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    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div173" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s6131" xml:space="preserve">
              <pb file="0076" n="76" rhead="GENVINVS VSVS"/>
            ducetur inuentum tertium, ſcilicet 105. </s>
            <s xml:id="echoid-s6132" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6133" xml:space="preserve">quod ſemper etiam maius eſt 90. </s>
            <s xml:id="echoid-s6134" xml:space="preserve">ſiquidẽ ſe-
              <lb/>
            cundum eo eſt maius, ſubduco igitur inuentum hoc de ſemicirculo. </s>
            <s xml:id="echoid-s6135" xml:space="preserve">& </s>
            <s xml:id="echoid-s6136" xml:space="preserve">remanent in reſi-
              <lb/>
            duo 75. </s>
            <s xml:id="echoid-s6137" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6138" xml:space="preserve">ſinus eius eſt 96592, qui quia maior etiã diuiſor eſt, iam duco ſinũ primi in-
              <lb/>
            uenti. </s>
            <s xml:id="echoid-s6139" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6140" xml:space="preserve">66145. </s>
            <s xml:id="echoid-s6141" xml:space="preserve">in totũ, & </s>
            <s xml:id="echoid-s6142" xml:space="preserve">productũ diuido in ipſum diuiſorẽ, ꝓueniẽt in q̊tiente 68479.
              <lb/>
            </s>
            <s xml:id="echoid-s6143" xml:space="preserve">cuius arcus eſt 43. </s>
            <s xml:id="echoid-s6144" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6145" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6146" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6147" xml:space="preserve">arcus ille circuli uerticalis inter zenith & </s>
            <s xml:id="echoid-s6148" xml:space="preserve">circulum poſitio
              <lb/>
            nis tranſeuntem per corpus Solis. </s>
            <s xml:id="echoid-s6149" xml:space="preserve">Verum hæc quæ diximus omnia, de ſtellis & </s>
            <s xml:id="echoid-s6150" xml:space="preserve">punctis
              <lb/>
            illis uera ſunt, quæ ſupra horizontem cõſpiciuntur: </s>
            <s xml:id="echoid-s6151" xml:space="preserve">ſin a ũt ſub horizonte fuerint, tunc ti
              <lb/>
            bi propone punctum diametraliter ei oppoſitum, ut ſi uelim ſcire, quantum circulus poſi
              <lb/>
            tionũſub terra, qui ꝑ 2. </s>
            <s xml:id="echoid-s6152" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6153" xml:space="preserve">26. </s>
            <s xml:id="echoid-s6154" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6155" xml:space="preserve">♐ ducitur, à zenith diſtet, adſumo tũc mihi. </s>
            <s xml:id="echoid-s6156" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6157" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6158" xml:space="preserve">26. </s>
            <s xml:id="echoid-s6159" xml:space="preserve">
              <lb/>
            mi. </s>
            <s xml:id="echoid-s6160" xml:space="preserve">II, & </s>
            <s xml:id="echoid-s6161" xml:space="preserve">cũ eo ꝓcedo per oĩa operando ut ſupra, & </s>
            <s xml:id="echoid-s6162" xml:space="preserve">ꝓdibit tandem mihi quæſitum.</s>
            <s xml:id="echoid-s6163" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div175" type="section" level="1" n="91">
          <head xml:id="echoid-head95" xml:space="preserve">PRONVNCIATVM LXXIX.</head>
          <p>
            <s xml:id="echoid-s6164" xml:space="preserve">Altitudinem poli arctici ſuper ſemicirculum poſitionis breuiſsime & </s>
            <s xml:id="echoid-s6165" xml:space="preserve">ex-
              <lb/>
            peditiſsime inueſtigare.</s>
            <s xml:id="echoid-s6166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6167" xml:space="preserve">Altitudo illa poliſuꝑ ſemicirculũ poſitiõis nihil aliud eſt ̈ diſtantia poli arctici ſecun
              <lb/>
              <note position="left" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve">
                <emph style="it">Quid ſit al</emph>
                <lb/>
                <emph style="it">titudo poli</emph>
                <lb/>
                <emph style="it">ſuper ſemi-</emph>
                <lb/>
                <emph style="it">arculum po</emph>
                <lb/>
                <emph style="it">ſitionis.</emph>
              </note>
            dum circulum maiorẽ à ſemicirculo poſitionis, qui quidẽ circulus maior ſuꝑ ſemicirculũ
              <lb/>
