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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          <p>
            <s xml:id="echoid-s20386" xml:space="preserve">
              <pb o="8" file="0262" n="267" rhead="TRACTATVS"/>
            Noſtræ porto lineæ rectæ in plano Horarij ſunt communes ſectiones planorum circulorũm Ital. </s>
            <s xml:id="echoid-s20387" xml:space="preserve">& </s>
            <s xml:id="echoid-s20388" xml:space="preserve">
              <lb/>
            Babylon. </s>
            <s xml:id="echoid-s20389" xml:space="preserve">cum plano Horarij, quod Sphæram tangit in C. </s>
            <s xml:id="echoid-s20390" xml:space="preserve">eſtque paralellum circulo horę 6. </s>
            <s xml:id="echoid-s20391" xml:space="preserve">Aſtrono-
              <lb/>
            micę, quare etiam in plano Horarij hæ ſectiones facient eoſdem angulos.</s>
            <s xml:id="echoid-s20392" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20393" xml:space="preserve">Iam Ital. </s>
            <s xml:id="echoid-s20394" xml:space="preserve">& </s>
            <s xml:id="echoid-s20395" xml:space="preserve">Babylon. </s>
            <s xml:id="echoid-s20396" xml:space="preserve">terminandæ ſunt hac ra@ione. </s>
            <s xml:id="echoid-s20397" xml:space="preserve">Per puncta I V, ducantur duæ rectæ norma-
              <lb/>
            les ipſi tangenti T B V, donec occurrant lineis Italicæ, & </s>
            <s xml:id="echoid-s20398" xml:space="preserve">Babylonicæ productis in punctis E F G H,
              <lb/>
            ſicque E F, erit Italica terminata, & </s>
            <s xml:id="echoid-s20399" xml:space="preserve">G H, Babylonica pariter terminata, cuius ratio poſtea patebit.
              <lb/>
            </s>
            <s xml:id="echoid-s20400" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s20401" xml:space="preserve">ex his tribus lineis erit abſolutum Horarium, ſed ſimplex, & </s>
            <s xml:id="echoid-s20402" xml:space="preserve">quo tantum horas terminatas de-
              <lb/>
            ſcribere poſſes. </s>
            <s xml:id="echoid-s20403" xml:space="preserve">Si quis igitur contentus ſit hac breuitate, ei iam ſatis factum erit. </s>
            <s xml:id="echoid-s20404" xml:space="preserve">Opus tamen erit
              <lb/>
            Horarium iſtud in laminam ſolidam tranſcribere, atque ad vſum accommodare, vt poſt modum di-
              <lb/>
            cemus.</s>
            <s xml:id="echoid-s20405" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20406" xml:space="preserve">10 Verum vt nos Horarium habeamus quo videlicet. </s>
            <s xml:id="echoid-s20407" xml:space="preserve">præter horas etiam paralellos ſignorum,
              <lb/>
            necnon arcus diurnos in noſtris Horologiis delineare poſſimus. </s>
            <s xml:id="echoid-s20408" xml:space="preserve">addantur quæ ſequuntur.</s>
            <s xml:id="echoid-s20409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20410" xml:space="preserve">In arcu I B K, ponantur reliqua interualla accepta ex quinta columna, ideſt, arcus B L, & </s>
            <s xml:id="echoid-s20411" xml:space="preserve">B M, ſint
              <lb/>
              <note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve">Horæviũ
                <lb/>
              parfectũ
                <lb/>
              planum,
                <lb/>
              & parti-
                <lb/>
              culare.</note>
            vterq; </s>
            <s xml:id="echoid-s20412" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s20413" xml:space="preserve">21. </s>
            <s xml:id="echoid-s20414" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20415" xml:space="preserve">arcus B N, B O, ſint gr. </s>
            <s xml:id="echoid-s20416" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20417" xml:space="preserve">0. </s>
            <s xml:id="echoid-s20418" xml:space="preserve">qui accipiendi ſunt ex ſecunda parte columnæ quintæ
              <lb/>
            ſunt enim interualla in arcubus diurnis hor. </s>
            <s xml:id="echoid-s20419" xml:space="preserve">14. </s>
            <s xml:id="echoid-s20420" xml:space="preserve">& </s>
            <s xml:id="echoid-s20421" xml:space="preserve">hor. </s>
            <s xml:id="echoid-s20422" xml:space="preserve">10. </s>
            <s xml:id="echoid-s20423" xml:space="preserve">arcus B P, B Q, ſint ſint gr. </s>
            <s xml:id="echoid-s20424" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20425" xml:space="preserve">30. </s>
            <s xml:id="echoid-s20426" xml:space="preserve">arcus B r,
              <lb/>
            B q, ſint gr. </s>
            <s xml:id="echoid-s20427" xml:space="preserve">5. </s>
            <s xml:id="echoid-s20428" xml:space="preserve">45. </s>
            <s xml:id="echoid-s20429" xml:space="preserve">Deinde ex centr@ A, per puncta, L N P r q QOM, ducantur rectæ vſque ad tan-
              <lb/>
            gentem T B V, in punctis 0. </s>
            <s xml:id="echoid-s20430" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20431" xml:space="preserve">2. </s>
            <s xml:id="echoid-s20432" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20433" xml:space="preserve">ex vtraq; </s>
