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-div175" type="section" level="1" n="113">
          <pb o="89" file="0109" n="113" rhead="Liber Nonus."/>
        </div>
        <div xml:id="echoid-div176" type="section" level="1" n="114">
          <head xml:id="echoid-head126" style="it" xml:space="preserve">De numeris Aſironomicis, & eorum vſu. Cap. XIII.</head>
          <p>
            <s xml:id="echoid-s8352" xml:space="preserve">VT igitur hiſce Tabulis, vti poſſimus ad abſolutum Lunę locum in Zodiaco inueniendũ, opus eſt præmit-
              <lb/>
            torę cõpendioſam tractatione de numeris Aſtronomicis. </s>
            <s xml:id="echoid-s8353" xml:space="preserve">Verum quoniã numeri Aſtronomici peculiarẽ
              <lb/>
            doctriuam requirunt. </s>
            <s xml:id="echoid-s8354" xml:space="preserve">ideo hic ea ſolum breuiter indicabo, quæ vſui nobis futura ſunt. </s>
            <s xml:id="echoid-s8355" xml:space="preserve">Signum igitur vnum
              <lb/>
            continet gr. </s>
            <s xml:id="echoid-s8356" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8357" xml:space="preserve">Gr. </s>
            <s xml:id="echoid-s8358" xml:space="preserve">vnus continet 60. </s>
            <s xml:id="echoid-s8359" xml:space="preserve">min. </s>
            <s xml:id="echoid-s8360" xml:space="preserve">ſeu prima. </s>
            <s xml:id="echoid-s8361" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8362" xml:space="preserve">vnum continet 60. </s>
            <s xml:id="echoid-s8363" xml:space="preserve">ſecunda. </s>
            <s xml:id="echoid-s8364" xml:space="preserve">Secundum vnum 60.
              <lb/>
            </s>
            <s xml:id="echoid-s8365" xml:space="preserve">tertia: </s>
            <s xml:id="echoid-s8366" xml:space="preserve">& </s>
            <s xml:id="echoid-s8367" xml:space="preserve">ſic deinceps per ſexagenariam ſubdiuiſionem. </s>
            <s xml:id="echoid-s8368" xml:space="preserve">Præter gradus diuidunt etiam dies, & </s>
            <s xml:id="echoid-s8369" xml:space="preserve">horas, & </s>
            <s xml:id="echoid-s8370" xml:space="preserve">alia,
              <lb/>
            in prima, ſecunda, &</s>
            <s xml:id="echoid-s8371" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8372" xml:space="preserve">illud aut quod diuiditur in haſce ſexagenas particulas dicitur integrum.</s>
            <s xml:id="echoid-s8373" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div177" type="section" level="1" n="115">
          <head xml:id="echoid-head127" style="it" xml:space="preserve">ADDITIO.</head>
          <p>
            <s xml:id="echoid-s8374" xml:space="preserve">OMnes numeri addendi, ſcribendi ſunt, ita vt qui ſunt eiuſdem ſpeciei, ſint in eadem ſerie, ideſt, ſigna ſub
              <lb/>
            ſignis, gradus ſub gradibus, minuta ſub minutis recta deſcribãtur, vt in appoſito exemplo. </s>
            <s xml:id="echoid-s8375" xml:space="preserve">deinde incho,
              <lb/>
            anda eſt additio a numeris dextris ſeu a tenuioribus, vti a ſecundis in exemplo, ad-
              <lb/>
              <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">
                <lb/>
              Sig. # Gra. # ′. # ″
                <lb/>
              7 # 9 # 28 # 58
                <lb/>
              11 # 15 # 44 # 20
                <lb/>
              0 # 13 # 15
                <lb/>
              7 # 8 # 28 # 18
                <lb/>
              </note>
            duntur igitur omnia ſecunda ſimul, quæ in caſu noſtro ſunt 78. </s>
            <s xml:id="echoid-s8376" xml:space="preserve">quando autem colli-
              <lb/>
            gitur numerus maior quam 60. </s>
            <s xml:id="echoid-s8377" xml:space="preserve">pro ſingulis 60. </s>
            <s xml:id="echoid-s8378" xml:space="preserve">retinentur mente totidem vnita-
              <lb/>
            tates, & </s>
            <s xml:id="echoid-s8379" xml:space="preserve">reliquus numerus ſcribitur ſub ſua ſerie. </s>
            <s xml:id="echoid-s8380" xml:space="preserve">nunc igitur quia in 78. </s>
            <s xml:id="echoid-s8381" xml:space="preserve">ſemel conti-
              <lb/>
            netur 60. </s>
            <s xml:id="echoid-s8382" xml:space="preserve">quę faciunt minutum vnum; </s>
            <s xml:id="echoid-s8383" xml:space="preserve">ideo retineo mente vnam tantum vnitatem.
