Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis
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          <p>
            <s xml:id="echoid-s6683" xml:space="preserve">
              <pb file="0081" n="81" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
            æquatoris inter aſcenſiones ipſarum concluſum. </s>
            <s xml:id="echoid-s6684" xml:space="preserve">Mox ducito ſinum complementi de-
              <lb/>
              <note position="right" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">
                <emph style="it">Illud inueni</emph>
                <lb/>
                <emph style="it">es later ali-</emph>
                <lb/>
                <emph style="it">ter.</emph>
              </note>
            clinationis minoris in ſinum differentiæ aſcenſionum illarum, productum diuide in to-
              <lb/>
            tum, arcum porrò quotientis iſtius uocabimus inuentum primum. </s>
            <s xml:id="echoid-s6685" xml:space="preserve">Poſtea ſinum mino-
              <lb/>
            rem ex ſinu minoris declinationis & </s>
            <s xml:id="echoid-s6686" xml:space="preserve">complementi huius primi inuenti duc in totum, & </s>
            <s xml:id="echoid-s6687" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">primum.</emph>
              </note>
            productum diuide in maiorem, arcum quotientis ſubtrahe de declinatione maiori, reſi-
              <lb/>
            duum dic inuentum ſecundum. </s>
            <s xml:id="echoid-s6688" xml:space="preserve">Præterea duc ſinum complementi ſecundi inuenti in ſi-
              <lb/>
              <note position="right" xlink:label="note-0081-03" xlink:href="note-0081-03a" xml:space="preserve">
                <emph style="it">Hoc area-</emph>
                <lb/>
                <emph style="it">tim quæren</emph>
                <lb/>
                <emph style="it">ti pater.</emph>
              </note>
            dum cõplementi primi inuenti, & </s>
            <s xml:id="echoid-s6689" xml:space="preserve">diuide productum in totum, arcus quotientis pordu-
              <lb/>
            cet ipſas diſtantias ſtellarum. </s>
            <s xml:id="echoid-s6690" xml:space="preserve">Inſuper adhuc ſinum primi inuenti duc in totum, produ-
              <lb/>
              <note position="right" xlink:label="note-0081-04" xlink:href="note-0081-04a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum.</emph>
              </note>
            ctum diuide in ſinum diſtantiæ, & </s>
            <s xml:id="echoid-s6691" xml:space="preserve">arcus quotientis dabit inuentum tertium. </s>
            <s xml:id="echoid-s6692" xml:space="preserve">Ad extre-
              <lb/>
            mum duc etiam ſinum inuenti huius tertij in ſinum complementi declinationis maioris,
              <lb/>
              <note position="right" xlink:label="note-0081-05" xlink:href="note-0081-05a" xml:space="preserve">
                <emph style="it">Primum ba</emph>
                <lb/>
                <emph style="it">betur ꝑ late</emph>
                <lb/>
                <emph style="it">ra, ſecundũ</emph>
                <lb/>
                <emph style="it">uero per</emph>
                <lb/>
                <emph style="it">aream.</emph>
              </note>
            producto hinc in totum diuiſo, arcus quotientis monſtrabit altitudinem poli quæſitam.</s>
            <s xml:id="echoid-s6693" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6694" xml:space="preserve">?</s>
            <s xml:id="echoid-s6695" xml:space="preserve">? Anima duerte etiam hic exemplum quod tibi dabimus. </s>
            <s xml:id="echoid-s6696" xml:space="preserve">Eſto ut Auguſtæ in loco intro
              <lb/>
            nizat onis uiſæ ſint ſtellæ duæ in horizontem ſimul oriri, quarum etiam loca ſint cogni-
              <lb/>
            ta, & </s>
            <s xml:id="echoid-s6697" xml:space="preserve">altera quidem habuerit in declinatione 18. </s>
            <s xml:id="echoid-s6698" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6699" xml:space="preserve">11. </s>
            <s xml:id="echoid-s6700" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6701" xml:space="preserve">altera autem 34. </s>
            <s xml:id="echoid-s6702" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6703" xml:space="preserve">19. </s>
            <s xml:id="echoid-s6704" xml:space="preserve">mi.