            poſitionis ducitur ad angulos rectos. </s>
            <s xml:id="echoid-s6168" xml:space="preserve">Ea altitudo multũ ꝓderit ad dirigendos quin ſi-
              <lb/>
            gnificatores, ̈uis ita loꝗ Pontanus nõ ꝑmittat, nõ libet tamẽ hic à priſco uocabulo re-
              <lb/>
            cedere, melius quidẽ diceretur peragratio ſiue permeatio gradus aſcendentis, unde inqui
              <lb/>
            ritur quicquid accidit in corpore. </s>
            <s xml:id="echoid-s6169" xml:space="preserve">Peragratio igitur Solis facit ad quærendũ dignitates,
              <lb/>
            exaltationes honoris & </s>
            <s xml:id="echoid-s6170" xml:space="preserve">regni ipſius nati, gradus aũt ☽ peragratio fit propter eſſe animæ,
              <lb/>
            corporis, at coniugij. </s>
            <s xml:id="echoid-s6171" xml:space="preserve">Quarta dehinc peragratio ſiue directio partis fortunæ, ſiue horo-
              <lb/>
            ſcopi gradus ☽ fit propter acquiſitiones & </s>
            <s xml:id="echoid-s6172" xml:space="preserve">profectus ſubſtantiæ. </s>
            <s xml:id="echoid-s6173" xml:space="preserve">Vltima aũt quæ & </s>
            <s xml:id="echoid-s6174" xml:space="preserve">gra
              <lb/>
            dus eſt ipſius medij cœli, fit ꝓpter magiſteriũ & </s>
            <s xml:id="echoid-s6175" xml:space="preserve">reliquas particulares diſpoſitiones. </s>
            <s xml:id="echoid-s6176" xml:space="preserve">Pro-
              <lb/>
              <note position="left" xlink:label="note-0076-02" xlink:href="note-0076-02a" xml:space="preserve">
                <emph style="it">Qua ratio</emph>
                <lb/>
                <emph style="it">ne poſitio</emph>
                <lb/>
                <emph style="it">circuli ſit</emph>
                <lb/>
                <emph style="it">inuenta.</emph>
              </note>
            pter eiuſmodi directiones ſiue ꝓfectiones inuẽtus eſt circulus poſitionũ, & </s>
            <s xml:id="echoid-s6177" xml:space="preserve">altitudo eius
              <lb/>
            reperta. </s>
            <s xml:id="echoid-s6178" xml:space="preserve">Porrò inquiſita iã ex ſuperiori ꝓnunc, diſtantiaà ſemicirculi à uertice capitis ſiue
              <lb/>
            zenith horizõtis in circulo uerticali, duc ſinum diſtantiæ huius in ſinũ latitudinis regio
              <lb/>
            nis, ꝓductũ diuide in ſinũ, & </s>
            <s xml:id="echoid-s6179" xml:space="preserve">arcus quotientis dabit altitudinẽ poliſeptentrionalis
              <lb/>
            quæſitã ſuꝑ ſemicirculũ poſitiõis. </s>
            <s xml:id="echoid-s6180" xml:space="preserve">?</s>
            <s xml:id="echoid-s6181" xml:space="preserve">? Exemplũ hoc habe. </s>
            <s xml:id="echoid-s6182" xml:space="preserve">Ex ſuꝑiori pronunc, inueni ad
              <lb/>
              <note position="left" xlink:label="note-0076-03" xlink:href="note-0076-03a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſcopi.</emph>
              </note>
            horã intronziationis etiã diſtantiã ſemicirculi poſitionis à zenith, qui ductus eſt ꝑ gradũ
              <lb/>
            ſiue locum Solis 43. </s>
            <s xml:id="echoid-s6183" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6184" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6185" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6186" xml:space="preserve">ſinum eius 68479. </s>
            <s xml:id="echoid-s6187" xml:space="preserve">duco in ſinum altitudinis poli 48. </s>
            <s xml:id="echoid-s6188" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s6189" xml:space="preserve">20. </s>
            <s xml:id="echoid-s6190" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6191" xml:space="preserve">ita ut eſt Auguſtæ, ſinu eius 74702. </s>
            <s xml:id="echoid-s6192" xml:space="preserve">diuiſo in perfectum, produco 51155. </s>
            <s xml:id="echoid-s6193" xml:space="preserve">cuius ar-
              <lb/>
            cus eſt 30. </s>
            <s xml:id="echoid-s6194" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6195" xml:space="preserve">46. </s>
            <s xml:id="echoid-s6196" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6197" xml:space="preserve">altitudo illa poli ſuper ſemicirculum poſitionis quæſita.</s>
            <s xml:id="echoid-s6198" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div177" type="section" level="1" n="92">
          <head xml:id="echoid-head96" xml:space="preserve">PRONVNCIATVM LXXX.</head>
