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

Table of contents

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[211.] SCHOLIVM.
Page: 271 (255)
[212.] PROBLEMA 36. PROPOSITIO 36. HOROLOGIVM Antiquum Meridianum conſtituere.
Page: 272 (256)
[213.] SCHOLIVM.
Page: 272 (256)
[214.] DE HOROLOGIIS POLARIBVS. PROBLEMA 37. PROPOSITIO 37.
Page: 272 (256)
[215.] SCHOLIVM.
Page: 274 (258)
[216.] PROBLEMA 38. PROPOSITIO 38.
Page: 274 (258)
[217.] PROBLEMA 39. PROPOSITIO 39.
Page: 276 (260)
[218.] PROBLEMA 40. PROPOSITIO 40.
Page: 276 (260)
[219.] PROBLEMA 41. PROPOSITIO 41.
Page: 278 (262)
[220.] PROBLEMA 42. PROPOSITIO 42.
Page: 280 (264)
[221.] PROBLEMA 43. PROPOSITIO 43.
Page: 281 (265)
[222.] PROBLEMA 44. PROPOSITIO 44.
Page: 281 (265)
[223.] SCHOLIVM.
Page: 282 (266)
[224.] PROBLEMA. 45. PROPOSITIO 45.
Page: 282 (266)
[225.] SCHOLIVM.
Page: 284 (268)
[226.] PROBLEMA 46. PROPOSITIO 46.
Page: 285 (269)
[227.] PROBLEMA 47. PROPOSITIO 47.
Page: 288 (272)
[228.] SCHOLIVM.
Page: 288 (272)
[229.] PROBLEMA 48. PROPOSITIO 48.
Page: 288 (272)
[230.] SCHOLIVM.
Page: 289 (273)
[231.] DE HOROLOGIIS ÆQVINOCTIALIBVS. PROBLEMA 49. PROPOSITIO 49.
Page: 289 (273)
[232.] SCHOLIVM.
Page: 290 (274)
[233.] PROBLEMA 50. PROPOSITIO 50.
Page: 290 (274)
[234.] SCHOLIVM.
Page: 292 (276)
[235.] PROBLEMA 51. PROPOSITIO 51.
Page: 293 (277)
[236.] PROBLEMA 52. PROPOSITIO 52.
Page: 293 (277)
[237.] SCHOLIVM.
Page: 294 (278)
[238.] PROBLEMA 53. PROPOSITIO 53.
Page: 295 (279)
[239.] SCHOLIVM.
Page: 297 (281)
[240.] PROBLEMA 54. PROPOSITIO 54.
Page: 297 (281)
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        <div xml:id="echoid-div659" type="section" level="1" n="170">
          <p style="it">
            <s xml:id="echoid-s12500" xml:space="preserve">
              <pb o="191" file="0211" n="211" rhead="LIBER SECVNDVS."/>
            trabamus, initio facto à maioribus, ſiue poſterioribus, reliquę erunt aſcenſiones rectę omnium punctorum
              <lb/>
            ſecundi quadrantis Eclipticę. </s>
            <s xml:id="echoid-s12501" xml:space="preserve">Rurſus ſi eaſdem ſemicir culo apponamus, facto initio à minoribus, ſiue prio
              <lb/>
            ribus, conficientur aſcenſiones rectæ omnium punctorum tertij quadrantis Eclipticę. </s>
            <s xml:id="echoid-s12502" xml:space="preserve">Si denique eaſdem
              <lb/>
            auferamus ex toto circulo, initio rurſus facto à maioribus, ſiue poſterioribus, remanebunt aſcenſiones re-
              <lb/>
            ctę omnium punctorum vltimi quadrantis Eclipticę. </s>
            <s xml:id="echoid-s12503" xml:space="preserve">Itaque totus labor poſitus eſt in perueſtigatione
              <lb/>
            aſcenſionum rectarum omnium punctorum primi quadrantis Eclipticæ inchoati à principio ♈, & </s>
            <s xml:id="echoid-s12504" xml:space="preserve">in fi-
              <lb/>
            ne ♊, terminati.</s>
            <s xml:id="echoid-s12505" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12506" xml:space="preserve">SIT rurſum Horizon obliquus A B C D; </s>
            <s xml:id="echoid-s12507" xml:space="preserve">Aequator B D; </s>
            <s xml:id="echoid-s12508" xml:space="preserve">Ecliptica E F; </s>
            <s xml:id="echoid-s12509" xml:space="preserve">principium ♈, in ſecunda
              <lb/>
              <note position="right" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">Differentia in-
                <lb/>