              <lb/>
            </s>
            <s xml:id="echoid-s8384" xml:space="preserve">Et reliquum 18. </s>
            <s xml:id="echoid-s8385" xml:space="preserve">ſcribo ſub ſecundis. </s>
            <s xml:id="echoid-s8386" xml:space="preserve">poſtea procedo ad minuta quibus addo retentã
              <lb/>
            vnitatem, & </s>
            <s xml:id="echoid-s8387" xml:space="preserve">omnia ſimul efficiunt 88′. </s>
            <s xml:id="echoid-s8388" xml:space="preserve">ſcribo igitur 28. </s>
            <s xml:id="echoid-s8389" xml:space="preserve">vnumque retineo pro ſexa-
              <lb/>
            gena, quæ efficit gradum vnum: </s>
            <s xml:id="echoid-s8390" xml:space="preserve">ideo addo vnum gradibus, quibus ſimul collectis
              <lb/>
            fiunt gr.</s>
            <s xml:id="echoid-s8391" xml:space="preserve">, 8. </s>
            <s xml:id="echoid-s8392" xml:space="preserve">& </s>
            <s xml:id="echoid-s8393" xml:space="preserve">quoniam gr. </s>
            <s xml:id="echoid-s8394" xml:space="preserve">38. </s>
            <s xml:id="echoid-s8395" xml:space="preserve">conflant ſignum vnum, & </s>
            <s xml:id="echoid-s8396" xml:space="preserve">præterea gr. </s>
            <s xml:id="echoid-s8397" xml:space="preserve">8. </s>
            <s xml:id="echoid-s8398" xml:space="preserve">ideo ſcribo
              <lb/>
            8. </s>
            <s xml:id="echoid-s8399" xml:space="preserve">ſub gradibus: </s>
            <s xml:id="echoid-s8400" xml:space="preserve">& </s>
            <s xml:id="echoid-s8401" xml:space="preserve">poſtea vnum addo ſignis: </s>
            <s xml:id="echoid-s8402" xml:space="preserve">& </s>
            <s xml:id="echoid-s8403" xml:space="preserve">cõputo ſigna 19. </s>
            <s xml:id="echoid-s8404" xml:space="preserve">ſed tamen ſcribo tantum 7. </s>
            <s xml:id="echoid-s8405" xml:space="preserve">quia ſigna 12. </s>
            <s xml:id="echoid-s8406" xml:space="preserve">om-
              <lb/>
            nia conficiunt integrum circulum, qui numquam ſcribitur, quia inutilis eſt calculationi, vt poſtea melius pa-
              <lb/>
            tebit. </s>
            <s xml:id="echoid-s8407" xml:space="preserve">quapropter obſeruandum eſt, ne vnquam in ſeriebus ſecundorum, aut primorum, ſcribatur numerus
              <lb/>
            maior quam 59. </s>
            <s xml:id="echoid-s8408" xml:space="preserve">in ſerie graduum nullus ſit maior, quam 29. </s>
            <s xml:id="echoid-s8409" xml:space="preserve">in ſerie ſignorum, nullus maior, quam 11. </s>
            <s xml:id="echoid-s8410" xml:space="preserve">ſiue in-
              <lb/>
            ter minuta, & </s>
            <s xml:id="echoid-s8411" xml:space="preserve">ſecunda omnes numeri ſint infra 60. </s>
            <s xml:id="echoid-s8412" xml:space="preserve">inter gradus ſint infra 30. </s>
            <s xml:id="echoid-s8413" xml:space="preserve">inter ſigna ſint infra 12.</s>
            <s xml:id="echoid-s8414" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div179" type="section" level="1" n="116">
          <head xml:id="echoid-head128" style="it" xml:space="preserve">SVBTRACTIO.</head>
