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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LIBER SECVNDVS.
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memus arcus ſemidiurnos ſignorum auſtralium pro horologio auſtrali, eosq́ue numerabimus ab
<
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<
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xlink:label
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note-0249-01
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xlink:href
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note-0249-01a
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xml:space
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">Qua ratione in
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linea horizonta
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li horologii Ver
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ticalis puncta
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inueniantur, in
<
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quibus Sol ori-
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tur, aut occidit
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in principiis @ſi-
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gnorũ exiſtens.</
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N, in vtramque partem, & </
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>
<
s
xml:id
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xml:space
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">à terminis numerationum per E, rectas ducemus ſecantes lineam æqui
<
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noctialem in punctis, per quæ rectæ ex H, emiſſæ ſecabunt horizontalem lineam in punctis C, D,
<
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F, K, L, M, per quæ ſignorum arcus tranſeunt. </
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>
<
s
xml:id
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xml:space
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">In illis enim punctis oritur, & </
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>
<
s
xml:id
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xml:space
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">occidit Sol in prin
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cipiis ſignorum exiſtens, propterea quòd dictæ rectæ ex H, egredientes indicant horas, quando
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Sol oritur, & </
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>
<
s
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>
<
s
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xml:space
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">c. </
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<
s
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xml:space
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">Pro horologio vero boreali ſumemus arcus ſemidiurnos ſignorum bo-
<
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realium, eoſq́ue numerabimus ab M, in vtramque partem, &</
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>
<
s
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xml:space
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<
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</
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<
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<
s
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xml:space
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">GEOMETRICE quoque, & </
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>
<
s
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xml:space
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">certius per latitudines ortiuas, & </
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>
<
s
xml:id
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xml:space
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">occiduas eadem puncta, in
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<
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xlink:label
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note-0249-02
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xlink:href
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xml:space
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">Qua ratione
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inueniãtur ea-
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dem puncta per
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Analemma.</
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>
quibus Sol oritur in principiis ſignorum exiſtens, inueniemus hoc modo. </
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>
<
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xml:space
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">Sit Horizon A B C D,
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cuius cẽtrum E; </
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<
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number
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0249-01
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illius cum Meridiano B D; </
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>
<
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communis ſectio cum Verticali,
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atque adeò cum Aequatore, A C.
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</
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<
s
xml:id
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xml:space
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">In recta B D, quærantur puncta,
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vbi à ſignorum parallelis ſecatur,
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quod ita fiet. </
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>
<
s
xml:id
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xml:space
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">Ex B, verſus A, com
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puretur altitudo Æquatoris B e, vel
<
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ex A, verſus B, altitudo poli A e; </
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>
<
s
xml:id
="
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xml:space
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">& </
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à puncto e, vtrinque ducantur, vt
<
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<
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position
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xlink:label
="
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xml:space
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">20</
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>
in Analemmate, diametri paralle-
<
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lorum ſignorum diametro Aequa-
<
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toris ef, æquidiſtantes. </
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>
<
s
xml:id
="
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xml:space
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">Hæ enim
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ſecabunt rectam B D, in punctis F,
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G, H, I, K, L, quæ quæruntur. </
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>
<
s
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xml:space
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">I
<
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d
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quod facile demonſtrabitur, ſi ſe-
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<
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xlink:label
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xlink:href
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xml:space
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">Demonſtratio
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poſterioris inué
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rionis dictorum
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punctorum.</
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>
micirculus B A D, intelligatur cir
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ca B D, circumuerti, vſque dum ad
<
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Horizontem rectus ſit, & </
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>
<
s
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xml:space
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ridiano coniunctus. </
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<
s
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tunc dictæ parallelę communes ſe
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-
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ctiones Meridiani, & </
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<
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">parallelorum
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ſignorum Zodiaci, atque adeò ipſi
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paralleli rectam B D, in punctis F, G, H, I, K, L, ſecabunt, cum per dictas lineas parallelas du-
<
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cantur. </
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>
<
s
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xml:space
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">Deinde per puncta F, G, H, I, K, L, ad B D, ducantur perpendiculares M N, O P, Q R,
<
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S T, V X, Y Z. </
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>
<
s
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xml:space
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">Erunt hæ communes ſectiones parallelorum ſignorum Zodiaci, & </
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>
<
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xml:space
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">Horizontis.