            <s xml:id="echoid-s20434" xml:space="preserve">parte ex prædictis lineis adſcribantur characteres ſigno-
              <lb/>
            rum, per quorum interualla tranieunt: </s>
            <s xml:id="echoid-s20435" xml:space="preserve">duabus vero A N, A D, apponantur hor. </s>
            <s xml:id="echoid-s20436" xml:space="preserve">10 & </s>
            <s xml:id="echoid-s20437" xml:space="preserve">hor. </s>
            <s xml:id="echoid-s20438" xml:space="preserve">14. </s>
            <s xml:id="echoid-s20439" xml:space="preserve">quia,
              <lb/>
            tranſeunt per finem interuallorum in arcubus diurnis hor. </s>
            <s xml:id="echoid-s20440" xml:space="preserve">10. </s>
            <s xml:id="echoid-s20441" xml:space="preserve">& </s>
            <s xml:id="echoid-s20442" xml:space="preserve">14. </s>
            <s xml:id="echoid-s20443" xml:space="preserve">vt apparet in figura. </s>
            <s xml:id="echoid-s20444" xml:space="preserve">poſtea ſecus
              <lb/>
            puncta 1. </s>
            <s xml:id="echoid-s20445" xml:space="preserve">2. </s>
            <s xml:id="echoid-s20446" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20447" xml:space="preserve">omiſſis in præſentia 0. </s>
            <s xml:id="echoid-s20448" xml:space="preserve">0. </s>
            <s xml:id="echoid-s20449" xml:space="preserve">applicata regula normaliter ad tangentem B V. </s>
            <s xml:id="echoid-s20450" xml:space="preserve">vbi ipſa regu-
              <lb/>
              <note position="left" xlink:label="note-0262-02" xlink:href="note-0262-02a" xml:space="preserve">Deſcri-
                <lb/>
              prio para
                <lb/>
              lellorum
                <lb/>
              in Hera-
                <lb/>
              ri@.</note>
            la ſecuerit lineas horarias Italicam, & </s>
            <s xml:id="echoid-s20451" xml:space="preserve">Babylonicam, vbi imprime puncta, vnum pro ſingulis. </s>
            <s xml:id="echoid-s20452" xml:space="preserve">ſic ap-
              <lb/>
            plicata, v.</s>
            <s xml:id="echoid-s20453" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20454" xml:space="preserve">regula ſecus punctum 3. </s>
            <s xml:id="echoid-s20455" xml:space="preserve">ſecabit Italicam, & </s>
            <s xml:id="echoid-s20456" xml:space="preserve">Babylonicam in punctis notatis litera s. </s>
            <s xml:id="echoid-s20457" xml:space="preserve">Idem
              <lb/>
            fac ex puncto 2. </s>
            <s xml:id="echoid-s20458" xml:space="preserve">& </s>
            <s xml:id="echoid-s20459" xml:space="preserve">habebis alia duo pũcta in Ital. </s>
            <s xml:id="echoid-s20460" xml:space="preserve">& </s>
            <s xml:id="echoid-s20461" xml:space="preserve">Babylon. </s>
            <s xml:id="echoid-s20462" xml:space="preserve">& </s>
            <s xml:id="echoid-s20463" xml:space="preserve">ſic de cęteris, etiam ex altera parte tan-
              <lb/>
            gentis B T. </s>
            <s xml:id="echoid-s20464" xml:space="preserve">Porro ſi erratum non eſt, erunt omnia puncta hor. </s>
            <s xml:id="echoid-s20465" xml:space="preserve">Ital. </s>
            <s xml:id="echoid-s20466" xml:space="preserve">& </s>
            <s xml:id="echoid-s20467" xml:space="preserve">Babylon. </s>
            <s xml:id="echoid-s20468" xml:space="preserve">conſimiliter poſita
              <lb/>
            in vna, a tq; </s>
            <s xml:id="echoid-s20469" xml:space="preserve">in altera. </s>
            <s xml:id="echoid-s20470" xml:space="preserve">Et ſi imaginemur lineam curuam ductam per tria extrema E D G, linearum ho-
              <lb/>
            rariarum ipſa reſpondebit tropico ♌, ſeu erit portio hyperboles reſpondens paralello per initium,
              <lb/>
            ♌, pariter linea per@ria puncta ſequentia R T S, leniter curua, erit portio hyperboles reſpondens pa-
              <lb/>
            ralello per initium ♑, ducto, & </s>
            <s xml:id="echoid-s20471" xml:space="preserve">ſic de cęteris. </s>
            <s xml:id="echoid-s20472" xml:space="preserve">quibus apponantur proprij characteres, & </s>
            <s xml:id="echoid-s20473" xml:space="preserve">notæ, vt fi-
              <lb/>
            gura per ſe oſtendi@:</s>
            <s xml:id="echoid-s20474" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s20475" xml:space="preserve">Horarium abſolutum in plano deſcriptum.</s>
            <s xml:id="echoid-s20476" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20477" xml:space="preserve">11 Notanda quædam. </s>
            <s xml:id="echoid-s20478" xml:space="preserve">Primo, quamuis prædicta interualla omnia ponantur in eodem arcu I K,
              <lb/>
            debet tamen quodlibet illorum intelligi in proprijs eſſe paralellis, v. </s>
            <s xml:id="echoid-s20479" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20480" xml:space="preserve">I B in tropico ♑. </s>
            <s xml:id="echoid-s20481" xml:space="preserve">B K, in tro-
              <lb/>
            pico ♋, L B, in paralello ♐, B M, in paralello ♌, prout characteres lineis ea termi ã@ bus indicant.
