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

Page concordance

< >
Scan Original
111 87
112 88
113 89
114 90
115 91
116 92
117 93
118 94
119 95
120 96
121 97
122 98
123 99
124 100
125 101
126 102
127 103
128 104
129 105
130 106
131 107
132 108
133 109
134 110
135 111
136 112
137
138
139
140 113
< >
page |< < (90) of 300 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div181" type="section" level="1" n="117">
          <p>
            <s xml:id="echoid-s8509" xml:space="preserve">
              <pb o="90" file="0110" n="114" rhead="De Mundi Fabrica,"/>
            dae orum apices additi ſcribuntur ſupra productum, ſicque peracta eſt multiplicatio. </s>
            <s xml:id="echoid-s8510" xml:space="preserve">Aduertendum ta-
              <lb/>
            men eſt, quod apex, ſeu denominatio integrorum, v. </s>
            <s xml:id="echoid-s8511" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8512" xml:space="preserve">graduum, ſupponitur eſſe 0. </s>
            <s xml:id="echoid-s8513" xml:space="preserve">quæ addita aliorum
              <lb/>
            apicibus, eos non immutat: </s>
            <s xml:id="echoid-s8514" xml:space="preserve">quare quando ducuntur gradus, in alias ſexagenas, productus erit ſemper eiuſdem
              <lb/>
            apicis, cuius eſt illa ſexagena, vt ſi duco 3″. </s>
            <s xml:id="echoid-s8515" xml:space="preserve">in gr. </s>
            <s xml:id="echoid-s8516" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8517" xml:space="preserve">fiunt 45″. </s>
            <s xml:id="echoid-s8518" xml:space="preserve">&</s>
            <s xml:id="echoid-s8519" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8520" xml:space="preserve">ſic ductis inuicem gradibus producuntur
              <lb/>
            pariter gradus, quia 0. </s>
            <s xml:id="echoid-s8521" xml:space="preserve">addita cum alia 0. </s>
            <s xml:id="echoid-s8522" xml:space="preserve">facit 0.</s>
            <s xml:id="echoid-s8523" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8524" xml:space="preserve">3 Quoties numerus productus eſt maior, quam 60. </s>
            <s xml:id="echoid-s8525" xml:space="preserve">tunc quoties in ipſo continetur numerus 60. </s>
            <s xml:id="echoid-s8526" xml:space="preserve">tot vnita-
              <lb/>
            tes ſunt addendæ loco ſequenti ad ſiniſtram, ſiue loco proxime minoris denominationis ſiue pauciorum api-
              <lb/>
            cum, v. </s>
            <s xml:id="echoid-s8527" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8528" xml:space="preserve">ductus 3′. </s>
            <s xml:id="echoid-s8529" xml:space="preserve">in 25″. </s>
            <s xml:id="echoid-s8530" xml:space="preserve">productus eſt 75′″. </s>
            <s xml:id="echoid-s8531" xml:space="preserve">quæ omnia ſemel continent 60. </s>
            <s xml:id="echoid-s8532" xml:space="preserve">& </s>
            <s xml:id="echoid-s8533" xml:space="preserve">præterea 15. </s>
            <s xml:id="echoid-s8534" xml:space="preserve">ideo productus
              <lb/>
            ſic erit ſcribendus 1″. </s>
            <s xml:id="echoid-s8535" xml:space="preserve">15″. </s>
            <s xml:id="echoid-s8536" xml:space="preserve">ſub ſuis titulis. </s>
            <s xml:id="echoid-s8537" xml:space="preserve">ratio eſt quia 60. </s>
            <s xml:id="echoid-s8538" xml:space="preserve">ſcrupula maioris denominationis efficiunt vnum
              <lb/>
            tantum ſcrupulum minoris proximè appellationis.</s>
            <s xml:id="echoid-s8539" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8540" xml:space="preserve">4 Oportet ſingulos numeros multiplicantes in ſingulos multiplicandos ducere. </s>
            <s xml:id="echoid-s8541" xml:space="preserve">exemplum. </s>
            <s xml:id="echoid-s8542" xml:space="preserve">ſint igitur hi
              <lb/>
            numeri inuicem ducendi, hoc eſt ſigna 1. </s>
            <s xml:id="echoid-s8543" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s8544" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8545" xml:space="preserve">25′. </s>
            <s xml:id="echoid-s8546" xml:space="preserve">35″. </s>
            <s xml:id="echoid-s8547" xml:space="preserve">multiplicanda per gr. </s>
            <s xml:id="echoid-s8548" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8549" xml:space="preserve">2″. </s>
            <s xml:id="echoid-s8550" xml:space="preserve">ſcribantur vt in formu-
              <lb/>
              <note position="right" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">
                <lb/>
              Sig. # Gra. # ′. # ″. # ′″.
