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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    <echo version="1.0RC">
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        <div xml:id="echoid-div547" type="section" level="1" n="412">
          <p>
            <s xml:id="echoid-s20537" xml:space="preserve">
              <pb o="9" file="0263" n="268" rhead="DE HOROLOGIIS."/>
            diſtabit aliquantulum à linea Radiarij H A I, cum totum Horarium cadat extra arcum diſtantiarum;
              <lb/>
            </s>
            <s xml:id="echoid-s20538" xml:space="preserve">incumbit enim tangenti T V, quare radij non ſecabunt illud niſi producantur vitra lineã H A I, qua-
              <lb/>
            re producti facient in eo diuiſiones laxiores quam in B D, ſic generatim quãto magis diſtabunt a me-
              <lb/>
            dia B D, tanto magis etiam a Radiario, & </s>
            <s xml:id="echoid-s20539" xml:space="preserve">proinde laxioribus ſpatijs diuidentur.</s>
            <s xml:id="echoid-s20540" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20541" xml:space="preserve">14 Hinc pariter neceſſe erit hyperbolas, quas ſupra innuimus, ſeu puncta illarum eſſe illa eadem,
              <lb/>
            quæ reperta ſunt in lineis horarijs per latera erecta normaliter ſupra ſecantium extrema puncta, V,
              <lb/>
            3. </s>
            <s xml:id="echoid-s20542" xml:space="preserve">2. </s>
            <s xml:id="echoid-s20543" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20544" xml:space="preserve">&</s>
            <s xml:id="echoid-s20545" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20546" xml:space="preserve">ſeu per applicatam regulam normaliter, nam radius, v. </s>
            <s xml:id="echoid-s20547" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20548" xml:space="preserve">♋, E I T, in prædicto ſitu ſecat
              <lb/>
            latus G F, in F, vt vidimus, infra ſecantem A V, diſtantiæ horæ Italicæ in ♋. </s>
            <s xml:id="echoid-s20549" xml:space="preserve">Idem accidet reliquis
              <lb/>
            punctis extremis linearum Ital. </s>
            <s xml:id="echoid-s20550" xml:space="preserve">& </s>
            <s xml:id="echoid-s20551" xml:space="preserve">Babylon. </s>
            <s xml:id="echoid-s20552" xml:space="preserve">Idem intelligendum de alijs punctis, v.</s>
            <s xml:id="echoid-s20553" xml:space="preserve">g.</s>
            <s xml:id="echoid-s20554" xml:space="preserve">s.</s>
            <s xml:id="echoid-s20555" xml:space="preserve">s. </s>
            <s xml:id="echoid-s20556" xml:space="preserve">quia in il-
              <lb/>
            lis occurrunt radij ♌ & </s>
            <s xml:id="echoid-s20557" xml:space="preserve">♐, & </s>
            <s xml:id="echoid-s20558" xml:space="preserve">pariter in ijſmet ſecatur a regula normaliter applicata ſecus punctu@ 3.