              <lb/>
            </s>
            <s xml:id="echoid-s20482" xml:space="preserve">Ratio huius eſt, quia idem arcus I B K, ſecundum varia interualla in eo notata refert etiã varios pa-
              <lb/>
            ralellos, quibus ea interualla competunt: </s>
            <s xml:id="echoid-s20483" xml:space="preserve">quare ob interuallum I B, refer@ tropicum ♑, ob interuallũ
              <lb/>
            L B, paralellum ♐ &</s>
            <s xml:id="echoid-s20484" xml:space="preserve">c.</s>
            <s xml:id="echoid-s20485" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20486" xml:space="preserve">Secundo, notandum lineas à centro A, egredientes per puncta interuallorum eſſe ſingulas ſecan-
              <lb/>
            tes ſingulorum dictorũ interuallorum quibus interuallis reſpondent ſingulæ tangentes B 1. </s>
            <s xml:id="echoid-s20487" xml:space="preserve">B 2. </s>
            <s xml:id="echoid-s20488" xml:space="preserve">B 3.
              <lb/>
            </s>
            <s xml:id="echoid-s20489" xml:space="preserve">B V, ex vna parte. </s>
            <s xml:id="echoid-s20490" xml:space="preserve">ex altera vero ſimiliter B 1. </s>
            <s xml:id="echoid-s20491" xml:space="preserve">B 2. </s>
            <s xml:id="echoid-s20492" xml:space="preserve">B 3. </s>
            <s xml:id="echoid-s20493" xml:space="preserve">B T.</s>
            <s xml:id="echoid-s20494" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20495" xml:space="preserve">12 Aliter ſine altitudine poli poſſunt inueniri linea Italica, & </s>
            <s xml:id="echoid-s20496" xml:space="preserve">Babylonica, & </s>
            <s xml:id="echoid-s20497" xml:space="preserve">quidem termina-
              <lb/>
            tæ. </s>
            <s xml:id="echoid-s20498" xml:space="preserve">Oportet igitur primo diuidere, ac terminare ſimul duo latera Horarij F G, H E, in punctis de-
              <lb/>
            clinationum paralellorum aſſumptorum in Horario, ope Rad@arij: </s>
            <s xml:id="echoid-s20499" xml:space="preserve">ſi u@i etiam diuiſa eſt Aſtronomi-
              <lb/>
            ca B D. </s>
            <s xml:id="echoid-s20500" xml:space="preserve">Accipiatur igitur circino alterutra duarum ſecantium A T, vel A V, & </s>
            <s xml:id="echoid-s20501" xml:space="preserve">ponatur in Radiario,
              <lb/>
            ſitque E r, & </s>
            <s xml:id="echoid-s20502" xml:space="preserve">per punctum r, acta normalis S r T, ſecetur ſaltem a duobus radijs ex remis in punctis
              <lb/>
            S T, deinde a puncto C, Horarij applicata normali vſq; </s>
            <s xml:id="echoid-s20503" xml:space="preserve">ad latus G F, in a, erit a, punctum medium
              <lb/>
            ipſius. </s>
            <s xml:id="echoid-s20504" xml:space="preserve">iam ab a, ſupra, & </s>
            <s xml:id="echoid-s20505" xml:space="preserve">infra ponantur a G, & </s>
            <s xml:id="echoid-s20506" xml:space="preserve">a F, æquales ip is @ S, r @. </s>
            <s xml:id="echoid-s20507" xml:space="preserve">Radiarij. </s>
            <s xml:id="echoid-s20508" xml:space="preserve">ſimiſiter reliquæ
              <lb/>
            diuiſiones transferri hinc ad latus Horarij poterunt. </s>
            <s xml:id="echoid-s20509" xml:space="preserve">Idem aciendum eſt cum latere H E, eruntque
              <lb/>
            æqualia inuicem. </s>
            <s xml:id="echoid-s20510" xml:space="preserve">Iam ſi per puncta E F, & </s>
            <s xml:id="echoid-s20511" xml:space="preserve">per puncta G H, ducantur duæ rect@e, tranſibunt ambæ
              <lb/>
            per C, ipſæque erunt lineæ horariæ Italica, & </s>
            <s xml:id="echoid-s20512" xml:space="preserve">Babylonica, vt prius. </s>