                <lb/>
              1 # 3 # 25 # 35
                <lb/>
              0 # 3 # 2 # 0
                <lb/>
              # # # 1 # 10
                <lb/>
              # 1 # 6 # 50
                <lb/>
              # # 1
                <lb/>
              3 # 1 # 15 # 45
                <lb/>
              # 9
                <lb/>
              3 # 11 # 23 # 36 # 10
                <lb/>
              </note>
              <note position="right" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">
                <lb/>
              Multiplicandi \\ Multiplicant
                <unsure/>
              es
                <lb/>
              Producti.
                <lb/>
              Summa productorum
                <lb/>
              </note>
            la apparct, ducta ſub eis linea quæ produ-
              <lb/>
            ctos ſeparat. </s>
            <s xml:id="echoid-s8551" xml:space="preserve">Primo igitur duco duo prima
              <lb/>
            in 35. </s>
            <s xml:id="echoid-s8552" xml:space="preserve">ſecunda, ideſt, 2′. </s>
            <s xml:id="echoid-s8553" xml:space="preserve">in 35′ ′. </s>
            <s xml:id="echoid-s8554" xml:space="preserve">fiũtque 70′″.
              <lb/>
            </s>
            <s xml:id="echoid-s8555" xml:space="preserve">ex præſcriptis regulis: </s>
            <s xml:id="echoid-s8556" xml:space="preserve">in quibus quia ſemel
              <lb/>
            60. </s>
            <s xml:id="echoid-s8557" xml:space="preserve">continetur, ideo pono vnitatem ſub lo-
              <lb/>
            co proximè minoris apicis, ideſt, ſub ſecuu-
              <lb/>
            dis; </s>
            <s xml:id="echoid-s8558" xml:space="preserve">reliqua autem 10′″. </s>
            <s xml:id="echoid-s8559" xml:space="preserve">ſub tertijs, vt in For
              <lb/>
            mula vides. </s>
            <s xml:id="echoid-s8560" xml:space="preserve">poſtea duco 2′. </s>
            <s xml:id="echoid-s8561" xml:space="preserve">in 25. </s>
            <s xml:id="echoid-s8562" xml:space="preserve">fiuntque
              <lb/>
            50″. </s>
            <s xml:id="echoid-s8563" xml:space="preserve">ſecunda; </s>
            <s xml:id="echoid-s8564" xml:space="preserve">quia ſingulares apices additi
              <lb/>
            efficiunt ſecunda. </s>
            <s xml:id="echoid-s8565" xml:space="preserve">ſcribo igitur 50″. </s>
            <s xml:id="echoid-s8566" xml:space="preserve">ſub lo-
              <lb/>
            co ſecundorum. </s>
            <s xml:id="echoid-s8567" xml:space="preserve">deinde duco 2′. </s>
            <s xml:id="echoid-s8568" xml:space="preserve">in gr. </s>
            <s xml:id="echoid-s8569" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8570" xml:space="preserve">pro-
              <lb/>
            ducitur 6. </s>
            <s xml:id="echoid-s8571" xml:space="preserve">prima, quia apex gr. </s>
            <s xml:id="echoid-s8572" xml:space="preserve">eſt 0. </s>
            <s xml:id="echoid-s8573" xml:space="preserve">qui ad-
              <lb/>
            ditus appici 1′. </s>
            <s xml:id="echoid-s8574" xml:space="preserve">eum non immutat: </s>
            <s xml:id="echoid-s8575" xml:space="preserve">Scribo
              <lb/>
            igitur 6. </s>
            <s xml:id="echoid-s8576" xml:space="preserve">ſub loco primorum. </s>
            <s xml:id="echoid-s8577" xml:space="preserve">tandẽ duco 2′. </s>
            <s xml:id="echoid-s8578" xml:space="preserve">
              <lb/>
            in ſignum 1. </s>
            <s xml:id="echoid-s8579" xml:space="preserve">hoc eſt gr. </s>
            <s xml:id="echoid-s8580" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8581" xml:space="preserve">iuxtam primam re-
              <lb/>
            gulam; </s>
            <s xml:id="echoid-s8582" xml:space="preserve">fiuntque 60′. </s>
            <s xml:id="echoid-s8583" xml:space="preserve">prima, quæ, quia faciunt
              <lb/>
            gr. </s>