              ter aſcẽſionem
                <lb/>
              rectam & obli-
                <lb/>
              quam cuiusli
                <lb/>
              bet puncti Ecli
                <lb/>
              pticæ qua via
                <lb/>
              exploranda. ad
                <lb/>
              datam altitudi-
                <lb/>
              nem poli.</note>
            figura G; </s>
            <s xml:id="echoid-s12510" xml:space="preserve">in tertia verò principium ♎, idem punctum G; </s>
            <s xml:id="echoid-s12511" xml:space="preserve">Meridianus A C; </s>
            <s xml:id="echoid-s12512" xml:space="preserve">arcus Eclipticæ G E, à prin
              <lb/>
            cipio ♈, vel ♎, inchoatus qua drante minor, ita vt eius aſcenſio obliqua, hoc est, in obliqua ſphæra, ſit ar
              <lb/>
              <note position="left" xlink:label="note-0211-02" xlink:href="note-0211-02a" xml:space="preserve">10</note>
            cus Aequatoris G B, quem inueſtigare oportet. </s>
            <s xml:id="echoid-s12513" xml:space="preserve">Ducatur ex polo mundi H, per E, circulus maximus ſe-
              <lb/>
            cans Aequatorem in I, ita vt G I, ſit aſcenſio recta eiuſdem arcus Eclipticæ G E. </s>
            <s xml:id="echoid-s12514" xml:space="preserve">Quoniam ergo in trian-
              <lb/>
            gulo ſphęrico C E H, in quo angulus C, rectus est, est per propoſ. </s>
            <s xml:id="echoid-s12515" xml:space="preserve">16. </s>
            <s xml:id="echoid-s12516" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12517" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12518" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s12519" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s12520" xml:space="preserve">de triangulis, vel
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s12521" xml:space="preserve">16. </s>
            <s xml:id="echoid-s12522" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12523" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12524" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s12525" xml:space="preserve">41. </s>
            <s xml:id="echoid-s12526" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus arcus H E,
              <lb/>
            hoc eſt, vt ſinus complementi declinationis puncti Eclipticæ arcum G E, @terminantis (In tertia namque
              <lb/>
            figura idem ſinus eſt arcus H E, & </s>
            <s xml:id="echoid-s12527" xml:space="preserve">complementi declinationis E I, propterea quòd arcus H E, cum com-
              <lb/>
            plemento declinationis E I, ſemicir culum conficit) ad ſinum anguli C, hoc eſt, ad ſinum totum, ita ſinus
              <lb/>
            arcus C H, altitudinis poli, ad ſinum anguli C E H, qui in ſecunda figura æqualis eſt angulo B E I. </s>
            <s xml:id="echoid-s12528" xml:space="preserve">Rurſus
              <lb/>
            eadem ratione, & </s>
            <s xml:id="echoid-s12529" xml:space="preserve">conuertendo, intriangulo ſphærico B E I, eſt vt ſinus anguli E B I, complementi altitu
              <lb/>
            dinis poli, quem nimirum Aequator cum Horizonte conſtituit, ad ſinum arcus E I, declinationis, ita ſinus
              <lb/>
              <note position="left" xlink:label="note-0211-03" xlink:href="note-0211-03a" xml:space="preserve">20</note>
