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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<
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xml:space
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">Alia deſctiptio
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parallelorum
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Horizon@is in
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c
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odem horolo-
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gio polati.</
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vel in pauciores partes pro numero parallelorum Horizontis delineandorum, ducantu
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r ex A, cen-
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tro per puncta diuiſionum lineæ rectæ, quæ reſpondebunt radiis parallelorum Horizontis in qua-
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drante D C 90. </
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<
s
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xml:space
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">figuræ præcedentis contenti, initio ſumpto à recta A B, vt figura indicat. </
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<
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xml:space
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">Deinde
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ex figura antecedentis propoſ. </
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<
s
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xml:space
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">rectæ B C, ſumatur æqualis A D, in linea A C, huius figuræ; </
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xml:space
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">& </
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<
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xml:space
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ctæ D B, vel D E, in recta A B, acci-
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piatur æqualis A E, ducaturq́ue recta
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D E. </
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<
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xml:space
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">Erit triangulum hoc A D E,
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æquale omnino triangulo C B D, fi-
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xml:space
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guræ præcedentis propoſ. </
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<
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li ad A, & </
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<
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">B, recti ſint, continean-
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turq́; </
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<
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">lateribus æqualibus, ex conſtru
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ctione; </
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<
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xml:space
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">ita vt D E, meridianæ lineæ
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C D, ſit æqualis. </
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<
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xml:space
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">Idẽ quoque triangu-
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lum A D E, æquale erit triangulo
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D V T, proximè antecedentis figu-
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ræ, cum hoc æquale ſit prædicto triã
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gulo C B D. </
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<
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xml:space
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I D V, angulo A B C, ſit æqualis, cũ
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vterque ſit altitudinis poli, & </
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<
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<
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lus rectus D I V, recto angulo B A C,
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ſintq́ue latera D I, A B, inter ſe æqua
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lia, quòd vtrumque ſumptũ ſit æqua-
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le ſtylo; </
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<
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">erunt & </
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<
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">latera D V, V I, late-
<
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">26. primi.</
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ribus B A, C A, æqualia. </
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<
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">Eademq́ue
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ratione latera D T, T I, lateribus
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B D, D A, æqualia erũt, &</
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<
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">c. </
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<
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xml:space
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">Poſt hęc
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ex figura præcedentis propoſ. </
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<
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ualla omnia inter centrum E, & </
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<
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cta, in quibus Verticales lineæ horizontalem lineam interſecant, in hanc figuram transferantur ex
<
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A, in rectam A B, notatis punctis in recta A B, aſcriptisq́ue numeris linearum Verticalium, vt 90.
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</
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<
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<
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<
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<
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xml:space
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">Poſtremo ex D, per puncta in A B, ſignata educan-
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tur rectæ lineæ. </
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<
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xml:space
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">Pro Verticali autem linea proprie dicta, à qua principium aliarum ſumitur, du-
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cenda eſt per D, ipſi A B, parallela D F, & </
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<
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">in alteram partem transferendæ ſunt quoque lineæ iam
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ductæ ex puncto D, per puncta rectæ A B, vt habeantur lineæ Verticales trans, & </
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<
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ticalem propriè dictam, quemadmodum in horologio horizontali factum eſt de lineis ante 6. </
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ram, & </
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<
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<
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<
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">huius libri. </
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<
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xml:space
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">Nam lineæ ex D, per puncta rectæ A B, ductæ, ſunt Vertica-
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les lineæ vltra Verticalem lineam propriè dictam, in quas videlicet vmbra ſtyli proiicitur, Sole
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exiſtente in Verticalibus auſtralibus; </
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<
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xml:space
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">aliæ verò, Verticales lineæ citra Verticalem lineam pro-
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prie dictam, &</
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<
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</
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<
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xml:space
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<
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Horizontis grad. </
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<
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<
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xml:space
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">comprehenſa transferantur ex puncto C, figuræ præcedentis propoſ. </
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<
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">in lineas
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binas Verticales æqualiter à meridiana linea diſtantes, reſpondentesq́ue numeris in recta A B, hu-
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ius figuræ ſignatis, notando puncta in ipſis lineis Verticalibus, (ita tamen, vt interualla rectarum
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ex D, in A B, cadentium tranſportentur ex Zenith C, in lineas Verticales horologii ſupra lineam
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Verticalem propriè dictã, interualla vero rectarum ex D, cadentium ad dextram rectæ D F, tranſ-
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ferantur in Verticales lineas infra lineam propriè dictam Verticalem) & </
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<
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, & </
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concinne coniungantur linea quadam flexa, deſcriptus erit parallelus Horizontis grad. </
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<
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<
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demq́ue modo reliqui paralleli Horizontis deſcribentur. </
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<
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poſterioris hu-
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iuſce deſcriptio
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nis parallelorũ
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Horizontis.</
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ea, quam in horologio horizontali tradidimus in ſecundo modo deſcribendorum arcuum ſigno-
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<
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rum. </
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<
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xml:space
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">Nam hic linea horizontalis eſt veluti Aequatoris linea, & </
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<
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horariæ, quarum centrum eſt Zenith, nempe punctum C, &</
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<
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<
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">vt in præcedenti Analemmate di-
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ximus. </
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<
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xml:space
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">Itaque linea A B, huius figuræ reſpondebit radio Aequatoris D C, poſtremæ figuræ pro-
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poſ. </
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<
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<
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">huius libri, in qua radii ſignorum deſcripti ſunt, & </
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<
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">rectæ ex A, ductæ radiis aliorum ſigno-
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rum ex D, emiſſis in dicta illa figura; </
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<
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<
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<
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denique Verticales ex D, cadentes lineis horariis ex H, productis. </
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<
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erualla rectarũ
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ex D, progredientium inter rectam A B, quæ eſt, (vt diximus) inſtar Æquatoris, & </
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<
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emiſſas transferantur in reſpondentes lineas Verticales à linea horizontali horologii, &</
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<
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<
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modum in horizontali horologio interualla inter radium Aequatoris, & </
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<
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ta ſunt, vt arcus ſignorum deſcriberentur. </
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<
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xml:space
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">Pro horologio polari inferiori transferendi ſunt in hac
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figura radii parallelorum Horizontis ex A, educti ad ſiniſtrã partem rectæ A B, ita vt </
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