            <s xml:id="echoid-s8584" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8585" xml:space="preserve">ideo ſubſcribo 1. </s>
            <s xml:id="echoid-s8586" xml:space="preserve">loco graduum; </s>
            <s xml:id="echoid-s8587" xml:space="preserve">ſicque numerus 2′. </s>
            <s xml:id="echoid-s8588" xml:space="preserve">functus eſt munere ſuo. </s>
            <s xml:id="echoid-s8589" xml:space="preserve">Alterum igitur numero-
              <lb/>
            rum, ideſt, gr. </s>
            <s xml:id="echoid-s8590" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8591" xml:space="preserve">duco in ſi@gulos ſuperiores, eodem modo. </s>
            <s xml:id="echoid-s8592" xml:space="preserve">Primo in 35″. </s>
            <s xml:id="echoid-s8593" xml:space="preserve">producunturq; </s>
            <s xml:id="echoid-s8594" xml:space="preserve">105. </s>
            <s xml:id="echoid-s8595" xml:space="preserve">quo in nume-
              <lb/>
            ro continetur 60. </s>
            <s xml:id="echoid-s8596" xml:space="preserve">ſeme@. </s>
            <s xml:id="echoid-s8597" xml:space="preserve">Quareſcribo vnitatem loco primorum; </s>
            <s xml:id="echoid-s8598" xml:space="preserve">reliquum vero 45″. </s>
            <s xml:id="echoid-s8599" xml:space="preserve">ſub ſecundis. </s>
            <s xml:id="echoid-s8600" xml:space="preserve">deinde
              <lb/>
            ductis 3. </s>
            <s xml:id="echoid-s8601" xml:space="preserve">in 25′. </s>
            <s xml:id="echoid-s8602" xml:space="preserve">fiunt 75′. </s>
            <s xml:id="echoid-s8603" xml:space="preserve">hoc eſt gr. </s>
            <s xml:id="echoid-s8604" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8605" xml:space="preserve">& </s>
            <s xml:id="echoid-s8606" xml:space="preserve">15′. </s>
            <s xml:id="echoid-s8607" xml:space="preserve">quæ ſuis locis adſcribo, vt vides in formula. </s>
            <s xml:id="echoid-s8608" xml:space="preserve">rurſus ductis 3. </s>
            <s xml:id="echoid-s8609" xml:space="preserve">in 3. </s>
            <s xml:id="echoid-s8610" xml:space="preserve">
              <lb/>
            fiunt 9. </s>
            <s xml:id="echoid-s8611" xml:space="preserve">ideſt gr. </s>
            <s xml:id="echoid-s8612" xml:space="preserve">9. </s>
            <s xml:id="echoid-s8613" xml:space="preserve">ſub loco graduum ponendi. </s>
            <s xml:id="echoid-s8614" xml:space="preserve">Tandem ductis 3. </s>
            <s xml:id="echoid-s8615" xml:space="preserve">in ſignum 1. </s>
            <s xml:id="echoid-s8616" xml:space="preserve">ſeu in gr. </s>
            <s xml:id="echoid-s8617" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8618" xml:space="preserve">emergunt 90. </s>
            <s xml:id="echoid-s8619" xml:space="preserve">gra-
              <lb/>
            dus, ſeu ſigna 3. </s>
            <s xml:id="echoid-s8620" xml:space="preserve">quæ ſub titulo ſignorum ſunt ſubſcr@bẽda. </s>
            <s xml:id="echoid-s8621" xml:space="preserve">poſtremo hi omnes numeri in vnam ſummam ſunt
              <lb/>
            colligendi iuxta regulas Additionis; </s>
            <s xml:id="echoid-s8622" xml:space="preserve">conflaturque ſumma hæc; </s>
            <s xml:id="echoid-s8623" xml:space="preserve">Signa 3. </s>
            <s xml:id="echoid-s8624" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s8625" xml:space="preserve">11. </s>
            <s xml:id="echoid-s8626" xml:space="preserve">23′. </s>
            <s xml:id="echoid-s8627" xml:space="preserve">36″. </s>
            <s xml:id="echoid-s8628" xml:space="preserve">10′″. </s>
            <s xml:id="echoid-s8629" xml:space="preserve">Huius autem
              <lb/>
            rei de
              <unsure/>
            monſtratio pendet ex fractionibus vulgarium numerorum. </s>
            <s xml:id="echoid-s8630" xml:space="preserve">Fractiones enim Aſtronomicę poſſunt re-
              <lb/>
            duci ad vulgares, qua ratione vnum primum eſt {1/60}. </s>
            <s xml:id="echoid-s8631" xml:space="preserve">integr: </s>
