tantum diſtat à meridiano nocturno 4. </s>
            <s xml:id="echoid-s22295" xml:space="preserve">hora noctis, quantum 16. </s>
            <s xml:id="echoid-s22296" xml:space="preserve">diurna à meridiano diurno. </s>
            <s xml:id="echoid-s22297" xml:space="preserve">
              <lb/>
            Quod etiam patebit conſideranti, quod cum in ♋. </s>
            <s xml:id="echoid-s22298" xml:space="preserve">ſit meridies hora 16. </s>
            <s xml:id="echoid-s22299" xml:space="preserve">21,. </s>
            <s xml:id="echoid-s22300" xml:space="preserve">ſi ei addantur horæ 12. </s>
            <s xml:id="echoid-s22301" xml:space="preserve">
              <lb/>
            quæ intercedunt vſque ad mediam noctem, neceſiariò hora proximè præcedens mediam noctem di-
              <lb/>
            ſtabit min. </s>
            <s xml:id="echoid-s22302" xml:space="preserve">21. </s>
            <s xml:id="echoid-s22303" xml:space="preserve">à meridiano nocturno: </s>
            <s xml:id="echoid-s22304" xml:space="preserve">Quare quatuor horæ antemerinocturnæ tantum ſingulæ di-
              <lb/>
            ſtabunt à meridiano nocturno, & </s>
            <s xml:id="echoid-s22305" xml:space="preserve">inſeriori, quantum aliæ quatuor diurnæ proximè meridiem præ
              <lb/>
            cedentes diſtantà meridiano diurno, & </s>
            <s xml:id="echoid-s22306" xml:space="preserve">ſuperiori: </s>
            <s xml:id="echoid-s22307" xml:space="preserve">igitur diſtantiæ nocturnarum horarum 1, 2, 3, 4,. </s>
            <s xml:id="echoid-s22308" xml:space="preserve">
              <lb/>
            æquales erunt diſtantijs diurnarum 13. </s>
            <s xml:id="echoid-s22309" xml:space="preserve">14. </s>
            <s xml:id="echoid-s22310" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22311" xml:space="preserve">16 & </s>
            <s xml:id="echoid-s22312" xml:space="preserve">conſequenter reliquarum pomerinocturnarum
              <lb/>
            5, 6, 7, 8,. </s>
            <s xml:id="echoid-s22313" xml:space="preserve">diſtantię æquales erunt diſtantijs diurnarum 17, 18, 19, 20,. </s>
            <s xml:id="echoid-s22314" xml:space="preserve">Præterea conſiderandum, quod
              <lb/>
            cum portio nocturna ♋. </s>
            <s xml:id="echoid-s22315" xml:space="preserve">ſit eadem cum portione diurna ♑ ſi illa transferatur in locum huius, ita vt
              <lb/>
            pars antemerinocturna ♋. </s>
            <s xml:id="echoid-s22316" xml:space="preserve">euadat pomeridiana ♑; </s>
            <s xml:id="echoid-s22317" xml:space="preserve">pars vero pomerinocturna ♋. </s>
            <s xml:id="echoid-s22318" xml:space="preserve">euadat antemeri-
              <lb/>
            diana ♑, erunt horarum appellationes incipiendo ab occaſu in ♋, hæ 1, 2, 3, 4, 5, 6, 7, 8,. </s>
            <s xml:id="echoid-s22319" xml:space="preserve">in horas
              <lb/>
            24, 22, 21, 20, 19, 18, 17, 16. </s>
            <s xml:id="echoid-s22320" xml:space="preserve">& </s>
            <s xml:id="echoid-s22321" xml:space="preserve">habebimus arcum diurnum Capricorni ipſiſſimum, &</s>
            <s xml:id="echoid-s22322" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22323" xml:space="preserve">ac propterea
              <lb/>
            (vti dictum eſt) earum diſtantiæ eædem erunt cum diſtantijs totidem horarum Cancri. </s>
            <s xml:id="echoid-s22324" xml:space="preserve">qua de cau-
              <lb/>
            ſa has horas ♑. </s>
            <s xml:id="echoid-s22325" xml:space="preserve">ſcripſimus in Apparatu è regione illarum horarum ♋, quæ æqualiter cum illis diſtãt
              <lb/>
            à meridie.</s>
            <s xml:id="echoid-s22326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22327" xml:space="preserve">2 Vnde ſequitur horas Capricorni habere præterea eaſdem ſinus verſos diſtantiarum cum præ-
              <lb/>
            dictis horis Cancri: </s>
            <s xml:id="echoid-s22328" xml:space="preserve">& </s>
            <s xml:id="echoid-s22329" xml:space="preserve">conſequenter ex ductu eorum in ſemiſſem aggregati fore idem productum, & </s>
            <s xml:id="echoid-s22330" xml:space="preserve">
              <lb/>
            eundem quotientem ex eius diuiſionem per ſinum totum. </s>
            <s xml:id="echoid-s22331" xml:space="preserve">qui quotiens detrahendus eſt ex ſinu alti-
              <lb/>
            tudinis meridianæ Capricorni, qui eſt 38, 268. </s>
            <s xml:id="echoid-s22332" xml:space="preserve">qui cum differat à ſinu altitudinis meridianæ Cancri
              <lb/>
            relinquet neceſſariò alium numerum, qui reliquus numerus erit ſinus altitudinis horæ ſibi compe-
              <lb/>
            tentis. </s>
            <s xml:id="echoid-s22333" xml:space="preserve">cum vero hi quotientes ſint in Cancro ſeruati (vt monuimus) ijs nunc abſque vllo multipli-
              <lb/>
            candi, aut diuidendi labore vtemur. </s>
            <s xml:id="echoid-s22334" xml:space="preserve">hoc compendio altitudines horarum in ♑. </s>
            <s xml:id="echoid-s22335" xml:space="preserve">quas in Apparatu vi-
              <lb/>
            des, inuenimus.</s>
            <s xml:id="echoid-s22336" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22337" xml:space="preserve">3 Abſoluo calculo delendæ ſunt tabellarum multiplicationes, vt ſequentibus duobus oppoſitis
              <lb/>
            paralellis inſeruire poſſint. </s>
            <s xml:id="echoid-s22338" xml:space="preserve">quorum vnus eſſe per gra. </s>
            <s xml:id="echoid-s22339" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22340" xml:space="preserve">0′ ♋. </s>
            <s xml:id="echoid-s22341" xml:space="preserve">alter vero ei oppoſitus per gra. </s>
            <s xml:id="echoid-s22342" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22343" xml:space="preserve">0′
              <lb/>
            ♐. </s>
            <s xml:id="echoid-s22344" xml:space="preserve">in quibus eadem methodo cum ſuperioribus calculandum eſt, ideſt, prius pro boreali, poſtea per
              <lb/>
            auſtrali.</s>
            <s xml:id="echoid-s22345" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22346" xml:space="preserve">4 Aliud compendium ex vſu erit, ſi inter paralellos calculandos, aſſumamus paralellos arcuum
              <lb/>
              <note position="right" xlink:label="note-0277-05" xlink:href="note-0277-05a" xml:space="preserve">Aliudcõ
                <lb/>
              pendi{us}.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
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