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-div789" type="section" level="1" n="190">
          <p>
            <s xml:id="echoid-s15565" xml:space="preserve">
              <pb o="229" file="0249" n="249" rhead="LIBER SECVNDVS."/>
            memus arcus ſemidiurnos ſignorum auſtralium pro horologio auſtrali, eosq́ue numerabimus ab
              <lb/>
              <note position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">Qua ratione in
                <lb/>
              linea horizonta
                <lb/>
              li horologii Ver
                <lb/>
              ticalis puncta
                <lb/>
              inueniantur, in
                <lb/>
              quibus Sol ori-
                <lb/>
              tur, aut occidit
                <lb/>
              in principiis @ſi-
                <lb/>
              gnorũ exiſtens.</note>
            N, in vtramque partem, & </s>
            <s xml:id="echoid-s15566" xml:space="preserve">à terminis numerationum per E, rectas ducemus ſecantes lineam æqui
              <lb/>
            noctialem in punctis, per quæ rectæ ex H, emiſſæ ſecabunt horizontalem lineam in punctis C, D,
              <lb/>
            F, K, L, M, per quæ ſignorum arcus tranſeunt. </s>
            <s xml:id="echoid-s15567" xml:space="preserve">In illis enim punctis oritur, & </s>
            <s xml:id="echoid-s15568" xml:space="preserve">occidit Sol in prin
              <lb/>
            cipiis ſignorum exiſtens, propterea quòd dictæ rectæ ex H, egredientes indicant horas, quando
              <lb/>
            Sol oritur, & </s>
            <s xml:id="echoid-s15569" xml:space="preserve">occidit, &</s>
            <s xml:id="echoid-s15570" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15571" xml:space="preserve">Pro horologio vero boreali ſumemus arcus ſemidiurnos ſignorum bo-
              <lb/>
            realium, eoſq́ue numerabimus ab M, in vtramque partem, &</s>
            <s xml:id="echoid-s15572" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15573" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15574" xml:space="preserve">GEOMETRICE quoque, & </s>
            <s xml:id="echoid-s15575" xml:space="preserve">certius per latitudines ortiuas, & </s>
            <s xml:id="echoid-s15576" xml:space="preserve">occiduas eadem puncta, in
              <lb/>
              <note position="right" xlink:label="note-0249-02" xlink:href="note-0249-02a" xml:space="preserve">Qua ratione
                <lb/>
              inueniãtur ea-
                <lb/>
              dem puncta per
                <lb/>
              Analemma.</note>
            quibus Sol oritur in principiis ſignorum exiſtens, inueniemus hoc modo. </s>
            <s xml:id="echoid-s15577" xml:space="preserve">Sit Horizon A B C D,
              <lb/>
              <note position="left" xlink:label="note-0249-03" xlink:href="note-0249-03a" xml:space="preserve">10</note>
            cuius cẽtrum E; </s>
            <s xml:id="echoid-s15578" xml:space="preserve">communis ſectio
              <lb/>
              <figure xlink:label="fig-0249-01" xlink:href="fig-0249-01a" number="174">
                <image file="0249-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0249-01"/>
              </figure>
            illius cum Meridiano B D; </s>
            <s xml:id="echoid-s15579" xml:space="preserve">eiuſdẽ
              <lb/>
            communis ſectio cum Verticali,
              <lb/>
            atque adeò cum Aequatore, A C.
