Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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        <div xml:id="echoid-div637" type="section" level="1" n="165">
          <p>
            <s xml:id="echoid-s11846" xml:space="preserve">
              <pb o="181" file="0201" n="201" rhead="LIBER SECVNDVS."/>
            ordinatim applicatæ ex dictis punctis tropicorum ſint ad diametrum, perpendiculares) deſcripta
              <lb/>
            erunt aſcendentia ſigna.</s>
            <s xml:id="echoid-s11847" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11848" xml:space="preserve">ALITER deſcribentur aſcendentia ſigna hoc pacto. </s>
            <s xml:id="echoid-s11849" xml:space="preserve">Primum quęrantur puncta Eclipticæ in
              <lb/>
            circulo Meridiano exiſtentia, hoc eſt, mediationes cœli, cum principia ſignorum Zodiaci oriun-
              <lb/>
            tur, & </s>
            <s xml:id="echoid-s11850" xml:space="preserve">eorundem punctorum declinationes. </s>
            <s xml:id="echoid-s11851" xml:space="preserve">Deindeiiſdem ſignorum initiis aſcen dentibus, inue-
              <lb/>
            ſtigentur puncta Eclipticæ in circulo horæ 6. </s>
            <s xml:id="echoid-s11852" xml:space="preserve">à meridie, vel media nocte conſtituta, vna cum eo-
              <lb/>
            rundem declinationibus. </s>
            <s xml:id="echoid-s11853" xml:space="preserve">Quæ omnia ita abſoluemus. </s>
            <s xml:id="echoid-s11854" xml:space="preserve">Ex aſcenſione obliqua principii cuiusli-
              <lb/>
              <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">Quomodo me-
                <lb/>
              diationes cœli,
                <lb/>
              cũ initia ſigno-
                <lb/>
              rum oriuntur,
                <lb/>
              inue ſtigandę
                <lb/>
              ſint.</note>
            bet ſigni (quę vel ex tabulis aſcenſionum obliquarum, quæ in tabulis Directionum Ioan. </s>
            <s xml:id="echoid-s11855" xml:space="preserve">Regiom.
              <lb/>
            </s>
            <s xml:id="echoid-s11856" xml:space="preserve">vel in commentariis noſtris in ſphæram continentur, ſumenda eſt, vel certè ex doctrina ſinuum, vt
              <lb/>
            in cap. </s>
            <s xml:id="echoid-s11857" xml:space="preserve">3. </s>
            <s xml:id="echoid-s11858" xml:space="preserve">ſphęræ præcepimus, & </s>
            <s xml:id="echoid-s11859" xml:space="preserve">ad finem ſcholii huius propoſ. </s>
            <s xml:id="echoid-s11860" xml:space="preserve">oſtendemus, eruenda) quadrans
              <lb/>
              <note position="left" xlink:label="note-0201-02" xlink:href="note-0201-02a" xml:space="preserve">10</note>
            circuli auferatur, hoceſt, grad. </s>
            <s xml:id="echoid-s11861" xml:space="preserve">90. </s>
            <s xml:id="echoid-s11862" xml:space="preserve">adiecto prius integro circulo ad aſcenſionem obliquam, ſi de-
              <lb/>
            tractio fieri nequit, vt in calculo Aſtronomico ſieri ſolet. </s>
            <s xml:id="echoid-s11863" xml:space="preserve">Numerus en im reliquus erit aſcenſio
              <lb/>
            recta puncti Eclipticæ, quod tunc in Meridiano ſupra Horizontem reperitur, quodq́; </s>
            <s xml:id="echoid-s11864" xml:space="preserve">Mediatio-
              <lb/>
            nem cœli dicunt Aſtronomi. </s>
