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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        <div xml:id="echoid-div585" type="section" level="1" n="426">
          <pb o="18" file="0272" n="277" rhead="TRACTATVS"/>
          <p>
            <s xml:id="echoid-s21563" xml:space="preserve">4 Poſtea ad horarum deſcriptionem ſic aggrediemur. </s>
            <s xml:id="echoid-s21564" xml:space="preserve">ſit v. </s>
            <s xml:id="echoid-s21565" xml:space="preserve">g. </s>
            <s xml:id="echoid-s21566" xml:space="preserve">deſcribenda hora nona Italica ad
              <lb/>
              <note position="left" xlink:label="note-0272-01" xlink:href="note-0272-01a" xml:space="preserve">Horarũ
                <lb/>
              deſcripsio</note>
            altit. </s>
            <s xml:id="echoid-s21567" xml:space="preserve">poli 44 {1/2}. </s>
            <s xml:id="echoid-s21568" xml:space="preserve">pro qua eriam conſtructa eſt tabula. </s>
            <s xml:id="echoid-s21569" xml:space="preserve">primo in ſecundo verſu tab. </s>
            <s xml:id="echoid-s21570" xml:space="preserve">in quo numeri hora-
              <lb/>
            rum Italicarum continentur, inuen@as 9. </s>
            <s xml:id="echoid-s21571" xml:space="preserve">poſtea deicende per columnam eius infra gr. </s>
            <s xml:id="echoid-s21572" xml:space="preserve">& </s>
            <s xml:id="echoid-s21573" xml:space="preserve">min. </s>
            <s xml:id="echoid-s21574" xml:space="preserve">& </s>
            <s xml:id="echoid-s21575" xml:space="preserve">inue-
              <lb/>
            nies numeros altitudinum Solis horæ nonę in tribus verſibus deſcendentibus, ſunt aute n hi gr. </s>
            <s xml:id="echoid-s21576" xml:space="preserve">3. </s>
            <s xml:id="echoid-s21577" xml:space="preserve">22′.
              <lb/>
            </s>
            <s xml:id="echoid-s21578" xml:space="preserve">
              <note position="left" xlink:label="note-0272-02" xlink:href="note-0272-02a" xml:space="preserve">Horæ 9.</note>
            quæ eſt altitudo in tropico Cancri. </s>
            <s xml:id="echoid-s21579" xml:space="preserve">infra quos ſunt gr. </s>
            <s xml:id="echoid-s21580" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21581" xml:space="preserve">6′. </s>
            <s xml:id="echoid-s21582" xml:space="preserve">ſcilicet altitudo in paralello per gr. </s>
            <s xml:id="echoid-s21583" xml:space="preserve">15.
              <lb/>
            </s>
            <s xml:id="echoid-s21584" xml:space="preserve">Cancri. </s>
            <s xml:id="echoid-s21585" xml:space="preserve">infra quos ſunt gr. </s>
            <s xml:id="echoid-s21586" xml:space="preserve">0. </s>
            <s xml:id="echoid-s21587" xml:space="preserve">0′. </s>
            <s xml:id="echoid-s21588" xml:space="preserve">qui denotant in paralello per gr. </s>
            <s xml:id="echoid-s21589" xml:space="preserve">24. </s>
            <s xml:id="echoid-s21590" xml:space="preserve">25. </s>
            <s xml:id="echoid-s21591" xml:space="preserve">♋. </s>
            <s xml:id="echoid-s21592" xml:space="preserve">Solem nullam habe-
              <lb/>
            re altitudinem ſupra horizontem, ſed eſſe in ipſo horizonte. </s>
            <s xml:id="echoid-s21593" xml:space="preserve">quapropter initium horæ nonæ erit
              <lb/>
            etiam initium tertij paralelli ♋. </s>
            <s xml:id="echoid-s21594" xml:space="preserve">in Horologio, ſeu primum punctum horæ 9. </s>
            <s xml:id="echoid-s21595" xml:space="preserve">erit pariter punctum
              <lb/>
            primum huius paralelli in horizonte. </s>
            <s xml:id="echoid-s21596" xml:space="preserve">hoc puncto ſic animaduerſo, vt inuenias aliud punctum eiuſ-
              <lb/>
            dem horæ, aſcende ad ſecundum numerum 2. </s>
            <s xml:id="echoid-s21597" xml:space="preserve">6′. </s>
            <s xml:id="echoid-s21598" xml:space="preserve">& </s>
            <s xml:id="echoid-s21599" xml:space="preserve">ſecundum eum applica lineam fiduciæ regulæ