            <s xml:id="echoid-s8632" xml:space="preserve">vnum vero ſecundum eſt, {1/3600}. </s>
            <s xml:id="echoid-s8633" xml:space="preserve">& </s>
            <s xml:id="echoid-s8634" xml:space="preserve">ſic de cæteris: </s>
            <s xml:id="echoid-s8635" xml:space="preserve">
              <lb/>
            Si autem ſecundum regulas vulgariũ fractionum multiplicentur inuicem {1/60}. </s>
            <s xml:id="echoid-s8636" xml:space="preserve">{1/3600}. </s>
            <s xml:id="echoid-s8637" xml:space="preserve">producunt {1/360000}. </s>
            <s xml:id="echoid-s8638" xml:space="preserve">qui pro-
              <lb/>
            ductus æquiualet vni tertio. </s>
            <s xml:id="echoid-s8639" xml:space="preserve">qui etiam producitur ex multiplicatione 1′. </s>
            <s xml:id="echoid-s8640" xml:space="preserve">in 2″. </s>
            <s xml:id="echoid-s8641" xml:space="preserve">quia 1. </s>
            <s xml:id="echoid-s8642" xml:space="preserve">in 1. </s>
            <s xml:id="echoid-s8643" xml:space="preserve">facit 1. </s>
            <s xml:id="echoid-s8644" xml:space="preserve">& </s>
            <s xml:id="echoid-s8645" xml:space="preserve">eorum
              <lb/>
            apices additi faciunt′″. </s>
            <s xml:id="echoid-s8646" xml:space="preserve">ponendos ſupra productum, ſic 1′″. </s>
            <s xml:id="echoid-s8647" xml:space="preserve">eodem modo de reliquis Aſtrom. </s>
            <s xml:id="echoid-s8648" xml:space="preserve">fractionibus
              <lb/>
            æſtimandum eſt.</s>
            <s xml:id="echoid-s8649" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8650" xml:space="preserve">5 Scias tandem hanc multiplicationem poſſe fieri reductis omnibus partibus, tam numeri multiplican-
              <lb/>
            di
              <unsure/>
            , quam multiplicantis, ad eorum maximam dcnominationem, de qua reductione dicam in ſequenti tra-
              <lb/>
            ctatu de diuiſione num. </s>
            <s xml:id="echoid-s8651" xml:space="preserve">6.</s>
            <s xml:id="echoid-s8652" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div183" type="section" level="1" n="118">
          <head xml:id="echoid-head130" style="it" xml:space="preserve">DIVISIO.</head>
          <p>
            <s xml:id="echoid-s8653" xml:space="preserve">1 SIcut in multiplicatione non conſiderantur ſigna, ſed in gradus reſoluenda ſunt, ita pariter in di-
              <lb/>
            uiſione.</s>
            <s xml:id="echoid-s8654" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8655" xml:space="preserve">2 At in cognoſcenda denominatione quotientis, ſeu producti, contra hic agendũ eſt, ac in multiplica-
              <lb/>
            tione ibi enim per additionẽ apicum cõſtabatur apex producti: </s>
            <s xml:id="echoid-s8656" xml:space="preserve">hic vero per ſubtractionem. </s>
            <s xml:id="echoid-s8657" xml:space="preserve">nam in diuiſione
              <lb/>
            ſubtrahetur apex minor a maiori, & </s>
            <s xml:id="echoid-s8658" xml:space="preserve">reliquus apex erit dennminatio quotientis. </s>
            <s xml:id="echoid-s8659" xml:space="preserve">vb illud etiam repetendum,
              <lb/>
            apicem integrorum, v.</s>
            <s xml:id="echoid-s8660" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8661" xml:space="preserve">graduum eſſe 0. </s>
            <s xml:id="echoid-s8662" xml:space="preserve">exemplum; </s>
            <s xml:id="echoid-s8663" xml:space="preserve">diuidantur 24″. </s>
            <s xml:id="echoid-s8664" xml:space="preserve">per 6′. </s>
            <s xml:id="echoid-s8665" xml:space="preserve">primo numeri ipſi diuidẽdi ſunt
              <lb/>
            vti vulgares numeri, eritque quotiens 4. </s>
            <s xml:id="echoid-s8666" xml:space="preserve">cuius denom. </s>
            <s xml:id="echoid-s8667" xml:space="preserve">ſeu apex habetur detrahendo′. </s>
            <s xml:id="echoid-s8668" xml:space="preserve">a″. </s>
            <s xml:id="echoid-s8669" xml:space="preserve">remanent enim 1.
