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">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div542" type="section" level="1" n="410">
          <p>
            <s xml:id="echoid-s20165" xml:space="preserve">
              <pb o="6" file="0260" n="265" rhead="TRACTATVS"/>
            factum in appoſita figura. </s>
            <s xml:id="echoid-s20166" xml:space="preserve">Si quis tamen voluerit reliquas quoque arcuum declinationes, vt per eas
              <lb/>
            arcus diurnos reliquos in ſuis Horol. </s>
            <s xml:id="echoid-s20167" xml:space="preserve">deſcribere poſſit, eas pro arbitrio ex eadem Tabella accipiat,
              <lb/>
            atq; </s>
            <s xml:id="echoid-s20168" xml:space="preserve">in radiario ſimiliter notet. </s>
            <s xml:id="echoid-s20169" xml:space="preserve">Poſtea per ſingula declinationum puncta notata ducantur ex centro
              <lb/>
            E, lineæ rectæ aliquantulum extra peripheriam egredientes, & </s>
            <s xml:id="echoid-s20170" xml:space="preserve">per punctum A, ducantur linea H I,
              <lb/>
            recta tangens arcũ in A, ſeu normalis ipſi B A, ſecans productas lineas in punctis H K L M N O P I,
              <lb/>
            vt vides in figura. </s>
            <s xml:id="echoid-s20171" xml:space="preserve">erunt A N, A O, A P, A I, & </s>
            <s xml:id="echoid-s20172" xml:space="preserve">totidem ex altera parte tangens arcuum ſibi reſpon-
              <lb/>
            dentium. </s>
            <s xml:id="echoid-s20173" xml:space="preserve">Porro hæ lineæ è centro egredientes referunt radios Solis tranſeuntes per tales declina-
              <lb/>
              <note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">Ratio
                <unsure/>
                <lb/>
              huius
                <lb/>
              Radiarij.</note>
            tiones exiſtente Sole in ijſdem declinationibus: </s>
            <s xml:id="echoid-s20174" xml:space="preserve">arcus vero ipſe refert portionem coluri ſolſtitiorũ,
              <lb/>
            vel meridiani inter tropicos interceptam. </s>
            <s xml:id="echoid-s20175" xml:space="preserve">Radius E A, eſt radius Solis exiſtentis in principio ♎, vel
              <lb/>
            ♈, radij E H, E I, ſunt radij Solis exiſtentis in ♋, & </s>
            <s xml:id="echoid-s20176" xml:space="preserve">♌, &</s>
            <s xml:id="echoid-s20177" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20178" xml:space="preserve">vt apparet ex characteribus ſignorum
              <lb/>
            adſcriptis. </s>
            <s xml:id="echoid-s20179" xml:space="preserve">Sit tandem recta E Q, æqualis rectæ A I, hoc eſt parti axis m M, extantis ſupra regulam
              <lb/>
            tympano ſuperpoſitam. </s>
            <s xml:id="echoid-s20180" xml:space="preserve">Aduertendum Radiarium huiuſmodi eſſe vniuerſale ſecundum declina-
              <lb/>
            tiones ſignorum, non autem ſecundum declinationes arcuum diurnorum, vt ſupra tetigi. </s>
            <s xml:id="echoid-s20181" xml:space="preserve">Hoc Ra-
              <lb/>
            diarium fieri poteſt Geometricè per analemma. </s>
            <s xml:id="echoid-s20182" xml:space="preserve">vide Gnom. </s>
            <s xml:id="echoid-s20183" xml:space="preserve">Clau. </s>
            <s xml:id="echoid-s20184" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20185" xml:space="preserve">1.</s>
