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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        <div xml:id="echoid-div608" type="section" level="1" n="429">
          <p>
            <s xml:id="echoid-s21955" xml:space="preserve">
              <pb o="21" file="0275" n="280" rhead="DE HOROLOGIIS."/>
            quampiam, in qua videamus Solem per reflexionem, collimandum eſt deorſum in ipſum, ſuperiori
              <lb/>
              <note position="right" xlink:label="note-0275-01" xlink:href="note-0275-01a" xml:space="preserve">In vm-
                <lb/>
              bra per
                <lb/>
              reflexio-
                <lb/>
              nem.</note>
            tamen pinnula A. </s>
            <s xml:id="echoid-s21956" xml:space="preserve">oculo applicata, interim perpendiculo liberè pendente, & </s>
            <s xml:id="echoid-s21957" xml:space="preserve">faciem Horol. </s>
            <s xml:id="echoid-s21958" xml:space="preserve">radente,
              <lb/>
            nam paralellus currens ab eo ſecabitur, ac ſi in Solem ipſum ſupra horizontem præcedenti modo col-
              <lb/>
            limauerimus ratio eſt, quia radius ex aqua reflexus facit angulum cum ſuperficie aquæ æqualem an-
              <lb/>
            gulo radij incidentis, ideſt eodem modo eleuatur ſupra horizontem ac directus, vt optici demon-
              <lb/>
            ſtrant. </s>
            <s xml:id="echoid-s21959" xml:space="preserve">radius autẽ viſiuus in hac operatione coincidit cum radio Solis reflexo, ac proinde latus A B.
              <lb/>
            </s>
            <s xml:id="echoid-s21960" xml:space="preserve">quod congruit radio viſiuo, congruet pariter radio Solis reflexo, ac proinde eleuatum erit quantum
              <lb/>
            Sol ipſe.</s>
            <s xml:id="echoid-s21961" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21962" xml:space="preserve">3 Exiſtentibus nobis vnà cum quadrante pariter in vmbra (alterum paradoxum) veluti intra cu-
              <lb/>
              <note position="right" xlink:label="note-0275-02" xlink:href="note-0275-02a" xml:space="preserve">In vm-
                <lb/>
              bra per
                <lb/>
              arborem.</note>
            biculum, vel ſub porticu, abſq; </s>
            <s xml:id="echoid-s21963" xml:space="preserve">eo quod in Solem prodeamus, per vmbram cuiuſuis corporis, vti arbo-
              <lb/>
            ris alicuius, etiam ſatis diſtantis, ſic horam labentem venabimur. </s>
            <s xml:id="echoid-s21964" xml:space="preserve">ſed primo cõſiderandum eſt radium
              <lb/>
            Solis tranſire per verticem arboris aſſumptæ, & </s>
            <s xml:id="echoid-s21965" xml:space="preserve">ſimul definere ad verticem vmbræ illius. </s>
            <s xml:id="echoid-s21966" xml:space="preserve">huic igitur
              <lb/>
            radio debet latus pinnarum A B. </s>
            <s xml:id="echoid-s21967" xml:space="preserve">eſſe paralellum, vt ſit in eadem cum eo eleuatione ſupra horizon-
              <lb/>
            tem. </s>
            <s xml:id="echoid-s21968" xml:space="preserve">quod fiet ſi primo radius noſter viſiuus ſit ferè normalis plano illius verticalis, in quo eſt illic
              <lb/>
            radius Solis; </s>
            <s xml:id="echoid-s21969" xml:space="preserve">& </s>
            <s xml:id="echoid-s21970" xml:space="preserve">planum quadrantis ſtatuatur ad ſenſum plano prædicto paralellum. </s>
            <s xml:id="echoid-s21971" xml:space="preserve">debet autem pin-
              <lb/>
            na A. </s>
            <s xml:id="echoid-s21972" xml:space="preserve">eſſe ad partes arboris, pinna verò B. </s>
            <s xml:id="echoid-s21973" xml:space="preserve">ad partes vmbrę. </s>
            <s xml:id="echoid-s21974" xml:space="preserve">poſtea latus A B. </s>