              <lb/>
            præcisè ad totidem gr. </s>
            <s xml:id="echoid-s21600" xml:space="preserve">& </s>
            <s xml:id="echoid-s21601" xml:space="preserve">min. </s>
            <s xml:id="echoid-s21602" xml:space="preserve">quadrantis, ideſt ad gr. </s>
            <s xml:id="echoid-s21603" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21604" xml:space="preserve">6′. </s>
            <s xml:id="echoid-s21605" xml:space="preserve">& </s>
            <s xml:id="echoid-s21606" xml:space="preserve">vbi interim linea fiduciæ ſecuerit para-
              <lb/>
            rellum ſecundum ♋. </s>
            <s xml:id="echoid-s21607" xml:space="preserve">quadrantis, qui reſpondet pararello ſecundo tab. </s>
            <s xml:id="echoid-s21608" xml:space="preserve">per gr. </s>
            <s xml:id="echoid-s21609" xml:space="preserve">15. </s>
            <s xml:id="echoid-s21610" xml:space="preserve">o′. </s>
            <s xml:id="echoid-s21611" xml:space="preserve">Cancri, inibi pun-
              <lb/>
            ctum imprime. </s>
            <s xml:id="echoid-s21612" xml:space="preserve">poſtea vt tertium punctum habeas, aſſume numerum 3. </s>
            <s xml:id="echoid-s21613" xml:space="preserve">22′. </s>
            <s xml:id="echoid-s21614" xml:space="preserve">primi paralelli ♋. </s>
            <s xml:id="echoid-s21615" xml:space="preserve">tabulæ; </s>
            <s xml:id="echoid-s21616" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s21617" xml:space="preserve">ſecundum hunc numerum applica regulam totidem gradibus quadrantis, ſcilicet gr. </s>
            <s xml:id="echoid-s21618" xml:space="preserve">3. </s>
            <s xml:id="echoid-s21619" xml:space="preserve">22′. </s>
            <s xml:id="echoid-s21620" xml:space="preserve">& </s>
            <s xml:id="echoid-s21621" xml:space="preserve">vbi ab
              <lb/>
            ea ſecabitur paralellus primus ♋ quadrantis, inibi fac punctum. </s>
            <s xml:id="echoid-s21622" xml:space="preserve">iam ſi per tria hæc puncta in his tribus
              <lb/>
            paralellis notata, ducatur linea congruenter inſlexa, ea erit linea horæ 9. </s>
            <s xml:id="echoid-s21623" xml:space="preserve">ideſt quę horam 9. </s>
            <s xml:id="echoid-s21624" xml:space="preserve">indicabit,
              <lb/>
            cui propterea adſcribendus eſt numerus 9. </s>
            <s xml:id="echoid-s21625" xml:space="preserve">Percommodum autem eſt, incipere (vti nunc fecimus) a
              <lb/>
              <note position="left" xlink:label="note-0272-03" xlink:href="note-0272-03a" xml:space="preserve">Quoordi
                <lb/>
              @@.</note>
            numeris columnæ imis, & </s>
            <s xml:id="echoid-s21626" xml:space="preserve">paulatim ad ſuperiores aſcendere, ac ſecundum eorum ſingulos reperire
              <lb/>
            puncta in paralellis quadrantis. </s>
            <s xml:id="echoid-s21627" xml:space="preserve">hac enim ratione melius numerantur gradus, & </s>
            <s xml:id="echoid-s21628" xml:space="preserve">minuta quadrantis,
              <lb/>
            & </s>
            <s xml:id="echoid-s21629" xml:space="preserve">manifeſtè apparet quinam ex paralellis Horol. </s>
            <s xml:id="echoid-s21630" xml:space="preserve">ſit pungendus; </s>
            <s xml:id="echoid-s21631" xml:space="preserve">& </s>
            <s xml:id="echoid-s21632" xml:space="preserve">puncta iam notata, per regulam
              <lb/>
            nec tegunrur, nec delentur ab ea, ſicuti vſus edocet.</s>
            <s xml:id="echoid-s21633" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21634" xml:space="preserve">Eodem modo agendum eſt pro hora 10. </s>
            <s xml:id="echoid-s21635" xml:space="preserve">ideſt, ex columna ſub hora 10. </s>
            <s xml:id="echoid-s21636" xml:space="preserve">accipiendæ ſunt altitu-
              <lb/>
              <note position="left" xlink:label="note-0272-04" xlink:href="note-0272-04a" xml:space="preserve">De ca@e-
                <lb/>
              ris horis.
