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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[341.] III. SOLE EXISTENTE IN PRINCIPIO ♋.
[342.] IIII. SOLE EXISTENTE IN PRINCIPIO ♑.
[343.] PROBLEMA 2. PROPOSITIO 2.
[344.] PROBLEMA 3. PROPOSITIO 3.
[345.] PROBLEMA 4. PROPOSITIO 4.
[346.] PROBLEMA 5. PROPOSITIO 5.
[347.] PROBLEMA 6. PROPOSITIO 6.
[348.] PROBLEMA 7. PROPOSITIO 7.
[349.] PROBLEMA 8. PROPOSITIO 8.
[350.] PROBLEMA 9. PROPOSITIO 9.
[351.] PROBLEMA 10. PROPOSITIO 10.
[352.] PROBLEMA 11. PROPOSITIO 11.
[353.] SCHOLIVM.
[354.] PROBLEMA 12. PROPOSITIO 12.
[355.] SCHOLIVM.
[356.] PROBLEMA 13. PROPOSITIO 13.
[357.] PROBLEMA 14. PROPOSITIO 14.
[358.] SCHOLIVM.
[359.] FINIS QV ARTI LIBRI.
[360.] GNOMONICES LIBER QVINTVS.
[361.] AVCTORE
[362.] CHRISTOPHORO CLAVIO BAMBERGENSI SOCIETATIS IESV.
[363.] PROBLEMA 1. PROPOSITIO 1.
[364.] SCHOLIVM.
[365.] SEQVVNTVR TABELLAE.
[366.] I. Altitudines Solis ſupra Horizontem pro horis à mer. & med. noc. ſupputatæ, ad latitudinem Grad. 42.
[367.] II. Altitudines Solis ſupra Horizontem pro horis ab occaſu Solis ſup-putatæ, ad latitudinem Grad. 42.
[368.] III. Altitudines Solis ſupra faciem auſtralem Verticalis circuli pro horis à mer. & med. noc. ſupputatæ, ad latitudinem Grad. 42.
[369.] IIII. Altitudines Solis ſupra faciem borealem Verticalis circuli pro horis à mer. & med. noc. ſupputatæ, ad latitudinem Grad. 42.
[370.] V. Altitudines Solis ſupra ſaciem auſtralem Verticalis circuli pro horis ab occaſu Solis ſupputatæ, ad latitudinem Grad. 42.
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          <pb o="249" file="0265" n="265" rhead="LIBER SECVNDVS."/>
          <p style="it">
            <s xml:id="echoid-s16691" xml:space="preserve">CAETERVM quia eodem modo lineę domorum cęleſtium & </s>
            <s xml:id="echoid-s16692" xml:space="preserve">in orie
              <unsure/>
            ntali, & </s>
            <s xml:id="echoid-s16693" xml:space="preserve">in occidentali horo
              <lb/>
              <note position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">Lineæ domor@
                <lb/>
              cœleſtium eun-
                <lb/>
              dem ſ@@um in
                <lb/>
              vtroque horolo
                <lb/>
              gio Meridiano
                <lb/>
              habent. Vnde
                <lb/>
              ſatis eſt, vi de-
                <lb/>
              ſcribatur he
                <unsure/>
              ro-
                <lb/>
              logium dunta-
                <lb/>
              xat orientale@,
                <lb/>
              vel occidentale.</note>
            logio deſcribuntur, tam ſecundum Ioan. </s>
            <s xml:id="echoid-s16694" xml:space="preserve">Regi
              <unsure/>
            om. </s>
            <s xml:id="echoid-s16695" xml:space="preserve">quàm ex ſententia Campani, proptcrea in priori figura
              <lb/>
            @as delineauimus in horologio orientali. </s>
            <s xml:id="echoid-s16696" xml:space="preserve">Nam eædem deſcriptæ in facie occidentali illis correſpondentes
              <lb/>
            dabunt domos cęleſtes in horologio occidẽtali, vt numeri indicãt, quorũ illi, qui tropico ♋, appoſiti ſunt,
              <lb/>
            ad orientale horologium, alii vero tropico ♑, aſcripti ad occidentale pertinent. </s>
            <s xml:id="echoid-s16697" xml:space="preserve">In poſteriori autem fi-
              <lb/>