            anguli B E I, proximè inuenti ad ſinum arcus B I, quo aſcenſio recta G I, ab aſcenſione obliqua G B, dif-
              <lb/>
            fert: </s>
            <s xml:id="echoid-s12530" xml:space="preserve">Si fiat, vt ſinus complementi declinationis puncti arcum Eclipticæ terminantis ad ſinum totum, ita
              <lb/>
            ſinus altitudinis poli ad aliud, inuenietur ſinus anguli B E I: </s>
            <s xml:id="echoid-s12531" xml:space="preserve">Et ſi rurſus fiat, vt ſinus complementi al-
              <lb/>
            titudinis poli ad ſinum declinationis eiuſdem arcus Eclipticę, ita ſinus anguli B E I, proximè inuentus ad
              <lb/>
            aliud, inuenietur ſinus arcus B I, differentiæ aſcenſionis rectę, & </s>
            <s xml:id="echoid-s12532" xml:space="preserve">obliquę arcui Eelipticę G E, reſponden-
              <lb/>
            tis. </s>
            <s xml:id="echoid-s12533" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s12534" xml:space="preserve">Ponatur punctum E, in ſecunda figura grad. </s>
            <s xml:id="echoid-s12535" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12536" xml:space="preserve">♉, & </s>
            <s xml:id="echoid-s12537" xml:space="preserve">in tertia grad. </s>
            <s xml:id="echoid-s12538" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12539" xml:space="preserve">♏, ita vt
              <lb/>
            arcus G E, contineat grad. </s>
            <s xml:id="echoid-s12540" xml:space="preserve">59. </s>
            <s xml:id="echoid-s12541" xml:space="preserve">& </s>
            <s xml:id="echoid-s12542" xml:space="preserve">arcus E I, declinationis grad. </s>
            <s xml:id="echoid-s12543" xml:space="preserve">19. </s>
            <s xml:id="echoid-s12544" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12545" xml:space="preserve">59. </s>
            <s xml:id="echoid-s12546" xml:space="preserve">Si igitur fiat, vt 93979.
              <lb/>
            </s>
            <s xml:id="echoid-s12547" xml:space="preserve">ſinus complementi declinationis ad 100000. </s>
            <s xml:id="echoid-s12548" xml:space="preserve">ſinum totum, ita 66913. </s>
            <s xml:id="echoid-s12549" xml:space="preserve">ſinus altitudinis poli ad aliud, re-
              <lb/>
            perietur hic ferè ſinus 71199. </s>
            <s xml:id="echoid-s12550" xml:space="preserve">anguli E, qui ſeruetur. </s>
            <s xml:id="echoid-s12551" xml:space="preserve">Deinde ſi fiat, vt 74314. </s>
            <s xml:id="echoid-s12552" xml:space="preserve">ſinus complementi altitu
              <lb/>
            dinis poli ad 34174. </s>
            <s xml:id="echoid-s12553" xml:space="preserve">ſinum declinationis, ita 71199. </s>
            <s xml:id="echoid-s12554" xml:space="preserve">ſinus ſeruatus ad aliud, proueniet ferè hic ſinus
              <lb/>
              <note position="left" xlink:label="note-0211-04" xlink:href="note-0211-04a" xml:space="preserve">30</note>
            32741. </s>
            <s xml:id="echoid-s12555" xml:space="preserve">cuius arcus continet grad. </s>
            <s xml:id="echoid-s12556" xml:space="preserve">19. </s>
            <s xml:id="echoid-s12557" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12558" xml:space="preserve">7. </s>
            <s xml:id="echoid-s12559" xml:space="preserve">pro differentia aſcenſionis rectę, & </s>
            <s xml:id="echoid-s12560" xml:space="preserve">obliquę arcus G E.