                <lb/>
              Hora 10.</note>
            dines, & </s>
            <s xml:id="echoid-s21637" xml:space="preserve">ſecundum eas applicata regula gradibus quadrantis, notandæ ſunt ſectiones eius cum para-
              <lb/>
            lellis horologij reſpondentibus p@raleliis tabulæ per quas ſectiones ducta linea congruenter flexa, ea
              <lb/>
            erit hora 10. </s>
            <s xml:id="echoid-s21638" xml:space="preserve">cui ideo adſcribendum eſt 10. </s>
            <s xml:id="echoid-s21639" xml:space="preserve">vti figura monet. </s>
            <s xml:id="echoid-s21640" xml:space="preserve">codem modo cum reliquis agendum.
              <lb/>
            </s>
            <s xml:id="echoid-s21641" xml:space="preserve">ſolent nonnulli horas matutinas notare lineis continuis, veſpertinas vero lineis punctualibus vt figu-
              <lb/>
            ra oſtendit quod tamen non eſt neceſſe.</s>
            <s xml:id="echoid-s21642" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21643" xml:space="preserve">5 Poterit autem hoc examen adhiberi; </s>
            <s xml:id="echoid-s21644" xml:space="preserve">nam ſi rectè operatus fueris, horæ pomeridianæ, & </s>
            <s xml:id="echoid-s21645" xml:space="preserve">ante-
              <lb/>
              <note position="left" xlink:label="note-0272-05" xlink:href="note-0272-05a" xml:space="preserve">Examen.</note>
            meridianæ ſe mutuo ſecabunt in paralellis horarum inſignarum, ſeu in quibus Sol orirur hora inte-
              <lb/>
            gra: </s>
            <s xml:id="echoid-s21646" xml:space="preserve">ſic vides in figura hora n 23. </s>
            <s xml:id="echoid-s21647" xml:space="preserve">ſecare horam 10. </s>
            <s xml:id="echoid-s21648" xml:space="preserve">in para. </s>
            <s xml:id="echoid-s21649" xml:space="preserve">ello horarum integrarum 15. </s>
            <s xml:id="echoid-s21650" xml:space="preserve">ſeu quo Sol
              <lb/>
            oritur hora 9. </s>
            <s xml:id="echoid-s21651" xml:space="preserve">qui eſt tertius ♋. </s>
            <s xml:id="echoid-s21652" xml:space="preserve">pariter eandem 23. </s>
            <s xml:id="echoid-s21653" xml:space="preserve">ſecare 11. </s>
            <s xml:id="echoid-s21654" xml:space="preserve">in paralello, quo Sol oritur hora 10. </s>
            <s xml:id="echoid-s21655" xml:space="preserve">& </s>
            <s xml:id="echoid-s21656" xml:space="preserve">
              <lb/>
            ſecare 12. </s>
            <s xml:id="echoid-s21657" xml:space="preserve">in paralello quo Sol oritur hora 11. </s>
            <s xml:id="echoid-s21658" xml:space="preserve">& </s>
            <s xml:id="echoid-s21659" xml:space="preserve">ſecare 13. </s>
            <s xml:id="echoid-s21660" xml:space="preserve">in paralello ortus hora 12. </s>
            <s xml:id="echoid-s21661" xml:space="preserve">& </s>
            <s xml:id="echoid-s21662" xml:space="preserve">ſecare 14. </s>
            <s xml:id="echoid-s21663" xml:space="preserve">in
              <lb/>
            paralello ortus horæ 13. </s>
            <s xml:id="echoid-s21664" xml:space="preserve">& </s>
            <s xml:id="echoid-s21665" xml:space="preserve">ſic deinceps, vt videre eſt in figura. </s>
            <s xml:id="echoid-s21666" xml:space="preserve">quæ obſeruatio plurimum iuuat, non
              <lb/>
            ſolum ad horologia recte, ſed etiam facilius deſcribenda: </s>
            <s xml:id="echoid-s21667" xml:space="preserve">eadem cnim puncta iam inuenta in præ-
              <lb/>
            dictis paralellis pro horis matutinis inſeruiunt etiam pro veſpertinis. </s>
            <s xml:id="echoid-s21668" xml:space="preserve">ſic vides pro hora 23. </s>
            <s xml:id="echoid-s21669" xml:space="preserve">inuenta
              <lb/>
            iam fuiſſe prædicta ſeptem puncta. </s>
            <s xml:id="echoid-s21670" xml:space="preserve">ratio huius eſt quia horæ veſpertinæ @n prædictis paralellis habent
              <lb/>
            in tabula altitudines eaſdem cum altitudinibus horarũ matutinarum; </s>
            <s xml:id="echoid-s21671" xml:space="preserve">vt cõſideranti tabulam patebit.</s>
            <s xml:id="echoid-s21672" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21673" xml:space="preserve">6 Linea meridiana nõ videtur neceſſaria, etenim ſi deſcribatur incedit tam propè ima lineamen-
              <lb/>
              <note position="left" xlink:label="note-0272-06" xlink:href="note-0272-06a" xml:space="preserve">Linea
                <lb/>
              meridia-
                <lb/>
              na.</note>
            ta horarum 16. </s>
            <s xml:id="echoid-s21674" xml:space="preserve">17. </s>
            <s xml:id="echoid-s21675" xml:space="preserve">18. </s>
            <s xml:id="echoid-s21676" xml:space="preserve">19. </s>
            <s xml:id="echoid-s21677" xml:space="preserve">20. </s>
            <s xml:id="echoid-s21678" xml:space="preserve">vt ea paſſim contingat, ac proinde confuſionem pariat. </s>
            <s xml:id="echoid-s21679" xml:space="preserve">Quare ipſa prę-
              <lb/>
            dictarum horarum ima lineamenta ſatis poterunt indicare meridiem. </s>
            <s xml:id="echoid-s21680" xml:space="preserve">Veruntamen (ſi libuerit) eam
              <lb/>
            deſcribere per altitudines meridianas in propr a columna exiſtentes, eodem modo applicando regu-
              <lb/>
            lam quadranti ſecundum ſingulas altitudines, no@ãdo ſectiones eius cum paralellis horologij reſpon-
              <lb/>
            dentibus paralellis tabulæ. </s>
            <s xml:id="echoid-s21681" xml:space="preserve">ſed ea poſtea pingenda è vel colore, vel lineamento ab alijs diuerſo ad
              <lb/>
            confuſionem tollendam.</s>
            <s xml:id="echoid-s21682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21683" xml:space="preserve">7 Alij aliter hanc horarum deſcriptionem ſic inſtituunt; </s>
            <s xml:id="echoid-s21684" xml:space="preserve">nam vt in linea horizontali ſigant pun-
              <lb/>
              <note position="left" xlink:label="note-0272-07" xlink:href="note-0272-07a" xml:space="preserve">Al@ter.</note>
            cta extremorum paralellorum, ſeu tropicorum, primo accipiunt ex tabula maximam omnium altitu-
              <lb/>
            dinem, quæ ſunt in tropico cancri in verſu tabulæ in quo eſt tropicus cancri, quæ eſt gr. </s>
            <s xml:id="echoid-s21685" xml:space="preserve">68. </s>
            <s xml:id="echoid-s21686" xml:space="preserve">39′. </s>
            <s xml:id="echoid-s21687" xml:space="preserve">ſub
              <lb/>
            hora, ibidem a@q; </s>
            <s xml:id="echoid-s21688" xml:space="preserve">in quadrante applicata regula repertis grad. </s>
            <s xml:id="echoid-s21689" xml:space="preserve">68. </s>
            <s xml:id="echoid-s21690" xml:space="preserve">39. </s>
            <s xml:id="echoid-s21691" xml:space="preserve">& </s>
            <s xml:id="echoid-s21692" xml:space="preserve">ex puncto F. </s>
            <s xml:id="echoid-s21693" xml:space="preserve">vbi regula ſe-
              <lb/>
            cuerit quadrantem interiorem ducunt lineam rectam F D. </s>
            <s xml:id="echoid-s21694" xml:space="preserve">normalem horizontali A C. </s>
            <s xml:id="echoid-s21695" xml:space="preserve">eamque ſta-
              <lb/>
            @uunt eſſe para@ellũ primum ſeu trop. </s>
            <s xml:id="echoid-s21696" xml:space="preserve">♋. </s>
            <s xml:id="echoid-s21697" xml:space="preserve">pariter accepta maxima altitudine tropici Capricorni, quę
              <lb/>
            eſt gr. </s>
            <s xml:id="echoid-s21698" xml:space="preserve">21. </s>
            <s xml:id="echoid-s21699" xml:space="preserve">55′. </s>
            <s xml:id="echoid-s21700" xml:space="preserve">ſub hora 20. </s>
