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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      <text xml:lang="la" type="free">
        <div xml:id="echoid-div613" type="section" level="1" n="430">
          <p>
            <s xml:id="echoid-s22070" xml:space="preserve">
              <pb o="22" file="0276" n="281" rhead="TRACTATVS"/>
            tionem. </s>
            <s xml:id="echoid-s22071" xml:space="preserve">ſunt autem hi, ſinus totus, diſtantiæ ſingularum horarum à meridie in aſſumpto paralello;
              <lb/>
            </s>
            <s xml:id="echoid-s22072" xml:space="preserve">altitudo, & </s>
            <s xml:id="echoid-s22073" xml:space="preserve">depreſſio meridiana, vt fiat aggregatum ex vtriuſque ſinubus. </s>
            <s xml:id="echoid-s22074" xml:space="preserve">quæ omnia melius perci-
              <lb/>
            pientur ex ſequenti exemplo. </s>
            <s xml:id="echoid-s22075" xml:space="preserve">ſint igitur exempli gratia ad latit. </s>
            <s xml:id="echoid-s22076" xml:space="preserve">44. </s>
            <s xml:id="echoid-s22077" xml:space="preserve">calculandæ per regulam auream
              <lb/>
              <note position="left" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">Ex@mplũ</note>
            ſecundum præditam analogiam altitudines pro ſingulis horis Italicis paralellorum oppoſitorum ♋.
              <lb/>
            </s>
            <s xml:id="echoid-s22078" xml:space="preserve">& </s>
            <s xml:id="echoid-s22079" xml:space="preserve">♑. </s>
            <s xml:id="echoid-s22080" xml:space="preserve">ſeu tropicorum, cuius gratia fiat apparatus qualis eſt ſequens,</s>
          </p>
        </div>
        <div xml:id="echoid-div615" type="section" level="1" n="431">
          <head xml:id="echoid-head456" xml:space="preserve">LOCVS APPARATVS.</head>
          <p>
            <s xml:id="echoid-s22081" xml:space="preserve">PRo conſtruendo hoc apparatu ſecundũ præcepta P. </s>
            <s xml:id="echoid-s22082" xml:space="preserve">Clauij tradita, tum probl. </s>
            <s xml:id="echoid-s22083" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22084" xml:space="preserve">Nouæ deſcript.
              <lb/>
            </s>
            <s xml:id="echoid-s22085" xml:space="preserve">tum in Gnom. </s>
            <s xml:id="echoid-s22086" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22087" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s22088" xml:space="preserve">35. </s>
            <s xml:id="echoid-s22089" xml:space="preserve">in ſcholio, inſeruiunt Tabellæ, quæ ſunt partim in Sphæra eius, par-
              <lb/>
            tim in noua deſcript. </s>
            <s xml:id="echoid-s22090" xml:space="preserve">partim in Tabulis ſeorſim editis pro habẽdis arcubus, & </s>
            <s xml:id="echoid-s22091" xml:space="preserve">temporibus ſemidiur-
              <lb/>
            nis. </s>
            <s xml:id="echoid-s22092" xml:space="preserve">ſinus autem recti, & </s>
            <s xml:id="echoid-s22093" xml:space="preserve">verſi eadem opera commodè habentur ex Magno Canone Magini. </s>
            <s xml:id="echoid-s22094" xml:space="preserve">In hoc
              <lb/>
            igitur apparatu parauimus, omnes terminos neceſſarios ad operandum per regulam auream ſecundũ
              <lb/>
            ſuperiorem analogiam, vt altitudines Solis in quauis hora dati paralelli per calculum indagemus. </s>
            <s xml:id="echoid-s22095" xml:space="preserve">in
              <lb/>
            qua analogia primus terminus eſt ſinus totus ſaltem 100,000. </s>
            <s xml:id="echoid-s22096" xml:space="preserve">qui ſemper idem manet in caiculo om-
              <lb/>
            nium horarum atq; </s>
            <s xml:id="echoid-s22097" xml:space="preserve">in omni paralello. </s>
            <s xml:id="echoid-s22098" xml:space="preserve">Secundus terminus eſt ſinus verſus diſtantiæ illius horæ pro-
              <lb/>
            prius pro qua c lculus inſtituitur, qui in apparatu ſcribitur è regione ſuæ horæ: </s>
            <s xml:id="echoid-s22099" xml:space="preserve">quare hic variatur in