              <lb/>
            </s>
            <s xml:id="echoid-s20559" xml:space="preserve">extremum ſecãtis horæ Italicæ a meridie in paralello ♌, &</s>
            <s xml:id="echoid-s20560" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20561" xml:space="preserve">res per ſe obſcura indiget ſpeculatione. </s>
            <s xml:id="echoid-s20562" xml:space="preserve">
              <lb/>
            Quare patet aliter reperiri poſſe Italicam, & </s>
            <s xml:id="echoid-s20563" xml:space="preserve">Babylonicam, quam per altitudinem poli, quod pro-
              <lb/>
            poſueram.</s>
            <s xml:id="echoid-s20564" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20565" xml:space="preserve">15 Notandum tres prædictas lineas 18. </s>
            <s xml:id="echoid-s20566" xml:space="preserve">Italicam 12. </s>
            <s xml:id="echoid-s20567" xml:space="preserve">Aſtronomicam, & </s>
            <s xml:id="echoid-s20568" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20569" xml:space="preserve">Babylonicam poſſe in-
              <lb/>
            ſeruire in vſu Inſtrumenti etiam pro cęteris omnibus horis: </s>
            <s xml:id="echoid-s20570" xml:space="preserve">quod patebit conſideranti primo lineas
              <lb/>
            omnes horarias Italicas, & </s>
            <s xml:id="echoid-s20571" xml:space="preserve">Babylonicas habere vbiq; </s>
            <s xml:id="echoid-s20572" xml:space="preserve">eundem ſitum vel inclinationem ad æquatorẽ;
              <lb/>
            </s>
            <s xml:id="echoid-s20573" xml:space="preserve">cum enim omnes earum circuli horarij tangant paralellum maximum ſemper apparentium, necnon
              <lb/>
            ſemper occultorum habebunt omnes eandem inclinationem, quæ æqualis erit altitudini poli propo-
              <lb/>
            ſitæ regionis. </s>
            <s xml:id="echoid-s20574" xml:space="preserve">De Aſtronomicis etiam perſpicuum eſt, cum omnes circuli earum horarij faciant cum
              <lb/>
            æquatore angulos rectos: </s>
            <s xml:id="echoid-s20575" xml:space="preserve">cum igitur tres noſtræ lineę fint tangentes trium horum circulorum hora-
              <lb/>
            riorum, in mutuis eorum ſectionibus cum æquatore, ſequitur eas habere eandem inclinationem, & </s>
            <s xml:id="echoid-s20576" xml:space="preserve">
              <lb/>
            poſitionem ad æquatorem, quam habent cęteræ omnes tangentes cęterorum omnium arcuum, quas-
              <lb/>
            libet cum quibuslibet ſui generis comparando, ideſt 18. </s>
            <s xml:id="echoid-s20577" xml:space="preserve">Italicam coincidere poſſe cum qualibet alia
              <lb/>
            Italica, & </s>
            <s xml:id="echoid-s20578" xml:space="preserve">Babylonicam cum qualibet Babilonica, & </s>
            <s xml:id="echoid-s20579" xml:space="preserve">Aſtronomicam cum qualibet Aſtronomica, ſi
              <lb/>
            horarium transferatur ad aliam quamuis diuiſionem æquatoris factam in 24. </s>
            <s xml:id="echoid-s20580" xml:space="preserve">partes competentes 24. </s>
            <s xml:id="echoid-s20581" xml:space="preserve">
              <lb/>
            horis, &</s>
            <s xml:id="echoid-s20582" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20583" xml:space="preserve">quemadmodum accidit in vſu Inſtrumenti: </s>
            <s xml:id="echoid-s20584" xml:space="preserve">nam Horarium transfertur ad ſingulas partes
              <lb/>
            24. </s>
            <s xml:id="echoid-s20585" xml:space="preserve">æquatoris. </s>
            <s xml:id="echoid-s20586" xml:space="preserve">ex quibus patet propoſitum.</s>
            <s xml:id="echoid-s20587" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20588" xml:space="preserve">16 Deſcripto iam in charta Horario tranſcribendum illud eſt in laminam ęneam, aut in regulas