              <lb/>
            </s>
            <s xml:id="echoid-s8670" xml:space="preserve">apex quoti
              <unsure/>
            entis, ſcilicet 4′. </s>
            <s xml:id="echoid-s8671" xml:space="preserve">rurſuſ diuidẽda ſunt 18′. </s>
            <s xml:id="echoid-s8672" xml:space="preserve">per 9′. </s>
            <s xml:id="echoid-s8673" xml:space="preserve">erit quotiens. </s>
            <s xml:id="echoid-s8674" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8675" xml:space="preserve">nam detracto′. </s>
            <s xml:id="echoid-s8676" xml:space="preserve">ab′. </s>
            <s xml:id="echoid-s8677" xml:space="preserve">remanet 0. </s>
            <s xml:id="echoid-s8678" xml:space="preserve">qui
              <lb/>
            apex eſt integri, v.</s>
            <s xml:id="echoid-s8679" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8680" xml:space="preserve">gradus: </s>
            <s xml:id="echoid-s8681" xml:space="preserve">ergo quotiens erit 2. </s>
            <s xml:id="echoid-s8682" xml:space="preserve">ſeu gr. </s>
            <s xml:id="echoid-s8683" xml:space="preserve">2.</s>
            <s xml:id="echoid-s8684" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          # Sig. # Gra. # ′. # ″
            <lb/>
          D´uideudus. # 1 # 2 # 30 # 24
            <lb/>
          Diuiſor. # 0 # 6 # 0 # 0
            <lb/>
          Quotiens. # # 6 # 5 # 4
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s8685" xml:space="preserve">2 Quando igitur Aſtronomicus numerus diuiden-
              <lb/>
            dus, non fuerit minor diuiſore, ſed ei æqualis, aut maior:
              <lb/>
            </s>
            <s xml:id="echoid-s8686" xml:space="preserve">pariterque cum eo apex eius non fuerit minor apice di-
              <lb/>
            uiſoris ſed ei æqualis, aut maior; </s>
            <s xml:id="echoid-s8687" xml:space="preserve">& </s>
            <s xml:id="echoid-s8688" xml:space="preserve">præterea diuiſor ha-
              <lb/>
            neat vnicum membrum tũc facilima eſt partitio, v.</s>
            <s xml:id="echoid-s8689" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8690" xml:space="preserve">ſint
              <lb/>
            diuidenda, vt in exemplo apparet, ſigna 1. </s>
            <s xml:id="echoid-s8691" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s8692" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8693" xml:space="preserve">30′. </s>
            <s xml:id="echoid-s8694" xml:space="preserve">24″. </s>
            <s xml:id="echoid-s8695" xml:space="preserve">
              <lb/>
            per gr. </s>
            <s xml:id="echoid-s8696" xml:space="preserve">{0/6}. </s>
            <s xml:id="echoid-s8697" xml:space="preserve">Primo diuido 24′. </s>
            <s xml:id="echoid-s8698" xml:space="preserve">per {0/6}. </s>
            <s xml:id="echoid-s8699" xml:space="preserve">proueniuni 4″. </s>
            <s xml:id="echoid-s8700" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum