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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GNOMONICES
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nis minor eſt angulo D H μ, altitudinis poli, (Si enim æquales eſſent anguli A D a, D H μ, exter-
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nus, & </
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<
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<
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xml:space
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">ſi autem maior eſſet angulus A D a, angulo
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">28. primi.</
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D H μ, coirent inter ſe rectæ H B, & </
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<
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">D a, quod non ponitur) fit, vt Horizon parallelis illis oppoſi-
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xlink:label
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xml:space
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">Quando alicu-
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ius ſigni atcus
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eſt Parabola, vel
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Ellipſis, arcus ſi-
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gni oppoſiti in
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horologio de-
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ſcribi nequit.</
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tis neq; </
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<
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xml:space
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">æquidiſtet, neque eos tangat, neque ſecet, vt ex coroll. </
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<
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<
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">Quamobrem arcus ſigni illius, cuius radius ſecatur, erit per eandem propoſ. </
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ſtum autem eſt, quando alicuius ſigni arcus Parabola eſt, vel Ellipſis, oppoſiti ſigni arcum in horo-
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logio deſcribi non poſſe; </
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<
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">propterea quòd rectæ ex H, emiſſę radium illius non ſecant, vt diximus.</
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</
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<
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xml:space
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">CÆTERVM ſatis erit, ſi ex poſteriori figura huius propoſ. </
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<
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xml:space
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">portionem arcus cuiuslibet ſi-
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">Quo pacto ex
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portione vnius
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arcus alicuius ſi
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gni uſque ad li-
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neam meridia-
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nam deſcripti,
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deſcribatur re
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liqua portio, at-
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que etĩam arcus
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ſigni oppoſi ti, ſi
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arcus ſignorum
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õ
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ppoſitorũ ſue-
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@int hyperbolę.</
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gni vſque ad lineam meridianam ex vna duntaxat parte deſcribamus. </
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">Ex hac enim & </
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tio ex alia parte, (atque in ſequentibus quidem horologiis multo accuratius, quàm ſi totum arcũ
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ex figura radiorum Zodiaci deſcriberemus, vt ſuo loco dicemus) immo & </
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<
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">totus arcus ſigni oppo
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ſiti (ſi tamen diameter arcuum, nempe recta H B, in figura radiorum radios ſignorum oppoſito-
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rum ſecet. </
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<
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xml:space
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">Nam tunc ſolum, vt oſtendimus, illorum ſignorum arcus hyperbolæ oppoſitæ ſunt, & </
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ęquales) deſcribi poterit. </
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<
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">Ita autem propoſitum exequemur. </
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<
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">Sit hyperbolarum oppoſitarum, vel
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Parabolæ, vel Ellipſis axis A B, qualis eſt meridiana linea in horologio horizontali, & </
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<
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illius, vel ſectionis conicæ vſque ad axem deſcripta ſit C D: </
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">Inuento autem in axe A B, puncto E,
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per quod arcus ſigni oppofiti tranſire debet, (quod quidem habetur, ſi D E, ſumatur æqualis dia-
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metro tranſuerſæ arcuum oppoſiterum in figura radiorum, nempe ſegmento rectæ H B, inter ra-
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dios illorum ſignorum oppoſitorum) & </
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<
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">acceptis rectis D A, E B, inter ſe æqualibus cuiuſcunque
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magnitudinis; </
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<
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">diuiſaq́; </
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<
s
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xml:space
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">diametro D E, bifariam in F, ponemus vnum pedem circini in F, & </
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<
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">alterũ
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extendemus ad quodlibet punctum arcus C D, vtpote vſque ad C, & </
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<
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">circino non variato deſcribe-
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mus ex F, ex altera parte axis arcũ occultum alicuius circuli; </
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<
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xml:space
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">Item alios duos ex vtraque parte eiuſ-
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dem axis verſus partes E. </
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<
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xml:space
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">Rurſus vnum pedem circini ſtatuentes in A, extendemus alterum vſque
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ad C, & </
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<
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xml:space
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">ſic manentibus circini cruribus extenſis, deſcribemus ex A, arcum circuli, qui priorem ex
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F, deſcriptum ex altera parte axis ſecet in G; </
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<
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xml:space
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">Item duos alios ex B, qui priores duos ex F, ex vtraq;
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</
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<
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<
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parte eiuſdem axis verſus partes E, deſcriptos ſecent in H, I. </
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<
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xml:space
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">Nam per punctum G, tranſibit arcus
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C D, productus, & </
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<
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xml:space
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">per puncta H, I, incedet arcus oppoſitus, & </
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<
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">æqualis, qui per punctum E, poſi-
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tus eſt tranſire. </
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<
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xml:space
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">Eodem pacto, ſi circinum extendamus ex F, in K, & </
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<
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">ex F, tres arcus deſcribamus ad
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interuallum F K; </
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<
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<
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">B, alios tres ad interuallum A K, vnum quidem ex A, & </
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<
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">duos ex B,
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qui priores tres ſecent in L, M, N, tranſibunt ijdem arcus per puncta L, M, N; </
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<
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">Et ita alia atque alia
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puncta, quotquot voluerimus, inueniemus. </
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<
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xml:space
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">Hortarer tamen, vt ex F, in portione arcus C D, acci
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perentur puncta illa, vbi à lineis horarijs ſecatur. </
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<
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">Quòd ſi arcus ſignorum oppoſitorum non ſunt
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hyperbolę oppoſitæ, & </
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<
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">æquales, vt contingit, cum diameter arcuum, vel recta H B, in figura radio-
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rum Zodiaci radios oppoſitos non ſecat, ſed vnum tantum, ſatis eſt, ſi bini duntaxat arcus ex alte-
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ra parte axis D E, ſeſe ſecantes deſcribantur ex F, & </
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<
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">A, ita vt F, ſumatur in quocunque loco diame-
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tri A B, etiamſi illud non ſit centrum: </
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<
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xml:space
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">Nam tunc arcus oppoſiti ſigni deſcribi non poteſt, vt </
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