          <p>
            <s xml:id="echoid-s8415" xml:space="preserve">NVmerus ſubtrahendus ſcribendus eſt ſub altero, eadem ratione, qua in additione, deinceps inchoanda
              <lb/>
            eſt ſubtractio a dextris; </s>
            <s xml:id="echoid-s8416" xml:space="preserve">Et cum quiſpiam numerus maior eſt ſuo ſuperiori, augendus eſt ſuperior acce-
              <lb/>
            pta mutuo vna ſexagena, aut trigena, aut duodena, prout numerus ad ſiniſtram ſequens, fuerit; </s>
            <s xml:id="echoid-s8417" xml:space="preserve">exemplo pa-
              <lb/>
            tebit, in quo inferior numerus 3. </s>
            <s xml:id="echoid-s8418" xml:space="preserve">29. </s>
            <s xml:id="echoid-s8419" xml:space="preserve">30′. </s>
            <s xml:id="echoid-s8420" xml:space="preserve">3″. </s>
            <s xml:id="echoid-s8421" xml:space="preserve">quãuis ſit maior ſupe ioris 2. </s>
            <s xml:id="echoid-s8422" xml:space="preserve">28. </s>
            <s xml:id="echoid-s8423" xml:space="preserve">0′. </s>
            <s xml:id="echoid-s8424" xml:space="preserve">2″.
              <lb/>
            </s>
            <s xml:id="echoid-s8425" xml:space="preserve">
              <note position="right" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve">
                <lb/>
              Sig. # Gra. # ′. # ″
                <lb/>
              13 # 57 # 59 # 60
                <lb/>
              2 # 28 # 0 # 2
                <lb/>
              3 # 29 # 30 # 3
                <lb/>
              10 # 28 # 29 # 59
                <lb/>
              </note>
            ſic tamen ab eo ſubtrahatur.</s>
            <s xml:id="echoid-s8426" xml:space="preserve">
              <unsure/>
            quia 3″. </s>
            <s xml:id="echoid-s8427" xml:space="preserve">non poſium detrahere a 2″. </s>
            <s xml:id="echoid-s8428" xml:space="preserve">ideo accedo ad ſi-
              <lb/>
            niſtrum locum primorum, & </s>
            <s xml:id="echoid-s8429" xml:space="preserve">inde mutuo accipio vnum primum, vt inde habeam
              <lb/>
            60″. </s>
            <s xml:id="echoid-s8430" xml:space="preserve">quæ cum 2″. </s>
            <s xml:id="echoid-s8431" xml:space="preserve">faciant 62. </s>
            <s xml:id="echoid-s8432" xml:space="preserve">a quibus detrahere poſſim 3″. </s>
            <s xml:id="echoid-s8433" xml:space="preserve">ſed quoniam locus pri-
              <lb/>
            morum eſt, 0′: </s>
            <s xml:id="echoid-s8434" xml:space="preserve">ideo procedo ad gr. </s>
            <s xml:id="echoid-s8435" xml:space="preserve">28. </s>
            <s xml:id="echoid-s8436" xml:space="preserve">& </s>
            <s xml:id="echoid-s8437" xml:space="preserve">inde accipio gr. </s>
            <s xml:id="echoid-s8438" xml:space="preserve">vnum, ideſt, 60′. </s>
            <s xml:id="echoid-s8439" xml:space="preserve">quæ pono
              <lb/>
            loco 0′. </s>
            <s xml:id="echoid-s8440" xml:space="preserve">ex his 60. </s>
            <s xml:id="echoid-s8441" xml:space="preserve">accipio vnum primum, ideſt, 60″. </s>