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</
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<
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xml:space
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">Cum enim tam Horizon, quàm paralleli ſignorum Zodiaci ad Meridianum recti ſint, erunt quo-
<
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que communes ſectiones Horizontis, & </
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>
<
s
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">parallelorum ad Meridianum, atque adeò per defin. </
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<
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xml:space
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">3. </
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<
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xlink:label
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">19. vndec.</
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11. </
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<
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">Euclidis, & </
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<
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xml:space
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">ad rectam B D, in Meridiano exiſtentem, perpendiculares. </
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<
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xml:space
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">Quamobrem dictæ
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<
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xlink:label
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xml:space
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">Amplitudines
<
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ortiuæ, occi-
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duæq́uc per A-
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nalemma in-
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uentæ.</
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perpendiculares communes ſectiones ſunt parallelorum, & </
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>
<
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xml:space
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">Horizontis. </
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<
s
xml:id
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xml:space
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">Ex quo fit, cum Vertica-
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lis proprie dictus ducatur per rectam A C, arcus C M, C O, C Q, C S, C V, C Y, eſſe amplitu-
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<
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xlink:label
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dines ortiuas; </
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<
s
xml:id
="
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xml:space
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">arcus verò A N, A P, A R, A T, A X, A Z, latitudines occiduas.</
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<
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</
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<
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<
s
xml:id
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xml:space
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">ITAQVE ſi ex E D, abſcindatur recta E a, ſtylo æqualis, & </
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>
<
s
xml:id
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xml:space
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">per a, ducatur b d, ad E D, per-
<
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pendicularis, erit b d, linea horizontalis in auſtrali horologio Verticali; </
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>
<
s
xml:id
="
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xml:space
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">radii verò ex punctis S,
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V, Y, & </
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>
<
s
xml:id
="
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xml:space
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">T, X, Z, per centrum E, traiecti ſecabunt horizontalem lineam in punctis, in quæ vmbra
<
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ſtyli proiicitur, Sole oriente, & </
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>
<
s
xml:id
="
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xml:space
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">occidente, cum eſt in initiis ſignorum. </
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>
<
s
xml:id
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xml:space
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">Quare hæc puncta ex pun
<
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cto a, accepta, & </
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>
<
s
xml:id
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xml:space
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">in lineam horizontalem horologii translata ex loco gnomonis G, dabunt eadem
<
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puncta in horologio. </
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>
<
s
xml:id
="
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xml:space
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">Id quod liquido conſtare cuilibet poteſt, ſi Horizon A B C D, ponatur in
<
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horologio auſtrali in propria poſitione, ita vt punctum a, ſit in loco ſtyli G, & </
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>
<
s
xml:id
="
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xml:space
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">recta b d, eadem, quę
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horizontalis linea, atque adeò E, in centro mundi, tanquam vertex ſtyli. </
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>
<
s
xml:id
="
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xml:space
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">Hoc enim poſito, oriente
<
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Sole in punctis Horizontis S, V, Y, & </
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>
<
s
xml:id
="
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xml:space
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">occidente in T, X, Z, proiicietur vmbra ſtyli in dicta pun
<
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<
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position
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xlink:label
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">50</
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cta linęæ horizontalis: </
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>
<
s
xml:id
="
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xml:space
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">quæ quidem puncta ſunt ſignorum auſtralium. </
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>
<
s
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="
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xml:space
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">Eodem modo in boreali
<
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horologio reperientur puncta ſignorum borealium, ſi ex E B, auferatur recta E a, ſtylo æqualis, & </
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>
<
s
xml:id
="
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<
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per a, ducatur ad E B, perpendicularis b d, quæ rurſus erit linea horizontalis in horologio borea-
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li, &</
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>
<
s
xml:id
="
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xml:space
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">c. </
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<
s
xml:id
="
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xml:space
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">Ex hac porrò figura inueniemus eadem puncta in linea horizontali cuiuſcunque horolo-
<
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<
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="
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xlink:label
="
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xlink:href
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xml:space
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">Radii latitudi-
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num ortiuarũ,
<
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& occiduarum
<
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qui.</
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>
gii, vt ex ſequentibus manifeſtum fiet. </
s
>
<
s
xml:id
="
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xml:space
="
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">Poterunt autem diametri huius figuræ Y N, V P, &</
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>
<
s
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="
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">c. </
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>
<
s
xml:id
="
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xml:space
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">non
<
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ineptè vocari radii latitudinum ortiuarum, vel occiduarum.</
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>
<
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</
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<
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<
s
xml:id
="
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xml:space
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">PERSPICVE quoque hic apparet ratio, cur auſtralia ſigna mutentur in horologio boreali
<
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<
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="
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xlink:label
="
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xlink:href
="
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xml:space
="
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">Ratio, cur in bo
<
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reali horologio
<
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arcus ſignorum
<
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/>
auſtralium mu
<
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tentur in arcus
<
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/>
borealium ſi-
<
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gnorum.</
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>
in borealia; </
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>
<
s
xml:id
="
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"
xml:space
="
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">quia videlicet radii latitudinum ſignorum auſtralium per centrum E, ducti ſecant re-
<
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ctam b d, ductã ex parte Septentrionis per punctũ a, quæ refert horizontalem lineam in auſtrali
<
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/>
horologio; </
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>
<
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
<
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logio boreali, ſecant radii latitudinum ſignorũ borealiũ per centrũ E, ed ucti, vt ex figura conſtat.</
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>
<
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