              <lb/>
            </s>
            <s xml:id="echoid-s15580" xml:space="preserve">In recta B D, quærantur puncta,
              <lb/>
            vbi à ſignorum parallelis ſecatur,
              <lb/>
            quod ita fiet. </s>
            <s xml:id="echoid-s15581" xml:space="preserve">Ex B, verſus A, com
              <lb/>
            puretur altitudo Æquatoris B e, vel
              <lb/>
            ex A, verſus B, altitudo poli A e; </s>
            <s xml:id="echoid-s15582" xml:space="preserve">& </s>
            <s xml:id="echoid-s15583" xml:space="preserve">
              <lb/>
            à puncto e, vtrinque ducantur, vt
              <lb/>
              <note position="left" xlink:label="note-0249-04" xlink:href="note-0249-04a" xml:space="preserve">20</note>
            in Analemmate, diametri paralle-
              <lb/>
            lorum ſignorum diametro Aequa-
              <lb/>
            toris ef, æquidiſtantes. </s>
            <s xml:id="echoid-s15584" xml:space="preserve">Hæ enim
              <lb/>
            ſecabunt rectam B D, in punctis F,
              <lb/>
            G, H, I, K, L, quæ quæruntur. </s>
            <s xml:id="echoid-s15585" xml:space="preserve">I
              <unsure/>
            d
              <lb/>
            quod facile demonſtrabitur, ſi ſe-
              <lb/>
              <note position="right" xlink:label="note-0249-05" xlink:href="note-0249-05a" xml:space="preserve">Demonſtratio
                <lb/>
              poſterioris inué
                <lb/>
              rionis dictorum
                <lb/>
              punctorum.</note>
            micirculus B A D, intelligatur cir
              <lb/>
            ca B D, circumuerti, vſque dum ad
              <lb/>
            Horizontem rectus ſit, & </s>
            <s xml:id="echoid-s15586" xml:space="preserve">cum Me-
              <lb/>
            ridiano coniunctus. </s>
            <s xml:id="echoid-s15587" xml:space="preserve">Erunt enim
              <lb/>
              <note position="left" xlink:label="note-0249-06" xlink:href="note-0249-06a" xml:space="preserve">30</note>
            tunc dictæ parallelę communes ſe
              <unsure/>
            -
              <lb/>
            ctiones Meridiani, & </s>
            <s xml:id="echoid-s15588" xml:space="preserve">parallelorum
              <lb/>
            ſignorum Zodiaci, atque adeò ipſi
              <lb/>
            paralleli rectam B D, in punctis F, G, H, I, K, L, ſecabunt, cum per dictas lineas parallelas du-
              <lb/>
            cantur. </s>
            <s xml:id="echoid-s15589" xml:space="preserve">Deinde per puncta F, G, H, I, K, L, ad B D, ducantur perpendiculares M N, O P, Q R,
              <lb/>
            S T, V X, Y Z. </s>
            <s xml:id="echoid-s15590" xml:space="preserve">Erunt hæ communes ſectiones parallelorum ſignorum Zodiaci, & </s>
            <s xml:id="echoid-s15591" xml:space="preserve">Horizontis.
              <lb/>
            </s>
            <s xml:id="echoid-s15592" xml:space="preserve">Cum enim tam Horizon, quàm paralleli ſignorum Zodiaci ad Meridianum recti ſint, erunt quo-
              <lb/>
            que communes ſectiones Horizontis, & </s>
            <s xml:id="echoid-s15593" xml:space="preserve">parallelorum ad Meridianum, atque adeò per defin. </s>
            <s xml:id="echoid-s15594" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15595" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15596" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0249-07" xlink:href="note-0249-07a" xml:space="preserve">19. vndec.</note>
            11. </s>
            <s xml:id="echoid-s15597" xml:space="preserve">Euclidis, & </s>
            <s xml:id="echoid-s15598" xml:space="preserve">ad rectam B D, in Meridiano exiſtentem, perpendiculares. </s>
            <s xml:id="echoid-s15599" xml:space="preserve">Quamobrem dictæ
              <lb/>
              <note position="right" xlink:label="note-0249-08" xlink:href="note-0249-08a" xml:space="preserve">Amplitudines
                <lb/>
              ortiuæ, occi-
                <lb/>
              duæq́uc per A-
                <lb/>
              nalemma in-
                <lb/>
              uentæ.</note>
            perpendiculares communes ſectiones ſunt parallelorum, & </s>
            <s xml:id="echoid-s15600" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s15601" xml:space="preserve">Ex quo fit, cum Vertica-
              <lb/>
            lis proprie dictus ducatur per rectam A C, arcus C M, C O, C Q, C S, C V, C Y, eſſe amplitu-
              <lb/>
              <note position="left" xlink:label="note-0249-09" xlink:href="note-0249-09a" xml:space="preserve">40</note>
            dines ortiuas; </s>
            <s xml:id="echoid-s15602" xml:space="preserve">arcus verò A N, A P, A R, A T, A X, A Z, latitudines occiduas.</s>