            <s xml:id="echoid-s11865" xml:space="preserve">Quare ex tabula aſcenſionum rectarum, vel ex doctrina, quam in
              <lb/>
            ſcholio ſequenti trademus, punctum illud Eclipticæ notum fiet, cuius punctum oppoſitum in eo-
              <lb/>
            dem Meridiano exiſter infra Horizontem, quod angulum terræ dicere poſſumus cum Aſtrono-
              <lb/>
            mis. </s>
            <s xml:id="echoid-s11866" xml:space="preserve">Huius operationis demonſtratio difficilis non eſt, ſi poſitio Horizontis, Meridiani, Zodiaci,
              <lb/>
            & </s>
            <s xml:id="echoid-s11867" xml:space="preserve">Æ quatoris in ſphæra rectè concipiatur. </s>
            <s xml:id="echoid-s11868" xml:space="preserve">Nam quando aſcenſio obliqua maior fuerit quadran-
              <lb/>
            te, vel quadranti æqualis, perſpicuum eſt, ſi quadransÆ quatoris inter orientem, & </s>
            <s xml:id="echoid-s11869" xml:space="preserve">meridiem poſi-
              <lb/>
            tus ex ea auferatur, relinqui aſcenſionem rectam puncti Eclipticæ cœlum mediantis, nempe di-
              <lb/>
              <note position="left" xlink:label="note-0201-03" xlink:href="note-0201-03a" xml:space="preserve">20</note>
            ſtantiam principii ♈, à Meridiano circulo ſecundum ſignorum ſucceſſionem: </s>
            <s xml:id="echoid-s11870" xml:space="preserve">Quando vero aſcẽ-
              <lb/>
            ſio obliqua quadrante fuerit minor, liquido etiam conſtat, ſi quadrans Aequatoris inter orien-
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s11871" xml:space="preserve">meridiem conſtitutus ab integro circulo dematur, & </s>
            <s xml:id="echoid-s11872" xml:space="preserve">reliquis tribus quadrantibus aſcen-
              <lb/>
            ſio obliqua apponatur, (quod perinde eſt, ac ſi quadrans ab aggregato, quod ex aſcenſione obli-
              <lb/>
            qua, & </s>
            <s xml:id="echoid-s11873" xml:space="preserve">circulo integro fit, detrahatur) conflari aſcenſionem rectam puncti Eclipticæ cœlum me-
              <lb/>
            diantis. </s>
            <s xml:id="echoid-s11874" xml:space="preserve">In ſphæra quoquerecta eadem operatio locum habet, ſi loco aſcenſionis obliquæ aſcen-
              <lb/>
            dentis ſigni accipiatur aſcenſio recta eiuſdem.</s>
            <s xml:id="echoid-s11875" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11876" xml:space="preserve">EXEMPLVM. </s>
            <s xml:id="echoid-s11877" xml:space="preserve">Ad latitudinem grad. </s>
            <s xml:id="echoid-s11878" xml:space="preserve">42. </s>
            <s xml:id="echoid-s11879" xml:space="preserve">qualis ferè eſt Romæ, aſcenſio obliqua prine
              <unsure/>
            i-
              <lb/>
              <note position="right" xlink:label="note-0201-04" xlink:href="note-0201-04a" xml:space="preserve">Exemplum.</note>
            pii ♍, eſt grad. </s>
            <s xml:id="echoid-s11880" xml:space="preserve">141. </s>
            <s xml:id="echoid-s11881" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11882" xml:space="preserve">33. </s>
            <s xml:id="echoid-s11883" xml:space="preserve">ex qua ſi dematur quadrans, hoc eſt, grad. </s>
            <s xml:id="echoid-s11884" xml:space="preserve">90. </s>
            <s xml:id="echoid-s11885" xml:space="preserve">remanent grad. </s>
            <s xml:id="echoid-s11886" xml:space="preserve">51.