            <s xml:id="echoid-s20186" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20187" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20188" xml:space="preserve">Breuius. </s>
            <s xml:id="echoid-s20189" xml:space="preserve">ſi quis in ſuis Horologijs contentus ſit ſola deſcriptione horarum abſque arcubus
              <lb/>
            ſignorum, necnon arcubus diurnis, ſatis ei fuerit in ſuo Radiario ponere tantum maximas declina-
              <lb/>
            tiones tropicorum, & </s>
            <s xml:id="echoid-s20190" xml:space="preserve">tres tantũ lineas è centro E, egredientes E G H, E A, E F I, quare nec ei opus
              <lb/>
            eſt totis Tabellis præmiſſis, ſed ſatis erit habere declinationes extremas ♋, & </s>
            <s xml:id="echoid-s20191" xml:space="preserve">♌, vna cum tempori-
              <lb/>
            bus ſemidiurnis, meridiebus, interuallis, & </s>
            <s xml:id="echoid-s20192" xml:space="preserve">arcubus illis correſpondentibus in cęteris columnis.</s>
            <s xml:id="echoid-s20193" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20194" xml:space="preserve">4. </s>
            <s xml:id="echoid-s20195" xml:space="preserve">Habeantur tempora ſemidiurna competentia paralellis, & </s>
            <s xml:id="echoid-s20196" xml:space="preserve">arcubus in prima columna,
              <lb/>
            quorum radij inſcripti ſunt in Radiario. </s>
            <s xml:id="echoid-s20197" xml:space="preserve">quę tempora haberi poſſunt ex Tabula temporis ſemidiur-
              <lb/>
            ni ad datam latitudinem, quæ paſſim reperitur apud Authores; </s>
            <s xml:id="echoid-s20198" xml:space="preserve">optima vero in Sphæra P. </s>
            <s xml:id="echoid-s20199" xml:space="preserve">Clauij:
              <lb/>
            </s>
            <s xml:id="echoid-s20200" xml:space="preserve">ſunt autem in ſecunda columna congruentia latitudini, ſeu altitudini 44 {1/2}. </s>
            <s xml:id="echoid-s20201" xml:space="preserve">vt indicat titulus eius co-
              <lb/>
            lumnæ.</s>
            <s xml:id="echoid-s20202" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20203" xml:space="preserve">5. </s>
            <s xml:id="echoid-s20204" xml:space="preserve">Ex tempore ſemidiurno cuiuſuis paralelli poſito in ſecunda columna inquirendum eſt, quo-
              <lb/>
            ta hora Italica ſit meridies Sole eundem paralellum percurrente, hac ratione. </s>
            <s xml:id="echoid-s20205" xml:space="preserve">Detrahatur tem-
              <lb/>
            pus ſemid. </s>
            <s xml:id="echoid-s20206" xml:space="preserve">aſſumpti paralellis ab horis 24. </s>
            <s xml:id="echoid-s20207" xml:space="preserve">reliquæ enim horæ indicabunt meridiem ſecundum horas
              <lb/>
            I@alicas, v. </s>
            <s xml:id="echoid-s20208" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20209" xml:space="preserve">quia detracto tempore ſemid. </s>
            <s xml:id="echoid-s20210" xml:space="preserve">paralelli ♋, quod eſt hor. </s>
            <s xml:id="echoid-s20211" xml:space="preserve">7. </s>
            <s xml:id="echoid-s20212" xml:space="preserve">41. </s>
            <s xml:id="echoid-s20213" xml:space="preserve">ex 24. </s>
            <s xml:id="echoid-s20214" xml:space="preserve">remanent hor. </s>
            <s xml:id="echoid-s20215" xml:space="preserve">16.