            <s xml:id="echoid-s15603" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15604" xml:space="preserve">ITAQVE ſi ex E D, abſcindatur recta E a, ſtylo æqualis, & </s>
            <s xml:id="echoid-s15605" xml:space="preserve">per a, ducatur b d, ad E D, per-
              <lb/>
            pendicularis, erit b d, linea horizontalis in auſtrali horologio Verticali; </s>
            <s xml:id="echoid-s15606" xml:space="preserve">radii verò ex punctis S,
              <lb/>
            V, Y, & </s>
            <s xml:id="echoid-s15607" xml:space="preserve">T, X, Z, per centrum E, traiecti ſecabunt horizontalem lineam in punctis, in quæ vmbra
              <lb/>
            ſtyli proiicitur, Sole oriente, & </s>
            <s xml:id="echoid-s15608" xml:space="preserve">occidente, cum eſt in initiis ſignorum. </s>
            <s xml:id="echoid-s15609" xml:space="preserve">Quare hæc puncta ex pun
              <lb/>
            cto a, accepta, & </s>
            <s xml:id="echoid-s15610" xml:space="preserve">in lineam horizontalem horologii translata ex loco gnomonis G, dabunt eadem
              <lb/>
            puncta in horologio. </s>
            <s xml:id="echoid-s15611" xml:space="preserve">Id quod liquido conſtare cuilibet poteſt, ſi Horizon A B C D, ponatur in
              <lb/>
            horologio auſtrali in propria poſitione, ita vt punctum a, ſit in loco ſtyli G, & </s>
            <s xml:id="echoid-s15612" xml:space="preserve">recta b d, eadem, quę
              <lb/>
            horizontalis linea, atque adeò E, in centro mundi, tanquam vertex ſtyli. </s>
            <s xml:id="echoid-s15613" xml:space="preserve">Hoc enim poſito, oriente
              <lb/>
            Sole in punctis Horizontis S, V, Y, & </s>
            <s xml:id="echoid-s15614" xml:space="preserve">occidente in T, X, Z, proiicietur vmbra ſtyli in dicta pun
              <lb/>
              <note position="left" xlink:label="note-0249-10" xlink:href="note-0249-10a" xml:space="preserve">50</note>
            cta linęæ horizontalis: </s>
            <s xml:id="echoid-s15615" xml:space="preserve">quæ quidem puncta ſunt ſignorum auſtralium. </s>
            <s xml:id="echoid-s15616" xml:space="preserve">Eodem modo in boreali
              <lb/>
            horologio reperientur puncta ſignorum borealium, ſi ex E B, auferatur recta E a, ſtylo æqualis, & </s>
            <s xml:id="echoid-s15617" xml:space="preserve">
              <lb/>
            per a, ducatur ad E B, perpendicularis b d, quæ rurſus erit linea horizontalis in horologio borea-
              <lb/>
            li, &</s>
            <s xml:id="echoid-s15618" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15619" xml:space="preserve">Ex hac porrò figura inueniemus eadem puncta in linea horizontali cuiuſcunque horolo-
              <lb/>
              <note position="right" xlink:label="note-0249-11" xlink:href="note-0249-11a" xml:space="preserve">Radii latitudi-
                <lb/>
              num ortiuarũ,
                <lb/>
              & occiduarum
                <lb/>
              qui.</note>
            gii, vt ex ſequentibus manifeſtum fiet. </s>
            <s xml:id="echoid-s15620" xml:space="preserve">Poterunt autem diametri huius figuræ Y N, V P, &</s>
            <s xml:id="echoid-s15621" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15622" xml:space="preserve">non
              <lb/>
            ineptè vocari radii latitudinum ortiuarum, vel occiduarum.</s>
            <s xml:id="echoid-s15623" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15624" xml:space="preserve">PERSPICVE quoque hic apparet ratio, cur auſtralia ſigna mutentur in horologio boreali
              <lb/>
              <note position="right" xlink:label="note-0249-12" xlink:href="note-0249-12a" xml:space="preserve">Ratio, cur in bo
                <lb/>
              reali horologio
                <lb/>
              arcus ſignorum
                <lb/>
              auſtralium mu
                <lb/>
              tentur in arcus
                <lb/>
              borealium ſi-
                <lb/>
              gnorum.</note>
            in borealia; </s>
            <s xml:id="echoid-s15625" xml:space="preserve">quia videlicet radii latitudinum ſignorum auſtralium per centrum E, ducti ſecant re-
              <lb/>
            ctam b d, ductã ex parte Septentrionis per punctũ a, quæ refert horizontalem lineam in auſtrali
              <lb/>
            horologio; </s>
            <s xml:id="echoid-s15626" xml:space="preserve">at verò rectã b d, ductã per a, ex parte meridiei, quæ refert lineam horizontalẽ in horo
              <lb/>
            logio boreali, ſecant radii latitudinum ſignorũ borealiũ per centrũ E, ed ucti, vt ex figura conſtat.</s>
            <s xml:id="echoid-s15627" xml:space="preserve"/>
          </p>
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