              <lb/>
            </s>
            <s xml:id="echoid-s12561" xml:space="preserve">
              <note position="right" xlink:label="note-0211-05" xlink:href="note-0211-05a" xml:space="preserve">Aſcenſio obli-
                <lb/>
              qua cuiusuis pũ
                <lb/>
              cti Eclipticæ
                <lb/>
              qua ratione in-
                <lb/>
              ueniatur ex dif
                <lb/>
              ferentia aſcen-
                <lb/>
              ſionali.</note>
            Quę differentia ſi in ſecunda figura dematur ex aſcenſione recta G I, iam antea inuenta, (quia circulus ma
              <lb/>
            ximus H E, qui vices gerit recti Horizontis, Aequatorem ſecat infra Horizontem, cum medietas Zo-
              <lb/>
            diaci ab ♈, vſque ad ♎, ſit borealis) remanebit aſcenſio obliqua G B, grad. </s>
            <s xml:id="echoid-s12562" xml:space="preserve">37. </s>
            <s xml:id="echoid-s12563" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12564" xml:space="preserve">39. </s>
            <s xml:id="echoid-s12565" xml:space="preserve">arcui Eclipticę
              <lb/>
            boreali G E, debita: </s>
            <s xml:id="echoid-s12566" xml:space="preserve">Si verò eadem differentia in tertia figura rectæ aſcenſioni G I, addatur (quia
              <lb/>
            circulus maximus H E, ſecat Aequatorem ſupra Horizontem, propterea quòd medietas Zodiaci à ♎,
              <lb/>
            vſque ad ♈, australis eſt) conficietur aſcenſio obliqua G B, grad. </s>
            <s xml:id="echoid-s12567" xml:space="preserve">75. </s>
            <s xml:id="echoid-s12568" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12569" xml:space="preserve">53. </s>
            <s xml:id="echoid-s12570" xml:space="preserve">conueniens arcui Eclipticæ
              <lb/>
            auſtrali G E, à principio ♎, computato; </s>
            <s xml:id="echoid-s12571" xml:space="preserve">cui ſi apponatur ſemicirculus, conflabitur aſcenſio obliqua grad.
              <lb/>
            </s>
            <s xml:id="echoid-s12572" xml:space="preserve">255. </s>
            <s xml:id="echoid-s12573" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12574" xml:space="preserve">53. </s>
            <s xml:id="echoid-s12575" xml:space="preserve">arcui Eclipticæ à principio ♈, vſque ad grad. </s>
            <s xml:id="echoid-s12576" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12577" xml:space="preserve">♏, inchoato debita.</s>
            <s xml:id="echoid-s12578" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12579" xml:space="preserve">ALITER quoque eadem differentia B I, inter aſcenſionem rectam, & </s>
            <s xml:id="echoid-s12580" xml:space="preserve">obliquam inuenietur hac
              <lb/>
              <note position="left" xlink:label="note-0211-06" xlink:href="note-0211-06a" xml:space="preserve">40</note>
              <note position="right" xlink:label="note-0211-07" xlink:href="note-0211-07a" xml:space="preserve">Quomodo ea-
                <lb/>
              dem differẽtia
                <lb/>
              inter aſcenſio-
                <lb/>
              nem rectam &
                <lb/>
              obliquam cu-
                <lb/>
              iuſuis puncti
                <lb/>
              Eclipticæ, ad da
                <lb/>
              tam latitudinẽ
                <lb/>
              loci aliter inue-
                <lb/>
              ſtigetur.</note>
            ratione. </s>
            <s xml:id="echoid-s12581" xml:space="preserve">Quoniam in triangulo ſphęrico B E I, angulus I, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s12582" xml:space="preserve">19. </s>
            <s xml:id="echoid-s12583" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12584" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12585" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s12586" xml:space="preserve">Re-
              <lb/>
            giom. </s>
            <s xml:id="echoid-s12587" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s12588" xml:space="preserve">15. </s>
            <s xml:id="echoid-s12589" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12590" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12591" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s12592" xml:space="preserve">43. </s>
            <s xml:id="echoid-s12593" xml:space="preserve">noſtrorum triangulorum ſphęrico-
              <lb/>
            rum, vt ſinus complementi arcus B E, latitudinis ortiuę, cuius inuentionem in priori diſcurſu propoſ. </s>
            <s xml:id="echoid-s12594" xml:space="preserve">34.