            gura duximus lineas domorum in occidentali horologio, propterea quòd eædem in facie orientali ipſis cor
              <lb/>
            reſpondentes dant domos cęleſtes in horologio orie
              <unsure/>
            ntali. </s>
            <s xml:id="echoid-s16698" xml:space="preserve">Numeri enim tropico ♋, aſcripti ad horologium
              <lb/>
            occidentale, alii vero tropico ♑, appoſiti ad orientale ſpectant.</s>
            <s xml:id="echoid-s16699" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
        </div>
        <div xml:id="echoid-div857" type="section" level="1" n="206">
          <head xml:id="echoid-head209" xml:space="preserve">PROBLEMA 33. PROPOSITIO 33.</head>
          <p>
            <s xml:id="echoid-s16700" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem Meridiano horologio
              <lb/>
            deſcribere.</s>
            <s xml:id="echoid-s16701" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16702" xml:space="preserve">ACCIPIANTVR ex prioribus duabus tabellis propoſ. </s>
            <s xml:id="echoid-s16703" xml:space="preserve">42. </s>
            <s xml:id="echoid-s16704" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s16705" xml:space="preserve">Sole exiſtente in
              <lb/>
              <note position="right" xlink:label="note-0265-03" xlink:href="note-0265-03a" xml:space="preserve">Deſcriptio ſi-
                <lb/>
              gnorum aſcen-
                <lb/>
              dentium in eo-
                <lb/>
              dem horologio
                <lb/>
              Meridiano.</note>
            principio ♈, & </s>
            <s xml:id="echoid-s16706" xml:space="preserve">♎, horæ, quibus 12. </s>
            <s xml:id="echoid-s16707" xml:space="preserve">ſigna Zodiaci oriuntur, in horologio quidem orientali, ante
              <lb/>
            meridiẽ, in occidentali vero poſt meridiem; </s>
            <s xml:id="echoid-s16708" xml:space="preserve">que in circulo ex E, deſcripto numerentur à linea GI,
              <lb/>
            vel verſus ortũ, vel verſus occaſum, hoc eſt, vel verſus partẽ antemeridianã, aut pomeridianã, prout
              <lb/>
              <note position="left" xlink:label="note-0265-04" xlink:href="note-0265-04a" xml:space="preserve">20</note>
            tabellæ indicant. </s>
            <s xml:id="echoid-s16709" xml:space="preserve">In orientali horologio ſemper facienda eſt numeratio verſus dexterã, in occiden-
              <lb/>
            tali autem verſus ſiniſtram, hoc eſt, ſemper verſus F, vt patet, ſi circulus ex E, deſcriptus conſidere-
              <lb/>
            tur in propria poſitione in vtroque horologio. </s>
            <s xml:id="echoid-s16710" xml:space="preserve">Deinde per fines numerationum, & </s>
            <s xml:id="echoid-s16711" xml:space="preserve">centrum E, du
              <lb/>
            cantur occultæ rectæ ſecantes æquinoctialem lineam ſiue infra horizontalem lineam, ſiue ſupra,
              <lb/>
            in punctis, per quæ aſcendentium ſignorum lineæ duci debent. </s>
            <s xml:id="echoid-s16712" xml:space="preserve">Poſtea notentur ex propoſ. </s>
            <s xml:id="echoid-s16713" xml:space="preserve">26. </s>
            <s xml:id="echoid-s16714" xml:space="preserve">hu-
              <lb/>
            ius lib. </s>
            <s xml:id="echoid-s16715" xml:space="preserve">in linea horizontali puncta, quibus eam arcus ſignorum ſecant. </s>
            <s xml:id="echoid-s16716" xml:space="preserve">In hæc enim proiicientur