            <s xml:id="echoid-s21975" xml:space="preserve">ante oculos noſtros tranſ-
              <lb/>
            miſſum, ita ex parte A. </s>
            <s xml:id="echoid-s21976" xml:space="preserve">eleuetur, vt alter oculorũ ſolus (altero clauſo) collimans ſecundum ipſum latus
              <lb/>
            A B. </s>
            <s xml:id="echoid-s21977" xml:space="preserve">modo ad verticem arboris, modò ad verticem vmbræ, videatur ſibi videre ipſum latus; </s>
            <s xml:id="echoid-s21978" xml:space="preserve">quodam
              <lb/>
            modo tranſire per vtrumque verticem, fic enim ad ſenſum e@it radio illi paralellum, & </s>
            <s xml:id="echoid-s21979" xml:space="preserve">cum eo æquè
              <lb/>
            altum. </s>
            <s xml:id="echoid-s21980" xml:space="preserve">Idem exactius aſſequemur ſi dum aſpicimus, manente A. </s>
            <s xml:id="echoid-s21981" xml:space="preserve">centro quadrantis, B. </s>
            <s xml:id="echoid-s21982" xml:space="preserve">verò acceden-
              <lb/>
            te, & </s>
            <s xml:id="echoid-s21983" xml:space="preserve">recedente à plano verticalis prædicti, interim perpendiculum liberè pendens, radenſq; </s>
            <s xml:id="echoid-s21984" xml:space="preserve">quadran
              <lb/>
            tem, ſecuerit plurimos gradus eius, ideſt latus A B. </s>
            <s xml:id="echoid-s21985" xml:space="preserve">maximam habuerit altitudinem ſub tali collima-
              <lb/>
            tione. </s>
            <s xml:id="echoid-s21986" xml:space="preserve">in tali igitur ſituatione quadrans erit eleuatns perinde, ac ſi radius ille tranſiret per pinnarum
              <lb/>
            apices: </s>
            <s xml:id="echoid-s21987" xml:space="preserve">& </s>
            <s xml:id="echoid-s21988" xml:space="preserve">conſequenter perpendiculum ſecabit currentem paralellum, ac ſi eſſemus in Sole; </s>
            <s xml:id="echoid-s21989" xml:space="preserve">& </s>
            <s xml:id="echoid-s21990" xml:space="preserve">pro-
              <lb/>
            inde ea omnia præſtabit, & </s>
            <s xml:id="echoid-s21991" xml:space="preserve">manifeſtabit, quæ ſuperius in Sole cognouimus. </s>
            <s xml:id="echoid-s21992" xml:space="preserve">Idem quoque ſimili via
              <lb/>
            aſſequemur ex vmbris verſis, ideſt ex vmbris corporum ex parietibus extantium; </s>
            <s xml:id="echoid-s21993" xml:space="preserve">quod induſtriæ cu-
              <lb/>
            iuſuis relinquimus.</s>
            <s xml:id="echoid-s21994" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21995" xml:space="preserve">4 Nocturnas quoque horas indagabis, ſi Planetam, aut Stellam Soli oppoſitam, vice Solis aſſum-
              <lb/>
              <note position="right" xlink:label="note-0275-03" xlink:href="note-0275-03a" xml:space="preserve">Horas no
                <lb/>
              cturnas
                <lb/>
              cognoſce-
                <lb/>
              re.</note>
            pſeris, aſſumpto pariter paralello oppoſito paralello currenti; </s>
            <s xml:id="echoid-s21996" xml:space="preserve">horiſq; </s>
            <s xml:id="echoid-s21997" xml:space="preserve">Italicis commutatis in Baby-
              <lb/>
            lonicas: </s>
            <s xml:id="echoid-s21998" xml:space="preserve">ea enim Stella, occidente Sole, oritur, deſcribitq; </s>
            <s xml:id="echoid-s21999" xml:space="preserve">motu diuruo paralellum Soli oppoſitum,
              <lb/>
            qua propter ſortietur de nocte eaſdem altitudines ſupra horizontem, quas Sol noctu infra horizon-
              <lb/>
            @em in oppoſito paralello, in oppoſitis enim paralellis arcus diurnus vnius eſt æqualis arcui nocturno
