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-div1046" type="section" level="1" n="255">
          <p style="it">
            <s xml:id="echoid-s20805" xml:space="preserve">
              <pb o="309" file="0325" n="325" rhead="LIBER TERTIVS."/>
            & </s>
            <s xml:id="echoid-s20806" xml:space="preserve">vſui accommodatum ſtylum recipiat, licet in propoſito nobis plano, in quo delineandum eſt horologiũ,
              <lb/>
            centrum horologii notari non poſſit, ac prcinde fortaſſis neque linea horę 12. </s>
            <s xml:id="echoid-s20807" xml:space="preserve">niſi planum in latitudinem
              <lb/>
            @@gis porrigatur, quàm in altitudinem, adeò vt hora 12. </s>
            <s xml:id="echoid-s20808" xml:space="preserve">quidem deſignaripoſſit, plano ob inſignem lati-
              <lb/>
            tudinem, quam habet, ipſam recipiente, centrum verò propter modicam altitudinem eiuſdem plani de-
              <lb/>
            ſcribi non poſſit. </s>
            <s xml:id="echoid-s20809" xml:space="preserve">Quamuis enim lineæ horariæ ex C, prodeuntes, quæ per puncta æquinoctialis lineę H I,
              <lb/>
            inuenta beneficio circuli ex L, deſcripti ducuntur, ſemper magis ac magis inter ſe diſtent, ſi producãtur,
              <lb/>
            atque adeo ex aliquo puncto lineæ indicis C L, infra punctum M, ſtylus maior duci poſſit perpendicularis
              <lb/>
            ad C L, vſque ad axem C I, productum, vt in ſcbolio propoſ. </s>
            <s xml:id="echoid-s20810" xml:space="preserve">ſequentis docebimus, cum maius aut minus
              <lb/>
            horologium deſcribemus ex iisdem lineamentis, pro data magnitudine ſtyli: </s>
            <s xml:id="echoid-s20811" xml:space="preserve">tamen, quia cum planum à
              <lb/>
            meridiano parum deflectit, lineæ borariæ ferè parallelæ ſunt, ita vt opus ſit in infinitum ferè illas produ-
              <lb/>
              <note position="left" xlink:label="note-0325-01" xlink:href="note-0325-01a" xml:space="preserve">10</note>
            cere, antequam ſtylum propoſitæ magnitudinis ducere poſſimus, idcir co aliam rationem inire oportet. </s>
            <s xml:id="echoid-s20812" xml:space="preserve">Ita
              <lb/>
            igitur rem proſequemur.</s>
            <s xml:id="echoid-s20813" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20814" xml:space="preserve">IN æquinoctiali linea H I, ſumatur punctum O, quodcunque, tantò remotius ab H, quantò amplius
              <lb/>
            borologium deſideratur, at que ſtylus longior; </s>
            <s xml:id="echoid-s20815" xml:space="preserve">& </s>
            <s xml:id="echoid-s20816" xml:space="preserve">per O, agatur axi I C, parallela O P, ad quam ex H,
              <lb/>
            perpendic@laris ducatur H Q, quæ cum etiam perpendicularis ſit ad I C, ipſi O P, parallelam, tranſi-
              <lb/>
              <note position="right" xlink:label="note-0325-02" xlink:href="note-0325-02a" xml:space="preserve">29. primi.</note>
            bit omnino pork, quòd & </s>
            <s xml:id="echoid-s20817" xml:space="preserve">H K, perpendicularis ſit ducta ad I C: </s>
            <s xml:id="echoid-s20818" xml:space="preserve">alioquin ex H, ad I C, duæ perpendi-
              <lb/>
            culares ducerentur. </s>
            <s xml:id="echoid-s20819" xml:space="preserve">quod abſurdum eſt. </s>
            <s xml:id="echoid-s20820" xml:space="preserve">Deinde ex H F, producta, quę ad A B, perpendicularis eſt, abſcin
              <lb/>
            datur ipſi H O, ęqualis H R; </s>
            <s xml:id="echoid-s20821" xml:space="preserve">ducta{q́ue} R S, ipſi F E, parallela, excitetur ex R, ad R S, perpendicularis R T,
              <lb/>
            vol ipſi F N, parallela, ſecans A B, in T, puncto, per quod ipſi C N, parallela agatur T V, ſecans æqui-
              <lb/>
            noctialem lineam H O, in X.</s>
            <s xml:id="echoid-s20822" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s20823" xml:space="preserve">AD hęc, ſumpto in linea ſtyli H C, quocunque puncto Y, ducatur per illud rectę H Q, parallela
              <lb/>
            Y P, ſecans O P, in P, quæ ad O P, perpendicularis erit, quemadmodum & </s>
            <s xml:id="echoid-s20824" xml:space="preserve">H Q: </s>
            <s xml:id="echoid-s20825" xml:space="preserve">Item per Y, ducatur
              <lb/>
              <note position="right" xlink:label="note-0325-04" xlink:href="note-0325-04a" xml:space="preserve">29. primi.</note>
            ad H Y, perpendicularis Y V, vel ipſi H O, parallela, ſecans T V, in V.</s>