              <lb/>
            vmbrę gnomonis in orientali horologio, cum ſigna oriuntur, at in horologio occidentali, cum oc
              <lb/>
            cidunt. </s>
            <s xml:id="echoid-s16717" xml:space="preserve">Quæ quidem puncta hac etiam arte inueniemus, etiamſi in horologio arcus omnium ſi-
              <lb/>
              <note position="right" xlink:label="note-0265-05" xlink:href="note-0265-05a" xml:space="preserve">Inuentio
                <unsure/>
              pun-
                <lb/>
              ctorum in linea
                <unsure/>
                <lb/>
              horizontali u-
                <lb/>
              triuſque horolo
                <lb/>
              gii Met
                <unsure/>
              idiani,
                <lb/>
              in quæ vmbra
                <unsure/>
                <lb/>
              ſtyli ea dit, cum
                <lb/>
              ſigna oriuntur,
                <lb/>
              aut occidunt.</note>
            gnorum non ſint deſcripti. </s>
            <s xml:id="echoid-s16718" xml:space="preserve">Ex quinta tabella propoſ. </s>
            <s xml:id="echoid-s16719" xml:space="preserve">9. </s>
            <s xml:id="echoid-s16720" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s16721" xml:space="preserve">accipiemus arcus ſemidiurnos
              <lb/>
            ſignorum, eosq́ue in vtroque horologio à G, verſus F, ſupputabimus, & </s>
            <s xml:id="echoid-s16722" xml:space="preserve">à terminis ſupputationũ
              <lb/>
              <note position="left" xlink:label="note-0265-06" xlink:href="note-0265-06a" xml:space="preserve">30</note>
            per E, centrum ducemus rectas ſecantes æquinoctialem lineam in punctis, per quæ rectæ ęquino-
              <lb/>
            ctialem lineam ſecantes ad angulos rectos ſecabunt lineam horizontalem in punctis, in quibus ar-
              <lb/>
            cus ſignorum eandem diuidunt; </s>
            <s xml:id="echoid-s16723" xml:space="preserve">cum, Sole exiſtente in initiis ſignorũ, vmbra ſtyli in ea pũcta pro-
              <lb/>
            ijciatur, cum oritur, vel occidit, propterea quòd dictæ lineæ perpendiculares indicent horas or-
              <lb/>
            tus, & </s>
            <s xml:id="echoid-s16724" xml:space="preserve">occaſus ſolis in initiis ſignorum exiſtentis, vt ex iis, quæ propoſ. </s>
            <s xml:id="echoid-s16725" xml:space="preserve">25. </s>
            <s xml:id="echoid-s16726" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s16727" xml:space="preserve">demonſtraui-
              <lb/>
            mus, conſtat. </s>
            <s xml:id="echoid-s16728" xml:space="preserve">Cum ergo in ortu, & </s>
            <s xml:id="echoid-s16729" xml:space="preserve">occaſu Solis vmbra ſtyli proiiciatur in lineam horizontalẽ, ma-
              <lb/>
            nifeſtum eſt, in illis punctis Solem oriri, & </s>
            <s xml:id="echoid-s16730" xml:space="preserve">occidere, in quibus lineam horizontalem ſecant dictæ
              <lb/>
            lineæ perpendiculares.</s>
            <s xml:id="echoid-s16731" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16732" xml:space="preserve">EADEM puncta hoc modo reperiemus. </s>
            <s xml:id="echoid-s16733" xml:space="preserve">Ex recta E A, figuræ vltimæ propoſ. </s>
            <s xml:id="echoid-s16734" xml:space="preserve">21. </s>
            <s xml:id="echoid-s16735" xml:space="preserve">huius lib.