              <lb/>
              <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">Horari-
                <lb/>
              um ma-
                <lb/>
              teriale.</note>
            ęneas. </s>
            <s xml:id="echoid-s20589" xml:space="preserve">Si quis vellet eo vti ad horas tantum Italicas deſcribendas, ſatis eſſet tranſcribere triangulum
              <lb/>
            E F H, cum ſuis punctis. </s>
            <s xml:id="echoid-s20590" xml:space="preserve">Si tantum Aſtronomicas, ſatis ei fuerit in regulam ęneam tranſcribere li-
              <lb/>
            neam D C B, cum ſuis purctis. </s>
            <s xml:id="echoid-s20591" xml:space="preserve">Si tantum Babylonicam triangulum G H F, ſufficiet cum ſuis pun-
              <lb/>
            ctis. </s>
            <s xml:id="echoid-s20592" xml:space="preserve">Quod ſi latus E H, vel latus G E, ſint diuiſa vt ſupra, ea poſſunt inſeruire ad horas Aſtronomi-
              <lb/>
            cas delineandas. </s>
            <s xml:id="echoid-s20593" xml:space="preserve">ſatius tamen exiſtimo integrum Horarium in lamina ænea incidere hoc modo: </s>
            <s xml:id="echoid-s20594" xml:space="preserve">aſ-
              <lb/>
            ſumptum laminam feneſtrare ſecundum tres lineas horarias, ideſt excidere in ea tres feneſtellas ęqua-
              <lb/>
            les ſecundum longitudinem tribus lineis horarijs: </s>
            <s xml:id="echoid-s20595" xml:space="preserve">Obſeruando tamen vt latus vnum tantum fene-
              <lb/>
            ſtellę referat ſuam lineam horariam, ideſt ſit rectum omnino, & </s>
            <s xml:id="echoid-s20596" xml:space="preserve">diuiſum, &</s>
            <s xml:id="echoid-s20597" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20598" xml:space="preserve">ſicuti illa: </s>
            <s xml:id="echoid-s20599" xml:space="preserve">alterum vero
              <lb/>
            latus eiuſdem feneſtellę ſit modicè curuum, vt apparet in pręſenti figura 9. </s>
            <s xml:id="echoid-s20600" xml:space="preserve">Exurgunt ex hac exciſio-
              <lb/>
              <note position="right" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">9 figura.</note>
            ne ſex triangula, quorum apices deſinent ad centrum C, Horarij: </s>
            <s xml:id="echoid-s20601" xml:space="preserve">Diligenter igitur curandum eſt,
              <lb/>
            vt ij apices quam proximè ad centrum accedant, & </s>
            <s xml:id="echoid-s20602" xml:space="preserve">quaſi concurrant, vt punctum C, centrum Hora-
              <lb/>
            rij tutò adiri filo poſſit. </s>
            <s xml:id="echoid-s20603" xml:space="preserve">Hoc modo haberi poterunt omnia, & </s>
            <s xml:id="echoid-s20604" xml:space="preserve">ſingula puncta horaria in Horologij
              <lb/>
            deſcriptione, quod valde vtile, ac ſingulare huic Inſtrumento eſt.</s>
            <s xml:id="echoid-s20605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20606" xml:space="preserve">Alij illud in tribus oblongis laminis ponunt, qualem altera figura 10. </s>
            <s xml:id="echoid-s20607" xml:space="preserve">oſtendit, ſed non ſine quopiã
              <lb/>
              <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">10. figu-
                <lb/>
              ra.</note>
            incommodo quod propè centrum C, aliquanta pars linearum filo adiri nequit. </s>
            <s xml:id="echoid-s20608" xml:space="preserve">Atque hęc ſufficiant
              <lb/>
            pro Horario plano, & </s>
            <s xml:id="echoid-s20609" xml:space="preserve">partieulari.</s>
            <s xml:id="echoid-s20610" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20611" xml:space="preserve">17 Erit vniuerſale ſi circa centrum C, ita tres prędictę materiales lineę connectãtur, vt duę, Ital.