              <lb/>
            </s>
            <s xml:id="echoid-s6705" xml:space="preserve">quæ eſt declinatio maior. </s>
            <s xml:id="echoid-s6706" xml:space="preserve">Differentia aſcenſionum rectarum ſit 28. </s>
            <s xml:id="echoid-s6707" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6708" xml:space="preserve">25. </s>
            <s xml:id="echoid-s6709" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6710" xml:space="preserve">iam ſinũ
              <lb/>
            complementi minoris declinationis 95006. </s>
            <s xml:id="echoid-s6711" xml:space="preserve">duco in ſinum differentiæ aſcenſionum re-
              <lb/>
            ctarum ſcilicet 47588. </s>
            <s xml:id="echoid-s6712" xml:space="preserve">quotientem diuido in totum, is eſt 45211. </s>
            <s xml:id="echoid-s6713" xml:space="preserve">arcus ipſius 26. </s>
            <s xml:id="echoid-s6714" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6715" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0081-06" xlink:href="note-0081-06a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſcopi.</emph>
              </note>
            53. </s>
            <s xml:id="echoid-s6716" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6717" xml:space="preserve">dicetur inuentum primum. </s>
            <s xml:id="echoid-s6718" xml:space="preserve">ſinum minoris declinationis ſcilicet 31210. </s>
            <s xml:id="echoid-s6719" xml:space="preserve">duco in
              <lb/>
            totum, productum diuido in ſinum complementi primi inuenti ſcilicet 89192. </s>
            <s xml:id="echoid-s6720" xml:space="preserve">& </s>
            <s xml:id="echoid-s6721" xml:space="preserve">diuido
              <lb/>
            productum in totum, quotiens producit 34991. </s>
            <s xml:id="echoid-s6722" xml:space="preserve">arcus eius eſt 20. </s>
            <s xml:id="echoid-s6723" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6724" xml:space="preserve">29. </s>
            <s xml:id="echoid-s6725" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6726" xml:space="preserve">quo ſubtra
              <lb/>
            cto à maiori declinatione ſtellarum, ſcilicet 34. </s>
            <s xml:id="echoid-s6727" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6728" xml:space="preserve">19. </s>
            <s xml:id="echoid-s6729" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6730" xml:space="preserve">remanent 13. </s>
            <s xml:id="echoid-s6731" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6732" xml:space="preserve">50. </s>
            <s xml:id="echoid-s6733" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6734" xml:space="preserve">in-
              <lb/>
            uentum ſecundum. </s>
            <s xml:id="echoid-s6735" xml:space="preserve">Porrò ſinum complem@nti huius ſecundi inuenti 97099. </s>
            <s xml:id="echoid-s6736" xml:space="preserve">duco in ſinũ
              <lb/>
            complementi primi inuenti, ſcilicet 89192. </s>
            <s xml:id="echoid-s6737" xml:space="preserve">quotientem diuido in totum, eſt autem quo-
              <lb/>
            tiens 86604. </s>
            <s xml:id="echoid-s6738" xml:space="preserve">arcus ipſius eſt 60. </s>
            <s xml:id="echoid-s6739" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6740" xml:space="preserve">complementum uero 30. </s>
            <s xml:id="echoid-s6741" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6742" xml:space="preserve">diſtantia illa duarum
              <lb/>
            ſtellarum. </s>
            <s xml:id="echoid-s6743" xml:space="preserve">lam quo duco ſinum primi inuenti 45211. </s>
            <s xml:id="echoid-s6744" xml:space="preserve">in totum, & </s>
            <s xml:id="echoid-s6745" xml:space="preserve">diuido in ſinum di-
              <lb/>
            ſtantiæ, quotiens eſt 90422. </s>
            <s xml:id="echoid-s6746" xml:space="preserve">arcus illius 64, gra. </s>