          <p>
            <s xml:id="echoid-s6199" xml:space="preserve">Horam diurnã ex altitudine Solis ſuꝑ horizõtẽ in omni regione cõijcere.</s>
            <s xml:id="echoid-s6200" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6201" xml:space="preserve">Habita altitudine Solis ſuꝑ horizontẽ, q̃re etiã declinationẽ gradus ☉(sun) ꝑ 5. </s>
            <s xml:id="echoid-s6202" xml:space="preserve">huius, & </s>
            <s xml:id="echoid-s6203" xml:space="preserve">ſi
              <lb/>
            declinatio fuerit ſeptẽtrionalis, adde eã cõplemẽto altitudinis poli, uiciſsim ſubtrahe eã
              <lb/>
            ſi ſit Sol in ſigno meridionali, & </s>
            <s xml:id="echoid-s6204" xml:space="preserve">ꝓueniet altitudo meridiana. </s>
            <s xml:id="echoid-s6205" xml:space="preserve">Deinde duc ſinũ altitudinis
              <lb/>
            huius meridianæ in ſinũ totũ, & </s>
            <s xml:id="echoid-s6206" xml:space="preserve">diuide ꝓductũ in ſinũ cõplementi altitudinis poli, quo-
              <lb/>
            tientẽ dic inuentũ primũ. </s>
            <s xml:id="echoid-s6207" xml:space="preserve">Poſtea duc etiã ſinũ altitudinis Solis ſupra horizontẽ in ſinum
              <lb/>
              <note position="left" xlink:label="note-0076-04" xlink:href="note-0076-04a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">primum.</emph>
              </note>
            totũ, & </s>
            <s xml:id="echoid-s6208" xml:space="preserve">diuide ꝓductũ in ſinũ cõplementi altitudinis poli, quotiens erit inuentũ ſecundũ.
              <lb/>
            </s>
            <s xml:id="echoid-s6209" xml:space="preserve">Atqui hoc inuentum ſecundũ inuenire etiã potes hoc modo. </s>
            <s xml:id="echoid-s6210" xml:space="preserve">Si ſinũ altitudinis Solis du
              <lb/>
            cas in inuentũ primũ, ꝓductũ uero diuidas in ſinũ altitudinis meridinæ, quotiens ille da-
              <lb/>
            bit quo inuentũ ſecundũ. </s>
            <s xml:id="echoid-s6211" xml:space="preserve">Vtro hoc inuẽto habito, ſubtrahe ſecundũ à priori, ſemꝑem̃
              <lb/>
              <note position="left" xlink:label="note-0076-05" xlink:href="note-0076-05a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum.</emph>
              </note>
            illud eſt minus, reliquum rurſus duc in totũ, & </s>
            <s xml:id="echoid-s6212" xml:space="preserve">ꝓductũ diuide in ſinũ cõplemẽti declina-
              <lb/>
            tionis gradus Solis. </s>
            <s xml:id="echoid-s6213" xml:space="preserve">q̊tiens uocabit̃ inuentũ tertiũ. </s>
            <s xml:id="echoid-s6214" xml:space="preserve">q̊d ſi minus fuerit ſinu toto, ſubtrahe
              <lb/>
            ipſum à toto ſinu, & </s>
            <s xml:id="echoid-s6215" xml:space="preserve">habebis arcũ tꝑis ante uel poſt meridiẽ. </s>
            <s xml:id="echoid-s6216" xml:space="preserve">Sed ſi extiterit hoc inuentũ
              <lb/>
            tertiũ maius toto ſinu, ſubtrahe hinc ſinũ totũ, & </s>
            <s xml:id="echoid-s6217" xml:space="preserve">arcũ reſidui adde ad 90. </s>
            <s xml:id="echoid-s6218" xml:space="preserve">ſi´ etiã babebis
              <lb/>
            arcum antemeridianũ uel pomeridianũ, eum ſi diuides per 15. </s>
            <s xml:id="echoid-s6219" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6220" xml:space="preserve">iamiã confeceris ho
              <lb/>
            ras. </s>
            <s xml:id="echoid-s6221" xml:space="preserve">Et ſi tẽpus illud fuerit antemeridiẽ, totidẽ horas cõnumera retrorſum uerſus à 12. </s>
            <s xml:id="echoid-s6222" xml:space="preserve">ho
              <lb/>
              <note position="left" xlink:label="note-0076-06" xlink:href="note-0076-06a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſcopi.</emph>
              </note>
            ra: </s>
            <s xml:id="echoid-s6223" xml:space="preserve">ſed ſi ſit pomeridianũ, adde tot horas ad 12. </s>
            <s xml:id="echoid-s6224" xml:space="preserve">hoc eſt meridianã horam, & </s>
            <s xml:id="echoid-s6225" xml:space="preserve">ꝓueniet ho-
              <lb/>
            ra diei quæſita. </s>
            <s xml:id="echoid-s6226" xml:space="preserve">?</s>
            <s xml:id="echoid-s6227" xml:space="preserve">? Exemplũ ni ſit etiã moleſtum tibi, eſto ut hora intronizatiõis </s>
          </p>
        </div>
      </text>
    </echo>
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