              <lb/>
            </s>
            <s xml:id="echoid-s20216" xml:space="preserve">19. </s>
            <s xml:id="echoid-s20217" xml:space="preserve">ideo hora meridiana erit hora 16. </s>
            <s xml:id="echoid-s20218" xml:space="preserve">19. </s>
            <s xml:id="echoid-s20219" xml:space="preserve">& </s>
            <s xml:id="echoid-s20220" xml:space="preserve">ſic de cęteris. </s>
            <s xml:id="echoid-s20221" xml:space="preserve">Hac ratione inuentæ ſunt horæ merid. </s>
            <s xml:id="echoid-s20222" xml:space="preserve">ter-
              <lb/>
            tiæ columnæ competentis paralellis primæ columnæ.</s>
            <s xml:id="echoid-s20223" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20224" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20225" xml:space="preserve">Inueſtigare oportet interuallum temporis inter horam 18. </s>
            <s xml:id="echoid-s20226" xml:space="preserve">Italicam, & </s>
            <s xml:id="echoid-s20227" xml:space="preserve">12. </s>
            <s xml:id="echoid-s20228" xml:space="preserve">aſtronomicam,
              <lb/>
            ſeu meridianam in quouis paralello, ſic. </s>
            <s xml:id="echoid-s20229" xml:space="preserve">Accipe differentiam inter tempus ſemidiurnum aſſumpti
              <lb/>
            paralello, & </s>
            <s xml:id="echoid-s20230" xml:space="preserve">horas 6. </s>
            <s xml:id="echoid-s20231" xml:space="preserve">ea enim eſt interuallum temporis inter horam 18. </s>
            <s xml:id="echoid-s20232" xml:space="preserve">Italicam, & </s>
            <s xml:id="echoid-s20233" xml:space="preserve">meridiem, v.</s>
            <s xml:id="echoid-s20234" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20235" xml:space="preserve">in
              <lb/>
            paralello ♋, tempus ſemidiurnum eſt hor. </s>
            <s xml:id="echoid-s20236" xml:space="preserve">7. </s>
            <s xml:id="echoid-s20237" xml:space="preserve">42. </s>
            <s xml:id="echoid-s20238" xml:space="preserve">quod ſuperat hor. </s>
            <s xml:id="echoid-s20239" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20240" xml:space="preserve">hor. </s>
            <s xml:id="echoid-s20241" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20242" xml:space="preserve">41. </s>
            <s xml:id="echoid-s20243" xml:space="preserve">ergo hora 1. </s>
            <s xml:id="echoid-s20244" xml:space="preserve">41. </s>
            <s xml:id="echoid-s20245" xml:space="preserve">eſt di-
              <lb/>
            ſtantia hor. </s>
            <s xml:id="echoid-s20246" xml:space="preserve">18. </s>
            <s xml:id="echoid-s20247" xml:space="preserve">Italicæ à meridie, ſeu ab hora 12. </s>
            <s xml:id="echoid-s20248" xml:space="preserve">a ſtronomica. </s>
            <s xml:id="echoid-s20249" xml:space="preserve">In paralello ♎, cum tempus ſemidlur-
              <lb/>
            num ſit hor. </s>
            <s xml:id="echoid-s20250" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20251" xml:space="preserve">nulla erit differentia, quare neq; </s>
            <s xml:id="echoid-s20252" xml:space="preserve">vllum interuallum. </s>
            <s xml:id="echoid-s20253" xml:space="preserve">In paralello ♌, tempus ſemidiur-
              <lb/>
            num eſt hor. </s>
            <s xml:id="echoid-s20254" xml:space="preserve">4. </s>
            <s xml:id="echoid-s20255" xml:space="preserve">19. </s>
            <s xml:id="echoid-s20256" xml:space="preserve">eius diſſerentia ad hor. </s>
            <s xml:id="echoid-s20257" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20258" xml:space="preserve">eſt hor. </s>
            <s xml:id="echoid-s20259" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20260" xml:space="preserve">41. </s>
            <s xml:id="echoid-s20261" xml:space="preserve">quare tantumdem erit interuallum inter
              <lb/>
            horam Italicam, & </s>