            <s xml:id="echoid-s6747" xml:space="preserve">44. </s>
            <s xml:id="echoid-s6748" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6749" xml:space="preserve">inuentum tertium. </s>
            <s xml:id="echoid-s6750" xml:space="preserve">Poſtremo du-
              <lb/>
            co & </s>
            <s xml:id="echoid-s6751" xml:space="preserve">ſinum complementi maioris declinationis 82593. </s>
            <s xml:id="echoid-s6752" xml:space="preserve">in ſinum tertij inuenti 90434. </s>
            <s xml:id="echoid-s6753" xml:space="preserve">ꝓ
              <lb/>
            ductum diuido in totum, & </s>
            <s xml:id="echoid-s6754" xml:space="preserve">quotiens erit 74692. </s>
            <s xml:id="echoid-s6755" xml:space="preserve">arcus eius 48. </s>
            <s xml:id="echoid-s6756" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6757" xml:space="preserve">20. </s>
            <s xml:id="echoid-s6758" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6759" xml:space="preserve">altitudo iſta
              <lb/>
            polinon ſine magnainduſtria ad locum intronizationis quæſita & </s>
            <s xml:id="echoid-s6760" xml:space="preserve">inuenta.</s>
            <s xml:id="echoid-s6761" xml:space="preserve"/>
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        <div xml:id="echoid-div197" type="section" level="1" n="101">
          <head xml:id="echoid-head105" xml:space="preserve">PRONVNCIATVM LXXXIX.</head>
          <p>
            <s xml:id="echoid-s6762" xml:space="preserve">Punctum iſtud eclypticæ cum quo ſtella ſeu punctum quoduis cœli me-
              <lb/>
            dium tangit, perſcrutari.</s>
            <s xml:id="echoid-s6763" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6764" xml:space="preserve">Ex ſuperiori pronunciato quære aſcenſionem rectam ſtellæ, deinde per 8. </s>
            <s xml:id="echoid-s6765" xml:space="preserve">pronuncia
              <lb/>
            tum quære gradum ſiue punctum eclypticæ, qui aſcendit in ſphæra recta unà cum gradu
              <lb/>
              <note position="right" xlink:label="note-0081-07" xlink:href="note-0081-07a" xml:space="preserve">
                <emph style="it">Illud diſces</emph>
                <lb/>
                <emph style="it">ſecundum</emph>
                <lb/>
                <emph style="it">latera.</emph>
              </note>
            æquatoris ſiue aſcenſione recta ſtellæ, & </s>
            <s xml:id="echoid-s6766" xml:space="preserve">inuenies punctum hoc modo. </s>
            <s xml:id="echoid-s6767" xml:space="preserve">Duc ſinum com-
              <lb/>
            plementi aſcenſionis rectæ in ſinum maximæ declinationis, productum diuide in ſinum
              <lb/>
            totum, & </s>
            <s xml:id="echoid-s6768" xml:space="preserve">arcum quotientis ſubtrahe de 90. </s>
            <s xml:id="echoid-s6769" xml:space="preserve">ſinus reſidui deinceps erit diuiſor. </s>
            <s xml:id="echoid-s6770" xml:space="preserve">Mox ubi
              <lb/>
            ſinum aſcenſionis recte duxeris in totum, & </s>
            <s xml:id="echoid-s6771" xml:space="preserve">productum in ipſum diuiſeris diuiſorem,
              <lb/>
              <note position="right" xlink:label="note-0081-08" xlink:href="note-0081-08a" xml:space="preserve">
                <emph style="it">Hoc area-</emph>
                <lb/>
                <emph style="it">tim quæren</emph>
                <lb/>
                <emph style="it">ti patet.</emph>
              </note>
            arcus quotientis oſtendet arcum eclypticæ, cuius extremitas mediat cœlum unà cum
              <lb/>
            ſtella propoſita. </s>
            <s xml:id="echoid-s6772" xml:space="preserve">Sin autem aſcenſio recta maior fuerit quàm 90. </s>
            <s xml:id="echoid-s6773" xml:space="preserve">operare cum comple-
              <lb/>
            mento eius, & </s>
            <s xml:id="echoid-s6774" xml:space="preserve">arcum inuentum computa â principio Libræ contra ordinem ſignorum.