            <s xml:id="echoid-s20826" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20827" xml:space="preserve">POSTREMO ſumptis in recta H Y, rectis H Z, Y a, que rectis H Q, Y P, ęquales ſint, deſcri-
              <lb/>
            bantur ex Z, a, circuli, ij{q́ue} in partes 24. </s>
            <s xml:id="echoid-s20828" xml:space="preserve">ęquales ſecentur, initio facto à rectis, quę ex centris Z, a,
              <lb/>
            per puncta X, V, ducuntur. </s>
            <s xml:id="echoid-s20829" xml:space="preserve">Nam rectę occultæ per centra Z, a, & </s>
            <s xml:id="echoid-s20830" xml:space="preserve">puncta diuiſionum ductæ ſecabunt
              <lb/>
            rectas H O, Y V, in punctis, per quæ eductæ lineæ rectæ (ſumendo bina ſemper puncta inter ſe reſpon-
              <lb/>
            dentia, hoc eſt, duo proxima punctis H, Y, deinde ſequentia duo, & </s>
            <s xml:id="echoid-s20831" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s20832" xml:space="preserve">dabunt lineas horarias, quas
              <lb/>
            eatenus hincinde producemus, quoad plani magnitudo patietur. </s>
            <s xml:id="echoid-s20833" xml:space="preserve">Earum enim longitudines ab arcubus
              <lb/>
            ſignorum terminabuntur. </s>
            <s xml:id="echoid-s20834" xml:space="preserve">Styli longitudo erit Q b, perpendicularis ex Q, ad H Y, demiſſa, eius{q́ue} lo-
              <lb/>
              <note position="left" xlink:label="note-0325-05" xlink:href="note-0325-05a" xml:space="preserve">30</note>
            cus in puncto b, in quod dicta perpendicularis cadit. </s>
            <s xml:id="echoid-s20835" xml:space="preserve">Quæ omnia hac ratione comprobabimus.</s>
            <s xml:id="echoid-s20836" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20837" xml:space="preserve">QVONIAM recta R S, rectę F E, parallela cum recta A B, tandem aliquando conueniat ne-
              <lb/>
              <note position="right" xlink:label="note-0325-06" xlink:href="note-0325-06a" xml:space="preserve">Demonſtratio
                <lb/>
              conſtruction is
                <lb/>
              horologii parũ
                <lb/>
              ã Meridiano
                <lb/>
              declinanus.</note>
            ceſſe eſt; </s>
            <s xml:id="echoid-s20838" xml:space="preserve">conueniat in puncto S, (hoc autem punctum S, vt plurimum extra planum, niſi immenſum fue
              <lb/>
            rit, cadet, cum remotiſſimum ſit à puncto E, ſi declinatio plani horologii parum à grad. </s>
            <s xml:id="echoid-s20839" xml:space="preserve">90. </s>
            <s xml:id="echoid-s20840" xml:space="preserve">differt. </s>
            <s xml:id="echoid-s20841" xml:space="preserve">Vnde
              <lb/>
            tunc animo concipiendum erit duntaxat) per quod ad A B, duci intelligatur perpendicularis S π, vel ipſi
              <lb/>
            C D, parallela, conueniens cum H C, productain π. </s>
            <s xml:id="echoid-s20842" xml:space="preserve">Et quoniam angulus H S R, angulo H E F, comple-
              <lb/>
              <note position="right" xlink:label="note-0325-07" xlink:href="note-0325-07a" xml:space="preserve">29. primi.</note>
            menti declinationis datæ æqualis est; </s>
            <s xml:id="echoid-s20843" xml:space="preserve">ſi recta π S, accipiatur pro linea meridiana in plano horologii, erit
              <lb/>
            S R, linea declinationis. </s>
            <s xml:id="echoid-s20844" xml:space="preserve">In qua cum ex puncto R, ad A B, ducta ſit perpendicularis R H, ducenda erit
              <lb/>
            linea indicis per punctum H, vt in priori deſcriptione huius propoſ. </s>
            <s xml:id="echoid-s20845" xml:space="preserve">oſtenſum eſt, faciens cum meridiana
              <lb/>
            linea S π, angulum ęqualem angulo E C H, quem linea ſtyli C H, in horologio, cuius centrum C, facit cum
              <lb/>
              <note position="left" xlink:label="note-0325-08" xlink:href="note-0325-08a" xml:space="preserve">40</note>
            meridiana linea C E; </s>
            <s xml:id="echoid-s20846" xml:space="preserve">propterea quòd in eodem plano declinante eundem ſemper angulum faciat linea
              <lb/>
            ſtyli cum linea meridiana, atque adeo & </s>
            <s xml:id="echoid-s20847" xml:space="preserve">cum recta A B, quæ Horizonti æquidiſtat, quæcunque ſtyli lon-
              <lb/>
            gitudo accipiatur; </s>
            <s xml:id="echoid-s20848" xml:space="preserve">alias linea æquinoctialis ducenda per punctum H, perpendicularis ad lineam indicis,
              <lb/>
            vt demonſtratum eſt, non ſemper eoſdem angulos cum recta A B, conſtitueret. </s>
            <s xml:id="echoid-s20849" xml:space="preserve">quod est abſurdum.