              <lb/>
            </s>
            <s xml:id="echoid-s11887" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11888" xml:space="preserve">33. </s>
            <s xml:id="echoid-s11889" xml:space="preserve">pro aſcenſione recta puncti Eclipticæ cœlum mediantis, cum principium ♍, oritur. </s>
            <s xml:id="echoid-s11890" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0201-05" xlink:href="note-0201-05a" xml:space="preserve">30</note>
            Huic autem aſcenſioni rectæ reſpondet in tabula aſcenſionum rectarum (adhibita tamen parte
              <lb/>
            proportionali, vt fieri conſuea
              <unsure/>
            it, quando numerus non præcisè in tabula aliqua continetur)
              <lb/>
            gradus 23. </s>
            <s xml:id="echoid-s11891" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11892" xml:space="preserve">57. </s>
            <s xml:id="echoid-s11893" xml:space="preserve">♉. </s>
            <s xml:id="echoid-s11894" xml:space="preserve">Hoc ergo punctum Eclipticæ in Meridiano tunc reperietur ſupra Ho-
              <lb/>
            rizontem, infra vero Horizontem in eodem Meridiano exiſtet gradus 23. </s>
            <s xml:id="echoid-s11895" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11896" xml:space="preserve">57. </s>
            <s xml:id="echoid-s11897" xml:space="preserve">♏. </s>
            <s xml:id="echoid-s11898" xml:space="preserve">Rurſus
              <lb/>
            obliqua aſcenſio principii ♋, continet grad. </s>
            <s xml:id="echoid-s11899" xml:space="preserve">66. </s>
            <s xml:id="echoid-s11900" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11901" xml:space="preserve">57. </s>
            <s xml:id="echoid-s11902" xml:space="preserve">Cui ſi addatur integer circulus, hoc
              <lb/>
            eſt, grad. </s>
            <s xml:id="echoid-s11903" xml:space="preserve">360. </s>
            <s xml:id="echoid-s11904" xml:space="preserve">fiunt grad. </s>
            <s xml:id="echoid-s11905" xml:space="preserve">426. </s>
            <s xml:id="echoid-s11906" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11907" xml:space="preserve">57. </s>
            <s xml:id="echoid-s11908" xml:space="preserve">à quibus ſi deducantur grad. </s>
            <s xml:id="echoid-s11909" xml:space="preserve">90. </s>
            <s xml:id="echoid-s11910" xml:space="preserve">relinquuntur grad. </s>
            <s xml:id="echoid-s11911" xml:space="preserve">336.
              <lb/>
            </s>
            <s xml:id="echoid-s11912" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11913" xml:space="preserve">57. </s>
            <s xml:id="echoid-s11914" xml:space="preserve">pro aſcenſione recta puncti Eclipticæ mediantis tunc cœlum, cum initium ♋, aſcendit
              <lb/>
            ſupra Horizontem. </s>
            <s xml:id="echoid-s11915" xml:space="preserve">Huic rectæ aſcenſioni reſpondet in tabula aſcenſionum rectarum gradus
              <lb/>
            5. </s>
            <s xml:id="echoid-s11916" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11917" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11918" xml:space="preserve">♓. </s>
            <s xml:id="echoid-s11919" xml:space="preserve">Quare hoc punctum eo tempore in Meridiano ſupra Horizontem exiſtet, angulus
              <lb/>
            autem terræ erit gradus 5. </s>
            <s xml:id="echoid-s11920" xml:space="preserve">
              <emph style="sc">M</emph>
            in. </s>
            <s xml:id="echoid-s11921" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11922" xml:space="preserve">♍. </s>
            <s xml:id="echoid-s11923" xml:space="preserve">Poſtremo in ſphera recta, (vt de hac exemplum etiam af-
              <lb/>
              <note position="left" xlink:label="note-0201-06" xlink:href="note-0201-06a" xml:space="preserve">40</note>
            feramus) aſcenſio recta ♐, complectitur grad. </s>
            <s xml:id="echoid-s11924" xml:space="preserve">237. </s>
            <s xml:id="echoid-s11925" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11926" xml:space="preserve">48. </s>
            <s xml:id="echoid-s11927" xml:space="preserve">Ex hac dempto quadrante, ſuper-
              <lb/>
            ſunt grad. </s>
            <s xml:id="echoid-s11928" xml:space="preserve">147. </s>
            <s xml:id="echoid-s11929" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11930" xml:space="preserve">48. </s>
            <s xml:id="echoid-s11931" xml:space="preserve">pro aſcenſione recta illius puncti Eclipticæ, quod tunc cœlum mediat.