              <lb/>
            </s>
            <s xml:id="echoid-s6775" xml:space="preserve">Et ſi aſcenſio etiamſi amplior fuerit quàm 180. </s>
            <s xml:id="echoid-s6776" xml:space="preserve">tunc arcum ipſum ſupputa à principio ♎
              <lb/>
            ſecundum ſeriem ſignorum: </s>
            <s xml:id="echoid-s6777" xml:space="preserve">ſed ſi aſcenſio illa maior fuerit quàm 270. </s>
            <s xml:id="echoid-s6778" xml:space="preserve">numera arcum
              <lb/>
            inuentum à principio Arietis contra ſignorum ordinem. </s>
            <s xml:id="echoid-s6779" xml:space="preserve">?</s>
            <s xml:id="echoid-s6780" xml:space="preserve">? Exemplum hoc conſidera
              <lb/>
              <note position="right" xlink:label="note-0081-09" xlink:href="note-0081-09a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoopi.</emph>
              </note>
            Aſſume iterum quartam ſtellam Agitatoris, quæ ſub ipſam horam intronizationis ferè
              <lb/>
            cum Sole in uno circulo poſitionis extitit, aſcenſio eius recta quam ex præcedentibus in
              <lb/>
            ueni, eſt 80. </s>
            <s xml:id="echoid-s6781" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6782" xml:space="preserve">25. </s>
            <s xml:id="echoid-s6783" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6784" xml:space="preserve">Complementum eius 9. </s>
            <s xml:id="echoid-s6785" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6786" xml:space="preserve">35. </s>
            <s xml:id="echoid-s6787" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6788" xml:space="preserve">ſinum ipſius. </s>
            <s xml:id="echoid-s6789" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6790" xml:space="preserve">16648. </s>
            <s xml:id="echoid-s6791" xml:space="preserve">duco
              <lb/>
            in ſinum maximæ declinationis, productum diuido in totum, quotiens eſt 6639. </s>
            <s xml:id="echoid-s6792" xml:space="preserve">arcus il
              <lb/>
            lius 3. </s>
            <s xml:id="echoid-s6793" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6794" xml:space="preserve">49. </s>
            <s xml:id="echoid-s6795" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6796" xml:space="preserve">ſinus autem complementi 99778. </s>
            <s xml:id="echoid-s6797" xml:space="preserve">eſt ipſe diuiſor, ſi iam duxero ſinum
              <lb/>
            aſcenſionis rectæ 80. </s>
            <s xml:id="echoid-s6798" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6799" xml:space="preserve">25. </s>
            <s xml:id="echoid-s6800" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6801" xml:space="preserve">ſcilicet 98604. </s>
            <s xml:id="echoid-s6802" xml:space="preserve">in totum, & </s>
            <s xml:id="echoid-s6803" xml:space="preserve">diuiſero in diuiſorem, quoti-
              <lb/>
            ens exhibebit mihi 98823. </s>
            <s xml:id="echoid-s6804" xml:space="preserve">cuius arcus eſt 81. </s>
            <s xml:id="echoid-s6805" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6806" xml:space="preserve">12. </s>
            <s xml:id="echoid-s6807" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6808" xml:space="preserve">eũ ſi ſupputemà principio ♈,
              <lb/>
            finietur in 21. </s>
            <s xml:id="echoid-s6809" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6810" xml:space="preserve">12. </s>
            <s xml:id="echoid-s6811" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6812" xml:space="preserve">II, cum quo etiam ſtella iſta medium attigit cœli.</s>
            <s xml:id="echoid-s6813" xml:space="preserve"/>
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