              <lb/>
            alterius. </s>
            <s xml:id="echoid-s22000" xml:space="preserve">indicabit igitur horas ab ortu ſuo, quæ eædem erunt cum horis ab occaſu Solis: </s>
            <s xml:id="echoid-s22001" xml:space="preserve">& </s>
            <s xml:id="echoid-s22002" xml:space="preserve">propterea
              <lb/>
            horæ Italicæ commutandæ ſunt in Babylonicas vti ſupra docui, ideſt 23. </s>
            <s xml:id="echoid-s22003" xml:space="preserve">erit 1. </s>
            <s xml:id="echoid-s22004" xml:space="preserve">22. </s>
            <s xml:id="echoid-s22005" xml:space="preserve">erit 2. </s>
            <s xml:id="echoid-s22006" xml:space="preserve">21. </s>
            <s xml:id="echoid-s22007" xml:space="preserve">erit 3. </s>
            <s xml:id="echoid-s22008" xml:space="preserve">&</s>
            <s xml:id="echoid-s22009" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s22010" xml:space="preserve">quæ tamen eædem erunt cum horis ab occaſu Solis. </s>
            <s xml:id="echoid-s22011" xml:space="preserve">cognita igitur hora quapiam ab ortu Stellæ, ea
              <lb/>
            erit eadem cum hora ab o ccaſu Solis.</s>
            <s xml:id="echoid-s22012" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div613" type="section" level="1" n="430">
          <head xml:id="echoid-head455" style="it" xml:space="preserve">De conſtruendis Tabulis pro alijs latitudini bus. Cap. III.</head>
          <p>
            <s xml:id="echoid-s22013" xml:space="preserve">1 VT huius Horologij tractatio vniuerſalior euadat, ac partim defectum Tabularum quę pro plu-
              <lb/>
            ribus locis, ſeu latitudinibus neceſſariæ eſſent, compenſemus, placet nunc mirifica aliquot
              <lb/>
            compendia tradere, quibus maximopere minuitur labor, & </s>
            <s xml:id="echoid-s22014" xml:space="preserve">tædium conſtruendæ tabulæ altit. </s>
            <s xml:id="echoid-s22015" xml:space="preserve">Solis
              <lb/>
            pro quauis latitudine. </s>
            <s xml:id="echoid-s22016" xml:space="preserve">hac enim difficultate ſuperata, poterit quilibet in quauis regione, conſtructa
              <lb/>
            prius tabula, Horol. </s>
            <s xml:id="echoid-s22017" xml:space="preserve">ſibi facilè conſtruere. </s>
            <s xml:id="echoid-s22018" xml:space="preserve">Suppono autem primo Lectorem eſſe aliquantulum ver-
              <lb/>
            ſatum in Tabula ſinuum, atq; </s>
            <s xml:id="echoid-s22019" xml:space="preserve">adeò in Additione, Subtractione, Multiplicatione, Diuiſione, huic ne-
              <lb/>
            gotio neceſſarijs.</s>
            <s xml:id="echoid-s22020" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22021" xml:space="preserve">2 Habeat Tabulam ſinuum 10,000,000. </s>
            <s xml:id="echoid-s22022" xml:space="preserve">vel ſaltem 100,000. </s>
            <s xml:id="echoid-s22023" xml:space="preserve">quales ſunt Tabulæ P. </s>
            <s xml:id="echoid-s22024" xml:space="preserve">Clauij, & </s>
            <s xml:id="echoid-s22025" xml:space="preserve">Ma-
              <lb/>
            gnus Canon 10: </s>
            <s xml:id="echoid-s22026" xml:space="preserve">Magini in ſuo primo Mobili, qui cæteris tabulis eſt commodior, quia eadem tabula
              <lb/>
            exhibet ſinus rectos, & </s>
            <s xml:id="echoid-s22027" xml:space="preserve">verſos, quorum perpetuus eſt vſus in hac calculatione.</s>
            <s xml:id="echoid-s22028" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22029" xml:space="preserve">3 Sequatur modum calculandi traditũ a P. </s>
            <s xml:id="echoid-s22030" xml:space="preserve">Clauio in noua deſcriptione Horol. </s>
            <s xml:id="echoid-s22031" xml:space="preserve">probl. </s>