              <lb/>
            ſingulis horis. </s>
            <s xml:id="echoid-s22100" xml:space="preserve">ij tamen qui reſpondent horis ♑. </s>
            <s xml:id="echoid-s22101" xml:space="preserve">reſpondent etiam totidem horis ♋. </s>
            <s xml:id="echoid-s22102" xml:space="preserve">quare ijde dua-
              <lb/>
            bus horis reſpondent. </s>
            <s xml:id="echoid-s22103" xml:space="preserve">Tertius terminus eſt ſemiſſis aggregati ex ſinubus rectis altit. </s>
            <s xml:id="echoid-s22104" xml:space="preserve">& </s>
            <s xml:id="echoid-s22105" xml:space="preserve">depreſſionis
              <lb/>
            meridianæ, qui cum primo termino ſemper idem manet in duobus oppoſitis paralellis. </s>
            <s xml:id="echoid-s22106" xml:space="preserve">Multipli-
              <lb/>
            candus eſt igitur ſinus verſus horæ aſſumptæ in prædictam ſemiſſem: </s>
            <s xml:id="echoid-s22107" xml:space="preserve">productum autem diuidendum
              <lb/>
            per ſinum totum: </s>
            <s xml:id="echoid-s22108" xml:space="preserve">& </s>
            <s xml:id="echoid-s22109" xml:space="preserve">quotiens inuentus, qui eſt quartus terminus huius analogiæ, demendus eſt ex ſi-
              <lb/>
            nu recto altitudinis meridianæ; </s>
            <s xml:id="echoid-s22110" xml:space="preserve">nam relictum erit ſinus altitudinis quæſitæ. </s>
            <s xml:id="echoid-s22111" xml:space="preserve">exe plo ſoquent@ res
              <lb/>
            melius percipietur.</s>
            <s xml:id="echoid-s22112" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22113" xml:space="preserve">Sit v.</s>
            <s xml:id="echoid-s22114" xml:space="preserve">g. </s>
            <s xml:id="echoid-s22115" xml:space="preserve">calculanda altit. </s>
            <s xml:id="echoid-s22116" xml:space="preserve">23. </s>
            <s xml:id="echoid-s22117" xml:space="preserve">horæ (ab ea enim vt ordine procedamus incipendum eſt.) </s>
            <s xml:id="echoid-s22118" xml:space="preserve">in aſſumpto
              <lb/>
              <note position="left" xlink:label="note-0276-02" xlink:href="note-0276-02a" xml:space="preserve">Exemplũ
                <lb/>
              calculi
                <lb/>
              horæ 23.</note>
            paralello ♋. </s>
            <s xml:id="echoid-s22119" xml:space="preserve">datæ latit. </s>
            <s xml:id="echoid-s22120" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s22121" xml:space="preserve">44. </s>
            <s xml:id="echoid-s22122" xml:space="preserve">Duco igitur ſinum verſum 117,078,. </s>
            <s xml:id="echoid-s22123" xml:space="preserve">in ſemiſſem aggregati 65,967.
              <lb/>
            </s>
            <s xml:id="echoid-s22124" xml:space="preserve">verum quia valdè tædioſum, laborioſum, pluribuſq; </s>
            <s xml:id="echoid-s22125" xml:space="preserve">erroribus obnoxium eſſet pro ſingulis 24. </s>
            <s xml:id="echoid-s22126" xml:space="preserve">noris
              <lb/>
            huiuſmodi multi plicationes iterare (in duobus enim oppoſitis paralellis ſunt 24 horæ) v@em@r miri-
              <lb/>
            fica, atque compendioſa hac induſtria, qua ſine labore multiplicationis, magna cum voluptate, fru-
              <lb/>
            ctum illius capiemus.</s>
            <s xml:id="echoid-s22127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22128" xml:space="preserve">I Parentur igitur circiter 20. </s>
            <s xml:id="echoid-s22129" xml:space="preserve">regulæ ſeu tabellę ex ligno, quales apparatus oſtendit ad dexteram.
              <lb/>
            </s>
            <s xml:id="echoid-s22130" xml:space="preserve">
              <note position="left" xlink:label="note-0276-03" xlink:href="note-0276-03a" xml:space="preserve">Induſtria
                <lb/>
              mirifica
                <lb/>
              in multi-
                <lb/>
              pl.</note>
            earum ſuperior ſuperficies ſit palimpſeſtus, ſeu deletiua, vt inſeruire poſſit pro alils etiam paralellis.