              <lb/>
            </s>
            <s xml:id="echoid-s16736" xml:space="preserve">
              <note position="right" xlink:label="note-0265-07" xlink:href="note-0265-07a" xml:space="preserve">Qua ratione all
                <lb/>
              ter inueniantur
                <lb/>
              puncta in linea
                <lb/>
              horizõtali, quæ
                <lb/>
              prius.</note>
            detrahatur recta æqualis ſtylo horologii Meridiani, & </s>
            <s xml:id="echoid-s16737" xml:space="preserve">per punctum extremum@huius ducatur ad
              <lb/>
              <note position="left" xlink:label="note-0265-08" xlink:href="note-0265-08a" xml:space="preserve">40</note>
            E A, perpendicularis, quæ erit linea horizontalis in orientali horologio. </s>
            <s xml:id="echoid-s16738" xml:space="preserve">Si igitur à puncto extre-
              <lb/>
            mo lineæ, quæ ſtylo ex E A, æqualis abſciſſa eſt, ſumantur interualla omnium punctorum, quibus
              <lb/>
            dicta perpendicularis à radijs ex M, O, Q, S, V, Y, per centrum E, ductis ſecatur, & </s>
            <s xml:id="echoid-s16739" xml:space="preserve">in lineã ho-
              <lb/>
            rizontalem horologii orientalis ex A, loco ſtyli transferantur, habebuntur puncta, quæ inquirun-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s16740" xml:space="preserve">vt perſpicuum eſt, ſi Horizon A B C D, in horologio orientali conc
              <unsure/>
            ipiatur in propria poſi-
              <lb/>
            tione, ita vt punctum extremum rectæ aſſumptæ in E A, ſit in A, loco ſtyli, & </s>
            <s xml:id="echoid-s16741" xml:space="preserve">perpendicularis per
              <lb/>
            illud punctum ducta fiat eadem, quæ horizontalis linea in horologio, ac proinde E, in centro mun
              <lb/>
            di, tanquam vertex gnomonis, ſtatuatur. </s>
            <s xml:id="echoid-s16742" xml:space="preserve">Ita enim fiet, vt Sole exoriente in pũctis M, O, Q, S, V, Y,
              <lb/>
            vmbra ſtyli proiiciatur in dicta puncta lineę horizontalis in orientali horologio, vt patet. </s>
            <s xml:id="echoid-s16743" xml:space="preserve">Eodem
              <lb/>
            pacto in occidentali horologio eadem puncta deprehendentur, ſi ex E C, eiuſdem figurę propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s16744" xml:space="preserve">
              <note position="left" xlink:label="note-0265-09" xlink:href="note-0265-09a" xml:space="preserve">50</note>
            21. </s>
            <s xml:id="echoid-s16745" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s16746" xml:space="preserve">abſcindatur recta æqualis ſtylo, & </s>
            <s xml:id="echoid-s16747" xml:space="preserve">per extremum punctum ad E C, perpendicula-
              <lb/>
            ris ducatur pro horizontali linea horologij occidentalis, &</s>
            <s xml:id="echoid-s16748" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16749" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16750" xml:space="preserve">ITAQVE ſi puncta inuẽta in æquinoctiali linea cum punctis reſpondentiũ ſignorũ in orien
              <lb/>
            tali horolog@o, oppoſitorũ vero in occidẽtali, inuentis in linea horizõtali iungantur rectis lineis,
              <lb/>
            deſcripta erunt ſigna aſcendentia. </s>
            <s xml:id="echoid-s16751" xml:space="preserve">Nam cum in horologio orientali vmbra proiicitur in aliquod
              <lb/>
            punctum horizontalis lineæ, oritur ſignum illud, in quo Sol exiſtit; </s>
            <s xml:id="echoid-s16752" xml:space="preserve">cum autem vmbra in occiden
              <lb/>
            tali horologio cadit in aliquod punctum lineæ horizontalis, oritur ſignum oppoſitum, cum illud
              <lb/>
            tunc, in quo Sol eſt, occidat,</s>
          </p>
          <p>
            <s xml:id="echoid-s16753" xml:space="preserve">POSSVMVS quoque in duobus tropicis pũcta reperire ex tertia, & </s>
            <s xml:id="echoid-s16754" xml:space="preserve">quarta tabella propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s16755" xml:space="preserve">
              <note position="right" xlink:label="note-0265-10" xlink:href="note-0265-10a" xml:space="preserve">Quomodo in
                <lb/>
              tropicis inueſti-
                <lb/>
              gentur puncta
                <lb/>
              aſcendentium
                <lb/>
              ſignorum.</note>
            9. </s>
            <s xml:id="echoid-s16756" xml:space="preserve">hu@us lib. </s>
            <s xml:id="echoid-s16757" xml:space="preserve">per quæ ſigna aſcendentia duci debent; </s>
            <s xml:id="echoid-s16758" xml:space="preserve">deſcribendo videlicet occulte lineam illius
              <lb/>
            horæ, qua ſignorum quodlibet oritur. </s>
            <s xml:id="echoid-s16759" xml:space="preserve">Vbi enim hæc tropicum ſecuerit, per illud punctum ducen
              <lb/>
            da eſt linea illius ſigni aſcedentis, vt in horologio horizontali factum eſt. </s>
            <s xml:id="echoid-s16760" xml:space="preserve">Perutile autẽ eſt, </s>
          </p>
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