            <s xml:id="echoid-s20513" xml:space="preserve">Porro ſi ab reliquis extremis
              <lb/>
            punctis ſecantium 3. </s>
            <s xml:id="echoid-s20514" xml:space="preserve">2. </s>
            <s xml:id="echoid-s20515" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20516" xml:space="preserve">erigantur latera alia normali@er, eaque eadem ra@oiſe ope Radiarij diui-
              <lb/>
            dantur, diuidentur in ijſdem punctis, in quibus ipſa ſecat horarias Italicam, & </s>
            <s xml:id="echoid-s20517" xml:space="preserve">Baby onicam, v.</s>
            <s xml:id="echoid-s20518" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20519" xml:space="preserve">la-
              <lb/>
            tus ex 3. </s>
            <s xml:id="echoid-s20520" xml:space="preserve">erectum, ſecaretur in punctiss, s, a Radiario, in quibus ipſum ſ@ca ſineas Italicam, & </s>
            <s xml:id="echoid-s20521" xml:space="preserve">Baby
              <lb/>
            lonicam.</s>
            <s xml:id="echoid-s20522" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20523" xml:space="preserve">13 Quorum rationes, vt intelligantur; </s>
            <s xml:id="echoid-s20524" xml:space="preserve">debemus primo imaginari Horarium ſitum in ſuo ſitu na-
              <lb/>
              <note position="left" xlink:label="note-0262-03" xlink:href="note-0262-03a" xml:space="preserve">Demon-
                <lb/>
              stratio
                <lb/>
              praceden
                <lb/>
              @ium.</note>
            turali, in quo ſupponitur deſcriptum, ideſt, in plano paralello circulo horæ 6. </s>
            <s xml:id="echoid-s20525" xml:space="preserve">Aſtronomicæ, quare & </s>
            <s xml:id="echoid-s20526" xml:space="preserve">
              <lb/>
            paralello axi mundi, necnon tangenti Sphæram mundi in puncto commun æquatoris, & </s>
            <s xml:id="echoid-s20527" xml:space="preserve">lineæ me-
              <lb/>
            ridianæ; </s>
            <s xml:id="echoid-s20528" xml:space="preserve">quod in Radiario eſt A, in Horario vero eſt C. </s>
            <s xml:id="echoid-s20529" xml:space="preserve">Debemus igitur concipere Radiarium ere-
              <lb/>
            ctum normaliter ſupra planum circuli interuallorum, & </s>
            <s xml:id="echoid-s20530" xml:space="preserve">linea tangens Radiarij A I, pariter normalis
              <lb/>
            ſupra B, circuli diſtantiarum. </s>
            <s xml:id="echoid-s20531" xml:space="preserve">quibus ſic poſitis, erigatur Horarium circa rectam T B V, nonmaliter
              <lb/>
            ſupra planum circuli diſtantiarum, ita vt linea B C D, Aſtronomica coincidat cum I A H, Radiarij,
              <lb/>
            ſicq; </s>
            <s xml:id="echoid-s20532" xml:space="preserve">erit in ſuo ſitu naturali: </s>
            <s xml:id="echoid-s20533" xml:space="preserve">in quo ſitu manifeſtum eſt radios Radiarij diuidere lineam B D, Hora-
              <lb/>
            rij in ijſdem punctis, quibus eam ſupra diuifimus. </s>
            <s xml:id="echoid-s20534" xml:space="preserve">Poſtea moueatur Radiarium, ſeu giretur circa ma-
              <lb/>
            nentem E Q, normalem donec Q I, linea eius ſit ſupra alterutram extremarum ſecantium circuli di-
              <lb/>
            ſtantiarum, v. </s>
            <s xml:id="echoid-s20535" xml:space="preserve">g. </s>
            <s xml:id="echoid-s20536" xml:space="preserve">coincidat cum ſecante A K V, eritq; </s>
            <s xml:id="echoid-s20537" xml:space="preserve">Radiarium directe è regione lateris
              <unsure/>
            F G, </s>
          </p>
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