              <lb/>
            </s>
            <s xml:id="echoid-s20612" xml:space="preserve">
              <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">Horariũ
                <lb/>
              vniuer-
                <lb/>
              ſale.</note>
            & </s>
            <s xml:id="echoid-s20613" xml:space="preserve">Babylon. </s>
            <s xml:id="echoid-s20614" xml:space="preserve">efficere poſſint cum Aſtronom. </s>
            <s xml:id="echoid-s20615" xml:space="preserve">angulum ęqualem cuiuis altitudini poli. </s>
            <s xml:id="echoid-s20616" xml:space="preserve">Curandum por-
              <lb/>
            ro vt punctum C, quantum fieri poteſt apertum maneat:</s>
            <s xml:id="echoid-s20617" xml:space="preserve">neq; </s>
            <s xml:id="echoid-s20618" xml:space="preserve">ſunt faciendę diuiſiones iu Italica, & </s>
            <s xml:id="echoid-s20619" xml:space="preserve">
              <lb/>
            Babylonica, ſed tantum in Aſtronomica. </s>
            <s xml:id="echoid-s20620" xml:space="preserve">Pręterea Italica, & </s>
            <s xml:id="echoid-s20621" xml:space="preserve">Babylonica ſint paulo longiores quam
              <lb/>
              <note position="right" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">11. figu-
                <lb/>
              ra.</note>
            ſupra determinauimus; </s>
            <s xml:id="echoid-s20622" xml:space="preserve">maiori enim altitudini maiores, minori minores inſeruient; </s>
            <s xml:id="echoid-s20623" xml:space="preserve">quapropter ne-
              <lb/>
            que certis diuiſionibus queunt notari. </s>
            <s xml:id="echoid-s20624" xml:space="preserve">Vt autem quemuis angulum cum Aſtronomica efficere poſ-
              <lb/>
            ſint, apponatur ſemicirculus ad ima earum diuiſus in duos quadrantes, qui diuiſi ſint in ſuos 90. </s>
            <s xml:id="echoid-s20625" xml:space="preserve">grad.
              <lb/>
            </s>
            <s xml:id="echoid-s20626" xml:space="preserve">facto initio a medio ſemicirculi. </s>
            <s xml:id="echoid-s20627" xml:space="preserve">ſicuti videre eſt in adiecta figura.</s>
            <s xml:id="echoid-s20628" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20629" xml:space="preserve">18 Abſolutum hoc modo Horarium ſeu particulare, ſeu vniuerſale, capiti D C E, regulę, quam
              <lb/>
            initium huius capitis pro baſi Horarij deſcripſimus, aut glutine, aut cochleis per foramina r, s, t, im-
              <lb/>
            miſſis, conſolidetur, ita vt normaliter ſupra eam erigatur, & </s>
            <s xml:id="echoid-s20630" xml:space="preserve">linea B D, Aſtronomica applicetur exa-
              <lb/>
            cte lineę fiducię B A C, faciens non ſolum cum eam rectum angulum, ſed etiam cum plano ipſius re-
              <lb/>
            gulę; </s>
            <s xml:id="echoid-s20631" xml:space="preserve">tantumque totum Horarium ſupra ipſam emineat, vt cum regula, cum Horario ſibi annexo, po-
              <lb/>
            ſita fuerit ſupra tympanum per axem mundi, partes Horarij inferiores a filo procedente ab axe attin
              <lb/>
            gi commodè poſſint: </s>
            <s xml:id="echoid-s20632" xml:space="preserve">ſicq; </s>
            <s xml:id="echoid-s20633" xml:space="preserve">Horarium erit etiam normale plano tympani, & </s>
            <s xml:id="echoid-s20634" xml:space="preserve">linea B D, erit pararella
              <lb/>
            axi, quod oportet. </s>
            <s xml:id="echoid-s20635" xml:space="preserve">Tantus præterea ſit axis ſupra regulam, vt apex eius exacte centro C, Horarij re-
              <lb/>
            ſpondeat, ideſt apex eius M, & </s>
            <s xml:id="echoid-s20636" xml:space="preserve">C, centrum Horarij æque alta ſint ſupra tympanum. </s>
            <s xml:id="echoid-s20637" xml:space="preserve">Tandem regu-
              <lb/>
            la axiculo per foramen m, ad pedem axis factum leniter confirmetur, vt poſſit ſupra ipſum ægre ali-
              <lb/>
            quantulum ad quamlibet partem conuolui, inibiq; </s>
            <s xml:id="echoid-s20638" xml:space="preserve">ſatis firma manere.</s>
            <s xml:id="echoid-s20639" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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