              <lb/>
            </s>
            <s xml:id="echoid-s12595" xml:space="preserve">pręcedentis libri tradidimus, ad ſinum complementi arcus E I, declinationis puncti Eclipticæ propoſiti,
              <lb/>
            ita ſinus complementi arcus B I, differentię quęſitæ ad ſinum totum: </s>
            <s xml:id="echoid-s12596" xml:space="preserve">Et conuertendo vt ſinus complemen
              <lb/>
            ti declinationis puncti Eclipticæ propoſiti ad ſinum complementi latitudinis ortiuæ eiuſdem puncti, ita
              <lb/>
            ſinus totus ad ſinum complementi differentiæ aſcenſionum. </s>
            <s xml:id="echoid-s12597" xml:space="preserve">Quamobrem ſi fiat, vt ſinus complementi de-
              <lb/>
            clinationis ad ſinum complementi latitudinis ortiuę, ita ſinus totus ad aliud, reperietur ſinus complemen-
              <lb/>
            ti differentię aſcenſionum quęſitę.</s>
            <s xml:id="echoid-s12598" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12599" xml:space="preserve">QVONIAM autem declinationes omnium punctorum Eclipticę à principio ♈, vſque ad princi-
              <lb/>
              <note position="left" xlink:label="note-0211-08" xlink:href="note-0211-08a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0211-09" xlink:href="note-0211-09a" xml:space="preserve">Differentiæ a-
                <lb/>
              ſcenſionales pũ
                <lb/>
              ctorum prioris
                <lb/>
              quadrantis Ecli
                <lb/>
              pticæ ab A riet
                <unsure/>
              e
                <lb/>
              vſque ad Can-
                <lb/>
              crũ æquales sũt
                <lb/>
              differentijs aſcẽ
                <lb/>
              ſionalibus poſte
                <lb/>
              riorum trium
                <lb/>
              quadrantum
                <lb/>
              Eclipticæ.</note>
            pium ♋, ęquales ſunt declinationibus omnium punctorum Eclipticę à principio ♎, vſque ad principium
              <lb/>
            ♋, contra ſucceſſionem ſignorum progrediendo, ſingulę ſingulis, cum huiuſmodi puncta eoſdem parallelos
              <lb/>
            deſcribant, bina nimirum ſingulos: </s>
            <s xml:id="echoid-s12600" xml:space="preserve">Rurſus declinationes omnium punctorum Eclipticę ab ♈, vſque ad
              <lb/>
            ♎, æquales ſunt declinationibus omnium punctorum Eclipticæ à ♎, vſque ad ♈, ſecundum ſignorum ſe-
              <lb/>
            riem procedendo, ſingulæ ſingulis, cum hæc puncta illis ſint oppoſita, ac proinde æquales parallelos deſcri-
              <lb/>
            bant: </s>
            <s xml:id="echoid-s12601" xml:space="preserve">Fit, vt declinationes prioris quadrantis Eclipticæ ab ♈, vſque ad ♋, ęquales ſint declinationibus
              <lb/>
            poſteriorum trium quadrantum, vt in tabula declinationum apparet. </s>
            <s xml:id="echoid-s12602" xml:space="preserve">Quare cum latitudines ortiuæ in-
              <lb/>
            ueſtigentur beneficio declinationum, & </s>
            <s xml:id="echoid-s12603" xml:space="preserve">altitudinis poli, vt ex propoſ. </s>
            <s xml:id="echoid-s12604" xml:space="preserve">34. </s>
            <s xml:id="echoid-s12605" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s12606" xml:space="preserve">liquet, manife-
              <lb/>
            ſtum eſt, latitudines ortiuas punctorum prioris quadrantis Eclipticæ ad quamcunque latitudinem inuen-
              <lb/>
            tas, æquales eſſe latitudinibus ortiuis poſteriorum trium quadrantum in eadem latitudine. </s>
            <s xml:id="echoid-s12607" xml:space="preserve">Ac proinde
              <lb/>
            eum differentiæ inter aſcenſiones rectas, & </s>
            <s xml:id="echoid-s12608" xml:space="preserve">obliquas inquirantur, vt proximè demonſtrauimus, per </s>
          </p>
        </div>
      </text>
    </echo>
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