              <lb/>
            </s>
            <s xml:id="echoid-s20850" xml:space="preserve">Quod hac etiam ratione confirmari poteſt. </s>
            <s xml:id="echoid-s20851" xml:space="preserve">Quoniam tam planum Meridiani proprii ipſius plani decli-
              <lb/>
            nantis faciens in ipſo plano lineam styli, quàm planum horologii horizont alis per rectam A B, ductum,
              <lb/>
            vt ex ſuperioribus patet, rectum est ad planum horologii declinantis, erit quoque communis corum ſectio
              <lb/>
              <note position="right" xlink:label="note-0325-09" xlink:href="note-0325-09a" xml:space="preserve">19. vndec.</note>
            ad idem planum perpendicularis, occurrens ei in puncto H, per quod linea ſtyli, ideoq́, & </s>
            <s xml:id="echoid-s20852" xml:space="preserve">Meridianus
              <lb/>
            proprius plani declinantis illam efficiens ducitur, vt dictum eſt; </s>
            <s xml:id="echoid-s20853" xml:space="preserve">ac propterea eadem ſectio, per defin. </s>
            <s xml:id="echoid-s20854" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s20855" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20856" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20857" xml:space="preserve">Euclidis rectos angulos faciet & </s>
            <s xml:id="echoid-s20858" xml:space="preserve">cum recta H E, & </s>
            <s xml:id="echoid-s20859" xml:space="preserve">cum linea indicis per H, ductam in plano ho
              <lb/>
              <note position="left" xlink:label="note-0325-10" xlink:href="note-0325-10a" xml:space="preserve">50</note>
            rologii. </s>
            <s xml:id="echoid-s20860" xml:space="preserve">Igitur ex defin. </s>
            <s xml:id="echoid-s20861" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20862" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20863" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20864" xml:space="preserve">Euclidis, cum viciſſim vtraque cum illa ſectione communi rectos angu-
              <lb/>
            los efficiat, angulus à recta H E, & </s>
            <s xml:id="echoid-s20865" xml:space="preserve">linea indicis comprehenſus, erit angulus inclinationis plani, in quo
              <lb/>
            exiſtit dictus Meridianus proprius plani declinantis, ad planum horologii horizontalis: </s>
            <s xml:id="echoid-s20866" xml:space="preserve">ac proinde cum
              <lb/>
            bæc inclinatio in eodem plano declinante non mutetur, efficiet linea indicis cum recta H E, eundem ſem-
              <lb/>
            per angulum. </s>
            <s xml:id="echoid-s20867" xml:space="preserve">Quamobrem cum H C, ſit linea indicis oſtenſa in horologio, cuius centrum C, demonſtra-
              <lb/>
            tum{q́ue} ſit, lineam indicis in horologio, in quo linea meridiana π S, tranſire per H, erit H C, producta, li-
              <lb/>
            nea indicis in eodem hoc horologio, quandoquidem in H, eundem angulum facit, & </s>
            <s xml:id="echoid-s20868" xml:space="preserve">in π, cum linea me-
              <lb/>
            ridiana π S, angulum æqualem angulo H C E, quem linea indicis in priore horologio cum meridiana li-
              <lb/>
            nea C E, conſtituit. </s>
            <s xml:id="echoid-s20869" xml:space="preserve">Aequales autem eſſe angulos H C E, H π S, perſpicuum eſt, propterea quòd C E,
              <lb/>
              <note position="right" xlink:label="note-0325-11" xlink:href="note-0325-11a" xml:space="preserve">29. primi.</note>
            π S, parallelæ ſunt. </s>
            <s xml:id="echoid-s20870" xml:space="preserve">Hinc efficitur, punctum π, eſſe centrum illius horologii, in quo linea meridiana eſt
              <lb/>
            π S; </s>
            <s xml:id="echoid-s20871" xml:space="preserve">ſiquidem in centro horologii conueniunt linea indicis, & </s>
            <s xml:id="echoid-s20872" xml:space="preserve">linea meridiana. </s>
            <s xml:id="echoid-s20873" xml:space="preserve">Efficitur </s>
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