Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

< >
[142.] VI.
[143.] VII.
[144.] VIII.
[145.] IX.
[146.] DE AEQVINOCTI ALI CIRCVLO.
[147.] COMMENTARIS.
[148.] COMMENTARIVS.
[149.] COMMENTARIVS.
[150.] OFFICIA ÆQVINOCTIALIS CIRCVLI. I.
[151.] II.
[152.] III.
[153.] IIII.
[154.] Libra, Ariesq́ue parem reddunt noctemq́ue, diemq́ue.
[156.] VI.
[157.] VII.
[158.] VIII.
[159.] DVPLEX TABVLA, QVA PARTES AEQVA-toris in tempus: & contra tempus in partes Aequa-toris conuertuntur.
[160.] CONVERSIO \\ gradum, minutorum, & \\ ſecundorum Aequatoris \\ in horas, minuta, ſecun- \\ da, & tertia. CONVERSIO \\ horarum, minutorum, \\ ſecundorum, & tertio- \\ rum in gradus, minuta, \\ & ſecunda Aequatoris.
[161.] VSVS TABVLARVM PRÆCEDENTIVM.
[162.] DE ZODIACO CIRCVLO.
[163.] COMMENTARIVS.
[164.] COMMENTARIVS.
[165.] COMMENTARIVS.
[166.] COMMENTARIVS.
[167.] COMMENTARIVS.
[168.] TABELLA CONTINENS NOMINA DVODECIM partium Aſſis, earumque ualorem.
[169.] COMMENTARIVS.
[170.] COMMENTARIVS.
< >
page |< < (223) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div444" type="section" level="1" n="138">
          <pb o="223" file="259" n="260" rhead="Ioan. de Sacro Boſco."/>
        </div>
        <div xml:id="echoid-div445" type="section" level="1" n="139">
          <head xml:id="echoid-head144" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s9048" xml:space="preserve">
              <emph style="sc">Circvli</emph>
            in ſphęra non maximi ſe inuicem ſecantes, ſe mutuo biſariam
              <lb/>
            non ſecant. </s>
            <s xml:id="echoid-s9049" xml:space="preserve">Nam ſi mutuo ſe bifariam ſecarent, eſſent ipſi per propoſ. </s>
            <s xml:id="echoid-s9050" xml:space="preserve">17. </s>
            <s xml:id="echoid-s9051" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9052" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s9053" xml:space="preserve">Theodoſij, circuli maximi, quod eſt contra hypotheſim. </s>
            <s xml:id="echoid-s9054" xml:space="preserve">Poteſt tamen unus eo
              <lb/>
            rum diuidi aliquando bifariam, ſed cum hoc accidit, alter tunc nequaquam bi
              <lb/>
            fariam ſecabitur, niſi ambo circuli ſint maximi.</s>
            <s xml:id="echoid-s9055" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div446" type="section" level="1" n="140">
          <head xml:id="echoid-head145" xml:space="preserve">IIII.</head>
          <p>
            <s xml:id="echoid-s9056" xml:space="preserve">
              <emph style="sc">Inter</emph>
            cir culos ſphęræ non maximos ſolum ij ſunt æquales inter ſe, qui
              <lb/>
            æqualiter a centro ſphærę remouentur. </s>
            <s xml:id="echoid-s9057" xml:space="preserve">Et contra circuli non maximi inter ſe
              <lb/>
            ęquales ęqualiter recedunt à centro ſphęræ. </s>
            <s xml:id="echoid-s9058" xml:space="preserve">Vtrumque demonſtratur à Theo
              <lb/>
            doſio lib. </s>
            <s xml:id="echoid-s9059" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9060" xml:space="preserve">prepoſ. </s>
            <s xml:id="echoid-s9061" xml:space="preserve">6.</s>
            <s xml:id="echoid-s9062" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div447" type="section" level="1" n="141">
          <head xml:id="echoid-head146" xml:space="preserve">V.</head>
          <p>
            <s xml:id="echoid-s9063" xml:space="preserve">
              <emph style="sc">Omnis</emph>
            circulus maximus in ſphęra tranſiens per polos alterius circuli
              <lb/>
            ſiue maximi, ſiue non maximi, diuidit eum bifariam, & </s>
            <s xml:id="echoid-s9064" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s9065" xml:space="preserve">Et
              <lb/>
            contra circulus in ſp hæra diuidens alium circulum bifariam, & </s>
            <s xml:id="echoid-s9066" xml:space="preserve">ad angulos re-
              <lb/>
            ctos eſt, circulus maximus, inceditq́; </s>
            <s xml:id="echoid-s9067" xml:space="preserve">per polos illius. </s>
            <s xml:id="echoid-s9068" xml:space="preserve">Illud demonſtrat Theo.