            <s xml:id="echoid-s21701" xml:space="preserve">ideo ex puncto G. </s>
            <s xml:id="echoid-s21702" xml:space="preserve">quadrantis interioris terminante gr. </s>
            <s xml:id="echoid-s21703" xml:space="preserve">21. </s>
            <s xml:id="echoid-s21704" xml:space="preserve">55′. </s>
            <s xml:id="echoid-s21705" xml:space="preserve">eriguntalte-
              <lb/>
            ram lineam G E. </s>
            <s xml:id="echoid-s21706" xml:space="preserve">normalter ad horizontalẽ A C. </s>
            <s xml:id="echoid-s21707" xml:space="preserve">eamq; </s>
            <s xml:id="echoid-s21708" xml:space="preserve">aſiumunt pro paralello ſeu tropico ♑. </s>
            <s xml:id="echoid-s21709" xml:space="preserve">hacq;
              <lb/>
            </s>
            <s xml:id="echoid-s21710" xml:space="preserve">ratione partem D E. </s>
            <s xml:id="echoid-s21711" xml:space="preserve">lineæ horizontalis aſſumũt pro loco omnium paralellorum: </s>
            <s xml:id="echoid-s21712" xml:space="preserve">in qua eorum loca
              <lb/>
            non ad æqualia interualla, ſed habita ratione declinationum paralellorum, ſic reperiunt.</s>
            <s xml:id="echoid-s21713" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21714" xml:space="preserve">8 Conſtruunt huius rei gratia Radiarium, quod contineat declinationes omnium 19. </s>
            <s xml:id="echoid-s21715" xml:space="preserve">paralello-
              <lb/>
              <note position="left" xlink:label="note-0272-08" xlink:href="note-0272-08a" xml:space="preserve">17. figu-
                <lb/>
              ra.</note>
            rum tabulæ, quale eſt preſens. </s>
            <s xml:id="echoid-s21716" xml:space="preserve">accipi autem poſſunt hæ declinationes ex Tabula declinat. </s>
            <s xml:id="echoid-s21717" xml:space="preserve">quæ eſt in
              <lb/>
            Sphæra Clauij, eſt enim valde copioſa. </s>
            <s xml:id="echoid-s21718" xml:space="preserve">in hoc Radiario accomodant l@neam D E. </s>
            <s xml:id="echoid-s21719" xml:space="preserve">quæ ſit æqualis alte-
              <lb/>
              <note position="left" xlink:label="note-0272-09" xlink:href="note-0272-09a" xml:space="preserve">Radiarij.</note>
            ri lineæ D E. </s>
            <s xml:id="echoid-s21720" xml:space="preserve">horizontali quadrantis, ſitq; </s>
            <s xml:id="echoid-s21721" xml:space="preserve">normalis cum paralello omnium medio, qui eſt ♎, & </s>
            <s xml:id="echoid-s21722" xml:space="preserve">♈.
              <lb/>
            </s>
            <s xml:id="echoid-s21723" xml:space="preserve">iam ijſdem punctis, & </s>
            <s xml:id="echoid-s21724" xml:space="preserve">interuallis quibus ſecatur a paralellis Radiarij, ijſdem omnino diuidunt D E. </s>
            <s xml:id="echoid-s21725" xml:space="preserve">
              <lb/>
            quadrantis. </s>
            <s xml:id="echoid-s21726" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s21727" xml:space="preserve">ex punctis diuiſionum ducunt reliquos omnes paralellos quadrantis, vt in figura 17. </s>
            <s xml:id="echoid-s21728" xml:space="preserve">
              <lb/>
            apparent. </s>
            <s xml:id="echoid-s21729" xml:space="preserve">quibus peractis horarum deſcriptionem peragunt per altitudines tabulæ, & </s>
            <s xml:id="echoid-s21730" xml:space="preserve">per gr. </s>
            <s xml:id="echoid-s21731" xml:space="preserve">qua-
              <lb/>
            drantis, notando puncta horaria in hiſce paralellis ſicuti in ſuperioribus. </s>
            <s xml:id="echoid-s21732" xml:space="preserve">quę puncta lineis vniformi-
              <lb/>
            ter inflexis coniuncta efficiunt lineas horarias, & </s>
            <s xml:id="echoid-s21733" xml:space="preserve">quidem pulchriores, quod non tam diformiter </s>
          </p>
        </div>
      </text>
    </echo>
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