            <s xml:id="echoid-s20262" xml:space="preserve">merid.</s>
            <s xml:id="echoid-s20263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20264" xml:space="preserve">Notandum eadem eſſe interualla in oppoſitis paralellis; </s>
            <s xml:id="echoid-s20265" xml:space="preserve">ſic in vtroq; </s>
            <s xml:id="echoid-s20266" xml:space="preserve">tropico eſt hor. </s>
            <s xml:id="echoid-s20267" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20268" xml:space="preserve">41. </s>
            <s xml:id="echoid-s20269" xml:space="preserve">vt vidi-
              <lb/>
            ſti. </s>
            <s xml:id="echoid-s20270" xml:space="preserve">In borealibus tamen ſignis eſt exceſſus ſupra 6. </s>
            <s xml:id="echoid-s20271" xml:space="preserve">in auſtralibus autem eſt defectus à 6. </s>
            <s xml:id="echoid-s20272" xml:space="preserve">Hæc inter-
              <lb/>
            ualla ſunt in quarta columna reſpondentia paralellis primæ columnæ. </s>
            <s xml:id="echoid-s20273" xml:space="preserve">Idem aſſequeris ſumendo de-
              <lb/>
            fectum horæ cuiuſuis meridiei tertiæ columnæ vſq; </s>
            <s xml:id="echoid-s20274" xml:space="preserve">ad hor. </s>
            <s xml:id="echoid-s20275" xml:space="preserve">18. </s>
            <s xml:id="echoid-s20276" xml:space="preserve">in borealibus, exceſſum autem ſupra
              <lb/>
            18. </s>
            <s xml:id="echoid-s20277" xml:space="preserve">in auſtralibus.</s>
            <s xml:id="echoid-s20278" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20279" xml:space="preserve">7. </s>
            <s xml:id="echoid-s20280" xml:space="preserve">Hæc interualla conuertenda ſunt in arcus, ſeu in grad. </s>
            <s xml:id="echoid-s20281" xml:space="preserve">paralellorum aſſumptorum, qui in-
              <lb/>
            tercipiuntur inter hor. </s>
            <s xml:id="echoid-s20282" xml:space="preserve">18. </s>
            <s xml:id="echoid-s20283" xml:space="preserve">Italicam, & </s>
            <s xml:id="echoid-s20284" xml:space="preserve">12. </s>
            <s xml:id="echoid-s20285" xml:space="preserve">aſtronomicam, v.</s>
            <s xml:id="echoid-s20286" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20287" xml:space="preserve">in ♋, interuallum eſt hor. </s>
            <s xml:id="echoid-s20288" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20289" xml:space="preserve">41. </s>
            <s xml:id="echoid-s20290" xml:space="preserve">qui
              <lb/>
            nihil aliud eſt, quam arcus tropici ♋, intercepti inter horam 18. </s>
            <s xml:id="echoid-s20291" xml:space="preserve">Italicam, & </s>
            <s xml:id="echoid-s20292" xml:space="preserve">12. </s>
            <s xml:id="echoid-s20293" xml:space="preserve">aſtronomicam, qui
              <lb/>
            arcus continet gr. </s>
            <s xml:id="echoid-s20294" xml:space="preserve">25. </s>
            <s xml:id="echoid-s20295" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20296" xml:space="preserve">vna enim hora continet gr. </s>
            <s xml:id="echoid-s20297" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20298" xml:space="preserve">41. </s>
            <s xml:id="echoid-s20299" xml:space="preserve">autem minuta efficiunt gr. </s>
            <s xml:id="echoid-s20300" xml:space="preserve">10. </s>
            <s xml:id="echoid-s20301" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20302" xml:space="preserve">quare
              <lb/>
            omnes ſimul ſunt gr. </s>
            <s xml:id="echoid-s20303" xml:space="preserve">25. </s>
            <s xml:id="echoid-s20304" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20305" xml:space="preserve">Omnes porro arcus facti ex grad. </s>
            <s xml:id="echoid-s20306" xml:space="preserve">& </s>
            <s xml:id="echoid-s20307" xml:space="preserve">minutis, ex interuallis, ſunt in quin-