              <lb/>
            </s>
            <s xml:id="echoid-s9069" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9070" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9071" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s9072" xml:space="preserve">15. </s>
            <s xml:id="echoid-s9073" xml:space="preserve">Hoc uero in ſcholio eiuſdem propos. </s>
            <s xml:id="echoid-s9074" xml:space="preserve">theoremate 3. </s>
            <s xml:id="echoid-s9075" xml:space="preserve">a nobis. </s>
            <s xml:id="echoid-s9076" xml:space="preserve">
              <lb/>
            eſt demonſtratum.</s>
            <s xml:id="echoid-s9077" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div448" type="section" level="1" n="142">
          <head xml:id="echoid-head147" xml:space="preserve">VI.</head>
          <p>
            <s xml:id="echoid-s9078" xml:space="preserve">
              <emph style="sc">Omnis</emph>
            circulus maximus in ſphęra, per cuius polos tranſit alius circulus
              <lb/>
            in ſphęra maximus, tranſit uiciſſi@@ per polos illius. </s>
            <s xml:id="echoid-s9079" xml:space="preserve">Hoc eſt demonſtratum à
              <lb/>
            nobis theoremate 1. </s>
            <s xml:id="echoid-s9080" xml:space="preserve">ſcholijs propoſ. </s>
            <s xml:id="echoid-s9081" xml:space="preserve">15. </s>
            <s xml:id="echoid-s9082" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9083" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9084" xml:space="preserve">Theodoſij.</s>
            <s xml:id="echoid-s9085" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div449" type="section" level="1" n="143">
          <head xml:id="echoid-head148" xml:space="preserve">VII.</head>
          <p>
            <s xml:id="echoid-s9086" xml:space="preserve">
              <emph style="sc">Circvlvs</emph>
            in ſphęra maximus, qui aliquem circulum non maximum
              <lb/>
            tangit, tanget quoque alium non maximum illi ęqualem, & </s>
            <s xml:id="echoid-s9087" xml:space="preserve">parallelũ. </s>
            <s xml:id="echoid-s9088" xml:space="preserve">Quod
              <lb/>
            quidem oſtendit Theodoſius lib. </s>
            <s xml:id="echoid-s9089" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9090" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s9091" xml:space="preserve">6.</s>
            <s xml:id="echoid-s9092" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div450" type="section" level="1" n="144">
          <head xml:id="echoid-head149" xml:space="preserve">VIII.</head>
          <p>
            <s xml:id="echoid-s9093" xml:space="preserve">
              <emph style="sc">Circvlvs</emph>
            in ſphęra maximus ſecãs circulos non maximos non per po
              <lb/>
            los eorum, hoc eſt, oblique, ſecat illos in partes inæquales, ita tamen, ut ęqua-
              <lb/>
            lium, ac parallelorum circulorum ſegmenta alterna inter ſe ſint ęqualia. </s>
            <s xml:id="echoid-s9094" xml:space="preserve">Hoc
              <lb/>
            perſpicuum eſt ex 19. </s>
            <s xml:id="echoid-s9095" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s9096" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9097" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9098" xml:space="preserve">Theodoſij.</s>
            <s xml:id="echoid-s9099" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div451" type="section" level="1" n="145">
          <head xml:id="echoid-head150" xml:space="preserve">IX.</head>
          <p>
            <s xml:id="echoid-s9100" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            tres circuli in ſphęra maximi ſe mutuo ſecant ad angulos
              <lb/>
            rectos, erunt duo poli cuiuslibet illorum præciſe in communibus ſectionibus
              <lb/>
            circunfer entiarum aliorum duorum. </s>
            <s xml:id="echoid-s9101" xml:space="preserve">Et contra, quando ſunt circuli maximi
              <lb/>
            in ſphæra, ita ut duo poli cuiuſuis illorum reperiantur in communibus ſectio-
              <lb/>
            nibus aliorum duorum, ſecabunt ſe mutuo ad angulos rectos. </s>
            <s xml:id="echoid-s9102" xml:space="preserve">Quorum utrun
              <lb/>
            que facile deduci poteſt ex Theodoſio, ſeu proprietatibus adductis, uidelicet
              <lb/>
            ex 5. </s>
            <s xml:id="echoid-s9103" xml:space="preserve">& </s>
            <s xml:id="echoid-s9104" xml:space="preserve">6.</s>
            <s xml:id="echoid-s9105" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9106" xml:space="preserve">
              <emph style="sc">Exemplvm</emph>
            quoque utriuſque habes in ſphæra materiali. </s>
            <s xml:id="echoid-s9107" xml:space="preserve">Si enim
              <lb/>
            Æquatuor, Meridianus, & </s>
            <s xml:id="echoid-s9108" xml:space="preserve">Horizon, ita adaptẽtur, ut ſe mutuo ad angulos re
              <lb/>
            ctos ſecent, quod tum demum fiet, cum uterque mundi polus præciſe in Ho-
              <lb/>
            rizonte iacebit, ficut accidit in ſphęra recta) uidebis polos Æquatoris eſſe in
              <lb/>
            communibus ſectiouibus Meridiani, atque Horizontis; </s>
            <s xml:id="echoid-s9109" xml:space="preserve">polos Meridiani in
              <lb/>
            communibus ſectionibus Aequatoris Horizontisq́ue; </s>
            <s xml:id="echoid-s9110" xml:space="preserve">polos denique Horizon
              <lb/>
            tis in communibus ſectionibus Aequatoris, ac Meridiani, &</s>
            <s xml:id="echoid-s9111" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9112" xml:space="preserve">Citauimus </s>
          </p>
        </div>
      </text>
    </echo>