              <lb/>
            </s>
            <s xml:id="echoid-s22131" xml:space="preserve">earum aliæ notentur nota 1. </s>
            <s xml:id="echoid-s22132" xml:space="preserve">aliæ 2. </s>
            <s xml:id="echoid-s22133" xml:space="preserve">aliæ 3. </s>
            <s xml:id="echoid-s22134" xml:space="preserve">aliæ o, & </s>
            <s xml:id="echoid-s22135" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22136" xml:space="preserve">quæ notæ nunquam delendę ſunt. </s>
            <s xml:id="echoid-s22137" xml:space="preserve">his paratis ac-
              <lb/>
            cedo ad multiplicationem hoc modo; </s>
            <s xml:id="echoid-s22138" xml:space="preserve">ſcribo ſinum verſum prædictum ſub ſemiſie aggregati, vti vi-
              <lb/>
            des in Apparatu; </s>
            <s xml:id="echoid-s22139" xml:space="preserve">& </s>
            <s xml:id="echoid-s22140" xml:space="preserve">quia prima figura multiplicans eſt 8. </s>
            <s xml:id="echoid-s22141" xml:space="preserve">ideo accipio regulam iam prænotatam figu-
              <lb/>
            ra eadem 8. </s>
            <s xml:id="echoid-s22142" xml:space="preserve">quam pono ſub numero multiplicante; </s>
            <s xml:id="echoid-s22143" xml:space="preserve">vt vides in exemplo apparatus. </s>
            <s xml:id="echoid-s22144" xml:space="preserve">Duco igitur 8. </s>
            <s xml:id="echoid-s22145" xml:space="preserve">in
              <lb/>
            ſingulas figuras ſemiſſis (omitto tamen fractionem {1/2}. </s>
            <s xml:id="echoid-s22146" xml:space="preserve">quæ tamen non eſt omittenda quotieſcunque
              <lb/>
              <note position="left" xlink:label="note-0276-04" xlink:href="note-0276-04a" xml:space="preserve">Quando
                <lb/>
              fractio
                <lb/>
              non ſit
                <lb/>
              omitten-
                <lb/>
              da.</note>
            dimidium ſinus verſi habet plures figuras quinque) excipiendo in tabella 8. </s>
            <s xml:id="echoid-s22147" xml:space="preserve">productum huius multi-
              <lb/>
            plicationis, ſcilicet 527,736. </s>
            <s xml:id="echoid-s22148" xml:space="preserve">deinde vtor probatione per 9. </s>
            <s xml:id="echoid-s22149" xml:space="preserve">quæ c tiſſimè perficitur: </s>
            <s xml:id="echoid-s22150" xml:space="preserve">præſertim quia
              <lb/>
            figura 6. </s>
            <s xml:id="echoid-s22151" xml:space="preserve">quæ re nanet ex dimidio aggregati, ſemper eadem manet per vtrumque paralellum decuſ-
              <lb/>
            ſato deinde 8. </s>
            <s xml:id="echoid-s22152" xml:space="preserve">aſſumo ſequentem figuram 7. </s>
            <s xml:id="echoid-s22153" xml:space="preserve">& </s>
            <s xml:id="echoid-s22154" xml:space="preserve">pariter tabellam 7 pono ſub priore tabella 8. </s>
            <s xml:id="echoid-s22155" xml:space="preserve">eo ſitu
              <lb/>
            quem vides in formula Apparatus; </s>
            <s xml:id="echoid-s22156" xml:space="preserve">atque in ea excipio multiplicationem 7. </s>
            <s xml:id="echoid-s22157" xml:space="preserve">in totam ſemiſſem, cum
              <lb/>
            probatione per 9. </s>
            <s xml:id="echoid-s22158" xml:space="preserve">Similiter decuſſata figura 7. </s>
            <s xml:id="echoid-s22159" xml:space="preserve">quia ſequens figura eſt o. </s>
            <s xml:id="echoid-s22160" xml:space="preserve">ſuppono tabellam 0. </s>
            <s xml:id="echoid-s22161" xml:space="preserve">duabus
              <lb/>
            præcedentibus, in quo deſcribo productum ex multipſicationeo. </s>
            <s xml:id="echoid-s22162" xml:space="preserve">in ſemiſſem. </s>
            <s xml:id="echoid-s22163" xml:space="preserve">Idem facio cum ſe-
              <lb/>
            quenti 7. </s>
            <s xml:id="echoid-s22164" xml:space="preserve">& </s>
            <s xml:id="echoid-s22165" xml:space="preserve">altera regula 7. </s>
            <s xml:id="echoid-s22166" xml:space="preserve">ſed abſq; </s>
            <s xml:id="echoid-s22167" xml:space="preserve">nouo labore multiplicandi deſcribo in ea productum prioris 7.
              <lb/>
            </s>
            <s xml:id="echoid-s22168" xml:space="preserve">Tandem propter binas 1, 1,. </s>
            <s xml:id="echoid-s22169" xml:space="preserve">ſuppono alijs duas regulas 1, 1,. </s>
            <s xml:id="echoid-s22170" xml:space="preserve">& </s>
            <s xml:id="echoid-s22171" xml:space="preserve">in vtraque deſcribo ipſam ſemiſſem
              <lb/>
            aggregati, quia 1,. </s>
            <s xml:id="echoid-s22172" xml:space="preserve">ducta in quemuis numerum, eundem numerum producit. </s>
            <s xml:id="echoid-s22173" xml:space="preserve">poſtremo ex omnibus
              <lb/>
            hiſce multiplicationibus fit ſumma; </s>
            <s xml:id="echoid-s22174" xml:space="preserve">vna cum probatione per 9 quo facto tabellas hiſce productis in-
              <lb/>
            ſcriptas ad partes ſeruo, erunt enim vſui, & </s>
            <s xml:id="echoid-s22175" xml:space="preserve">patebit.</s>
            <s xml:id="echoid-s22176" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22177" xml:space="preserve">2 Abſoluta hac prima multiplicatione, quæ eſt ſecundi termini analogiæ in tertium; </s>
            <s xml:id="echoid-s22178" xml:space="preserve">diuiden-
              <lb/>
              <note position="left" xlink:label="note-0276-05" xlink:href="note-0276-05a" xml:space="preserve">Diuiſio
                <lb/>
              facillima</note>
            dus eſt productus, ſumma ſcilicet prædicta per primum tern inum, ideſt, per ſinum totum, 100, 000.
              <lb/>
            </s>
            <s xml:id="echoid-s22179" xml:space="preserve">quę diuiſio abſque vllo labore fit demendo a numero diuidendo tot figuras ad dexteram ſitas, quot
              <lb/>
            ſunt cifræ in ſinu toto, ſcilicet quinq; </s>
            <s xml:id="echoid-s22180" xml:space="preserve">vt factum vides in formula apparatus. </s>
            <s xml:id="echoid-s22181" xml:space="preserve">Quotiens autem hui@s
              <lb/>
            diuiſionis erit reliquas numerus 77, 232. </s>
            <s xml:id="echoid-s22182" xml:space="preserve">& </s>
            <s xml:id="echoid-s22183" xml:space="preserve">quartus terminus analogiæ inuentus per auream regulam
              <lb/>
            quam quotiens ſeruandus eſt quando hora ♋. </s>
            <s xml:id="echoid-s22184" xml:space="preserve">habet aliam horam ſib in ♑, reſpondentem. </s>
            <s xml:id="echoid-s22185" xml:space="preserve">poſtea hic
              <lb/>
            quartus terminus detrahendus eſt ex ſinu altitudinis meridianæ 93, 667. </s>
            <s xml:id="echoid-s22186" xml:space="preserve">nam reliquus 16, 435. </s>
            <s xml:id="echoid-s22187" xml:space="preserve">erit
              <lb/>
            ſinus altitudinis horæ 23. </s>
            <s xml:id="echoid-s22188" xml:space="preserve">♋. </s>
            <s xml:id="echoid-s22189" xml:space="preserve">Igitur in Tabula ſinuum reperio hunc reliquum numerum (aut @altem
              <lb/>
            ei propinquiorem) cui in eadem tabula competunt gr. </s>
            <s xml:id="echoid-s22190" xml:space="preserve">9. </s>
            <s xml:id="echoid-s22191" xml:space="preserve">28. </s>
            <s xml:id="echoid-s22192" xml:space="preserve">altitudo ſcilicet Solis quæſita hora 23. </s>
            <s xml:id="echoid-s22193" xml:space="preserve">
              <lb/>
            in ♋. </s>
            <s xml:id="echoid-s22194" xml:space="preserve">quam altitudinem ſcribo in apparatu è regione horæ 23.</s>
            <s xml:id="echoid-s22195" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22196" xml:space="preserve">3 Deinde ſimiliter multiplico ſinum verſum horę 22, in eandẽ ſemiſſem, & </s>
            <s xml:id="echoid-s22197" xml:space="preserve">quoniam prima ſigu-
              <lb/>
              <note position="left" xlink:label="note-0276-06" xlink:href="note-0276-06a" xml:space="preserve">Calculus
                <lb/>
              her@, 22.</note>
            ra multiplicans eſt 4. </s>
            <s xml:id="echoid-s22198" xml:space="preserve">& </s>
            <s xml:id="echoid-s22199" xml:space="preserve">tabella 4. </s>
            <s xml:id="echoid-s22200" xml:space="preserve">adhuc vacua eſt, eam propterea accipio, ponoq; </s>
            <s xml:id="echoid-s22201" xml:space="preserve">ſub numeris mul-
              <lb/>
            ti plicandis, eorumq; </s>
            <s xml:id="echoid-s22202" xml:space="preserve">multiplicationem excipio in eadem tabella 4. </s>
            <s xml:id="echoid-s22203" xml:space="preserve">adhibita probatione per 9. </s>
            <s xml:id="echoid-s22204" xml:space="preserve">de-
              <lb/>
            inde volens multiplicare per ſecundam figuram, quę eſſe 99. </s>
            <s xml:id="echoid-s22205" xml:space="preserve">accipio tabellam 9. </s>
            <s xml:id="echoid-s22206" xml:space="preserve">pariter vacuam, atq;</s>
            <s xml:id="echoid-s22207" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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