            <s xml:id="echoid-s22032" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22033" xml:space="preserve">& </s>
            <s xml:id="echoid-s22034" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22035" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s22036" xml:space="preserve">Gnom. </s>
            <s xml:id="echoid-s22037" xml:space="preserve">probl. </s>
            <s xml:id="echoid-s22038" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22039" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s22040" xml:space="preserve">36. </s>
            <s xml:id="echoid-s22041" xml:space="preserve">proximè ante rationem ex triangulis ſphęricis deſumptam. </s>
            <s xml:id="echoid-s22042" xml:space="preserve">de quo etiam
              <lb/>
            tractat inibi in ſcholio pag. </s>
            <s xml:id="echoid-s22043" xml:space="preserve">139. </s>
            <s xml:id="echoid-s22044" xml:space="preserve">linea 26. </s>
            <s xml:id="echoid-s22045" xml:space="preserve">paragr. </s>
            <s xml:id="echoid-s22046" xml:space="preserve">At verò eſt autem hic:</s>
            <s xml:id="echoid-s22047" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22048" xml:space="preserve">Fiat vt ſinus totus ad ſinum verſum diſtantiæ Solis a meridie,</s>
          </p>
          <p>
            <s xml:id="echoid-s22049" xml:space="preserve">Ita ſemiſſis aggregati ex ſinibus altitudinis ac depreſſionis meridianæ ad aliud:</s>
            <s xml:id="echoid-s22050" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22051" xml:space="preserve">Nam inuentum illud ſubtractum ex ſinu altitudinis meridia@æ, relinquet ſinum quæſitæ altitudi.
              <lb/>
            </s>
            <s xml:id="echoid-s22052" xml:space="preserve">nis ſolaris.</s>
            <s xml:id="echoid-s22053" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22054" xml:space="preserve">4 Seruanda eſt hęc methodus, vt prius inueniamus altitudines Solis ad ſingulas horas eiuſdem pa-
              <lb/>
            ralelli, & </s>
            <s xml:id="echoid-s22055" xml:space="preserve">eadem ferè opera, altitudines oppoſiti paralelli, v.</s>
            <s xml:id="echoid-s22056" xml:space="preserve">g. </s>
            <s xml:id="echoid-s22057" xml:space="preserve">inueniantur primo altitudines ad ſin-
              <lb/>
            gulas horas primi paralelli ♋. </s>
            <s xml:id="echoid-s22058" xml:space="preserve">& </s>
            <s xml:id="echoid-s22059" xml:space="preserve">oppoſiti ♑. </s>
            <s xml:id="echoid-s22060" xml:space="preserve">poſtea idem faciendum pro paralello per gr. </s>
            <s xml:id="echoid-s22061" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22062" xml:space="preserve">0′. </s>
            <s xml:id="echoid-s22063" xml:space="preserve">♋.
              <lb/>
            </s>
            <s xml:id="echoid-s22064" xml:space="preserve">necnon oppoſiti per gr. </s>
            <s xml:id="echoid-s22065" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22066" xml:space="preserve">0′. </s>
            <s xml:id="echoid-s22067" xml:space="preserve">♑, &</s>
            <s xml:id="echoid-s22068" xml:space="preserve">c.</s>
            <s xml:id="echoid-s22069" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22070" xml:space="preserve">5 Vtautem ſecundum prædictam analogiam, per regulam auream, vti oportet, operemur, opus
              <lb/>
              <note position="right" xlink:label="note-0275-04" xlink:href="note-0275-04a" xml:space="preserve">Apparat.
                <lb/>
              ad calcu-
                <lb/>
              lu@.</note>
            eſt præmittere Apparatum quendam, in quo continentur omnes termini neceſſarij ad hanc </s>
          </p>
        </div>
      </text>
    </echo>
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