              <lb/>
            ta columna è directo ſuorum interuallorum, &</s>
            <s xml:id="echoid-s20308" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20309" xml:space="preserve">Extat Tabula apud Authores conuertendi horas, & </s>
            <s xml:id="echoid-s20310" xml:space="preserve">
              <lb/>
            min. </s>
            <s xml:id="echoid-s20311" xml:space="preserve">in grad. </s>
            <s xml:id="echoid-s20312" xml:space="preserve">& </s>
            <s xml:id="echoid-s20313" xml:space="preserve">minuta, quæ hic vſui erit.</s>
            <s xml:id="echoid-s20314" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20315" xml:space="preserve">8. </s>
            <s xml:id="echoid-s20316" xml:space="preserve">Quæ vt melius intelligantur ponam ob oculos Lectoris Horarij deſcribendi figuram præ-
              <lb/>
              <note position="left" xlink:label="note-0260-02" xlink:href="note-0260-02a" xml:space="preserve">Septima
                <lb/>
              figura
                <lb/>
              Horarij.</note>
            ſentem ſeptimam, in qua tres lineæ E C F, D C B, G C H, ſunt horariæ, 18. </s>
            <s xml:id="echoid-s20317" xml:space="preserve">Italica, 12. </s>
            <s xml:id="echoid-s20318" xml:space="preserve">Aſtronomi-
              <lb/>
            ca, & </s>
            <s xml:id="echoid-s20319" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20320" xml:space="preserve">Babylonica. </s>
            <s xml:id="echoid-s20321" xml:space="preserve">linea curua E D G. </s>
            <s xml:id="echoid-s20322" xml:space="preserve">eſt hyperbole referens paralellum ♌. </s>
            <s xml:id="echoid-s20323" xml:space="preserve">tranſeuntem per tria
              <lb/>
            puncta E D G. </s>
            <s xml:id="echoid-s20324" xml:space="preserve">Altera curua R T S. </s>
            <s xml:id="echoid-s20325" xml:space="preserve">refert paralellum ♂
              <unsure/>
            , vti characteres ſignorum appoſiti indicant.
              <lb/>
            </s>
            <s xml:id="echoid-s20326" xml:space="preserve">Tertia refert arcum diurnum hor. </s>
            <s xml:id="echoid-s20327" xml:space="preserve">10. </s>
            <s xml:id="echoid-s20328" xml:space="preserve">& </s>
            <s xml:id="echoid-s20329" xml:space="preserve">ſic de reliquis. </s>
            <s xml:id="echoid-s20330" xml:space="preserve">Interualla porro prędicta inter hor. </s>
            <s xml:id="echoid-s20331" xml:space="preserve">Italicam,
              <lb/>
            & </s>
            <s xml:id="echoid-s20332" xml:space="preserve">meridianam nihil aliud ſunt quam arcus prædictorum paralellorum inter lineam Italicam E F. </s>
            <s xml:id="echoid-s20333" xml:space="preserve">& </s>
            <s xml:id="echoid-s20334" xml:space="preserve">
              <lb/>
            meridianam D B, v.</s>
            <s xml:id="echoid-s20335" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20336" xml:space="preserve">arcus E D, eſt interuallum inter eas in paralello ♌, arcus R T. </s>
            <s xml:id="echoid-s20337" xml:space="preserve">eſt interuallum
              <lb/>
            inter eaſdem in paralello ♂, & </s>
            <s xml:id="echoid-s20338" xml:space="preserve">ſic de cęteris. </s>
            <s xml:id="echoid-s20339" xml:space="preserve">quare B F, eſt interuallum earundem in ♋, &</s>
            <s xml:id="echoid-s20340" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20341" xml:space="preserve">Eadem
              <lb/>
            prędictis ſunt interualla inter Babylon. </s>
            <s xml:id="echoid-s20342" xml:space="preserve">& </s>
            <s xml:id="echoid-s20343" xml:space="preserve">merid. </s>
            <s xml:id="echoid-s20344" xml:space="preserve">vt ex figura patet.</s>
            <s xml:id="echoid-s20345" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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