              <lb/>
            </s>
            <s xml:id="echoid-s11932" xml:space="preserve">Cui aſcenſioni conuenit gradus 25. </s>
            <s xml:id="echoid-s11933" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11934" xml:space="preserve">31. </s>
            <s xml:id="echoid-s11935" xml:space="preserve">♌, atque hoc punctum tuncin Meridiano exiſtet
              <lb/>
            ſupra Horizontem, & </s>
            <s xml:id="echoid-s11936" xml:space="preserve">in angulo propterea terræ erit gradus 25. </s>
            <s xml:id="echoid-s11937" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11938" xml:space="preserve">31. </s>
            <s xml:id="echoid-s11939" xml:space="preserve">♒. </s>
            <s xml:id="echoid-s11940" xml:space="preserve">Hac arte compo-
              <lb/>
            ſuimus ſequentem tabellam mediationum cœli, & </s>
            <s xml:id="echoid-s11941" xml:space="preserve">angulorum terræ, oriente principio cuiuſuis
              <lb/>
            ſigni Zodiaci, ad latitudinem grad. </s>
            <s xml:id="echoid-s11942" xml:space="preserve">42. </s>
            <s xml:id="echoid-s11943" xml:space="preserve">in qua etiam adſcripſimus earundem mediationum, & </s>
            <s xml:id="echoid-s11944" xml:space="preserve">
              <lb/>
            angulorum terræ declinationes per doctrinam ſinuum inuentas, vt in coroll. </s>
            <s xml:id="echoid-s11945" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s11946" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11947" xml:space="preserve">præce-
              <lb/>
            dentis libri tradidimus, licet eædem ex tabula declinationum, habita ratione partis proportiona-
              <lb/>
            lis, elici poſſint. </s>
            <s xml:id="echoid-s11948" xml:space="preserve">Perſpicuum autem eſt, declinationes punctorum ſeptentrionalium Eclipticæ
              <lb/>
            eſſe ſeptentrionales, auſtralium verò auſtrales. </s>
            <s xml:id="echoid-s11949" xml:space="preserve">Vnde facile iudicabis, quorumnam puncto-
              <lb/>
              <note position="left" xlink:label="note-0201-07" xlink:href="note-0201-07a" xml:space="preserve">50</note>
            rum declinatio in dicta tabula ſit borealis, & </s>
            <s xml:id="echoid-s11950" xml:space="preserve">quorum auſtralis: </s>
            <s xml:id="echoid-s11951" xml:space="preserve">quod quidem noſſe, magni re-
              <lb/>
            fert, vt ſigna aſcendentia deſcribantur.</s>
            <s xml:id="echoid-s11952" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div642" type="section" level="1" n="166">
          <head xml:id="echoid-head169" xml:space="preserve">VI. Mediationes cœli, & anguli terræ, eorumq́; declinationes, orientibus 12.
            <lb/>
          ſignorum Zodiaci initiis, ad latitudinem grad. 42.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          Signa aſcen- # ♈ # ♉ # ♊ # ♋ # dentia
            <lb/>
          Gradus & # G. M. # G. M. # G. M. # G. M. # Minuta
            <lb/>
          Mediationes # 0. 0. ♑. # 15. 59. ♑. # 6. 3. ♒. # 5. 6. ♓. # cœli
            <lb/>
          Anguli # 0. 0. ♋ # 15. 59. ♋. # 6. 3. ♌. # 5. 6. ♍. # terræ
            <lb/>
          Declina- # 23. 30. # 22. 32. # 18. 48. # 9. 40. # tiones
            <lb/>
          </note>
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