            <s xml:id="echoid-s8442" xml:space="preserve">quæ pono cum 2″. </s>
            <s xml:id="echoid-s8443" xml:space="preserve">ſicque poſ-
              <lb/>
            ſum ſubtrahere: </s>
            <s xml:id="echoid-s8444" xml:space="preserve">detraho igitur 3″. </s>
            <s xml:id="echoid-s8445" xml:space="preserve">a 62″. </s>
            <s xml:id="echoid-s8446" xml:space="preserve">& </s>
            <s xml:id="echoid-s8447" xml:space="preserve">remanent 59″. </s>
            <s xml:id="echoid-s8448" xml:space="preserve">ſubſcribenda. </s>
            <s xml:id="echoid-s8449" xml:space="preserve">numeri
              <lb/>
            13. </s>
            <s xml:id="echoid-s8450" xml:space="preserve">57. </s>
            <s xml:id="echoid-s8451" xml:space="preserve">59. </s>
            <s xml:id="echoid-s8452" xml:space="preserve">60. </s>
            <s xml:id="echoid-s8453" xml:space="preserve">ſunt poſi i ſupra numeros 2. </s>
            <s xml:id="echoid-s8454" xml:space="preserve">28. </s>
            <s xml:id="echoid-s8455" xml:space="preserve">0. </s>
            <s xml:id="echoid-s8456" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8457" xml:space="preserve">ad iuuandam memoriam Lecto-
              <lb/>
            ris. </s>
            <s xml:id="echoid-s8458" xml:space="preserve">deinde detraho 30′. </s>
            <s xml:id="echoid-s8459" xml:space="preserve">non a 0. </s>
            <s xml:id="echoid-s8460" xml:space="preserve">ſed a 59. </s>
            <s xml:id="echoid-s8461" xml:space="preserve">quæ i
              <unsure/>
            bi mente collocauiantea, remanent-
              <lb/>
            que 29′. </s>
            <s xml:id="echoid-s8462" xml:space="preserve">ſubſcribenda. </s>
            <s xml:id="echoid-s8463" xml:space="preserve">poſtea quia non poſſum detrahere 29. </s>
            <s xml:id="echoid-s8464" xml:space="preserve">a 27. </s>
            <s xml:id="echoid-s8465" xml:space="preserve">remanſerunt enim 27. </s>
            <s xml:id="echoid-s8466" xml:space="preserve">ob gradum accom-
              <lb/>
            modatum; </s>
            <s xml:id="echoid-s8467" xml:space="preserve">addo igitur gradus 30. </s>
            <s xml:id="echoid-s8468" xml:space="preserve">quos mutuo accipio a ſignis 2. </s>
            <s xml:id="echoid-s8469" xml:space="preserve">accipio enim ſignum
              <lb/>
              <note position="right" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve">
                <lb/>
              Sig. # Gra. # ′
                <lb/>
              6 # 5 # 4
                <lb/>
              4 # 3 # 4
                <lb/>
              2 # 2 # 0
                <lb/>
              </note>
            vnum, quod continet gradus 30. </s>
            <s xml:id="echoid-s8470" xml:space="preserve">& </s>
            <s xml:id="echoid-s8471" xml:space="preserve">fi
              <unsure/>
            unt grad. </s>
            <s xml:id="echoid-s8472" xml:space="preserve">57. </s>
            <s xml:id="echoid-s8473" xml:space="preserve">a quibus detractis 29. </s>
            <s xml:id="echoid-s8474" xml:space="preserve">reliqui ſunt 28.
              <lb/>
            </s>
            <s xml:id="echoid-s8475" xml:space="preserve">quos ſubi
              <unsure/>
            cribo. </s>
            <s xml:id="echoid-s8476" xml:space="preserve">Tandem demo ſigna 3. </s>
            <s xml:id="echoid-s8477" xml:space="preserve">a ſtgnis 1. </s>
            <s xml:id="echoid-s8478" xml:space="preserve">remanſit enim ſignum vnum ob mutua-
              <lb/>
            tionem alterius ſigni; </s>
            <s xml:id="echoid-s8479" xml:space="preserve">quod vt efficiam, debeo addere ſigna 12. </s>
            <s xml:id="echoid-s8480" xml:space="preserve">ideſt, circulum integrum
              <lb/>
            vni ſigno relicto; </s>
            <s xml:id="echoid-s8481" xml:space="preserve">fiuntque ſigna 13. </s>
            <s xml:id="echoid-s8482" xml:space="preserve">a quibus demo. </s>
            <s xml:id="echoid-s8483" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8484" xml:space="preserve">remanentque 10. </s>
            <s xml:id="echoid-s8485" xml:space="preserve">ſicque ſemper fa-
              <lb/>
            c
              <unsure/>
            iendum eſt.</s>
            <s xml:id="echoid-s8486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8487" xml:space="preserve">Quod ſi numeri inferiores ſint æquales, aut minores ſuperioribus, facillima eſt opera-
              <lb/>
            tio; </s>
            <s xml:id="echoid-s8488" xml:space="preserve">quia ſinguli inferiores detrahuntur a ſuis ſuperioribus, & </s>
            <s xml:id="echoid-s8489" xml:space="preserve">reſidui ſubſcribuntur, vt
              <lb/>
            hic vides.</s>
            <s xml:id="echoid-s8490" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div181" type="section" level="1" n="117">
          <head xml:id="echoid-head129" style="it" xml:space="preserve">MVLTIPLICATIO.</head>
          <p>
            <s xml:id="echoid-s8491" xml:space="preserve">1 IN hac operatione non conſiderantur ſigna, quatenus ſigna ſunt, verum ea reſoluenda ſunt in ſuos gra-
              <lb/>
            dus, i
              <unsure/>
            jque in loco graduum concipiendi ſunt, vt exemplo patebit.</s>
            <s xml:id="echoid-s8492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8493" xml:space="preserve">2 Præcipua difficultas eſt in inuenienda denominatione productorum, ſeu cognoſcenda ſpecie, ex mul-
              <lb/>
            tiplicatione, emergente. </s>
            <s xml:id="echoid-s8494" xml:space="preserve">ſit igitur hæc regula, quando duo numeri inuicem ducuntur, adde ſimul eorum de-
              <lb/>
            nominatores, ſeu apices, & </s>
            <s xml:id="echoid-s8495" xml:space="preserve">habebis denominationẽ producti, v. </s>
            <s xml:id="echoid-s8496" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8497" xml:space="preserve">ſi multiplicentur inuicem: </s>
            <s xml:id="echoid-s8498" xml:space="preserve">20′. </s>
            <s xml:id="echoid-s8499" xml:space="preserve">& </s>
            <s xml:id="echoid-s8500" xml:space="preserve">4″. </s>
            <s xml:id="echoid-s8501" xml:space="preserve">pro-
              <lb/>
            creabuntur 40′″. </s>
            <s xml:id="echoid-s8502" xml:space="preserve">quia ex additione, ‘
              <unsure/>
            cum,”
              <unsure/>
            quæ ſunt denominationes, ſeu apices eorum, fiunt’
              <unsure/>
            ”
              <unsure/>
            . </s>
            <s xml:id="echoid-s8503" xml:space="preserve">quæ ſunt
              <lb/>
            tertia. </s>
            <s xml:id="echoid-s8504" xml:space="preserve">igitur primo n@meri ipſi 10′. </s>
            <s xml:id="echoid-s8505" xml:space="preserve">& </s>
            <s xml:id="echoid-s8506" xml:space="preserve">4″. </s>
            <s xml:id="echoid-s8507" xml:space="preserve">multiplicantur tanquam numeri communes, & </s>
            <s xml:id="echoid-s8508" xml:space="preserve">fiunt 40″. </s>
            <s xml:id="echoid-s8509" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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