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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Table of Notes
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LIBER SECVNDVS.
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cumferentiam Aequatoris, initio facto à Meridiano, in totidem partes æquales: </
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<
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circuli horarum à meridie, vel media nocte eundem Aequatorem diuidant in partes 24. </
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<
s
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xml:space
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">æquales,
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initio quoque facto à Meridiano, vt patet ex propoſ. </
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<
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<
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<
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xml:space
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">efficitur, vt eędem rectę oc-
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cultę è centro E, egredientes ſint communes ſectiones Aequatoris, & </
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>
<
s
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xml:space
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">circulorum horariorũ, qui
<
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horas à mer. </
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<
s
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">vel med. </
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>
<
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<
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">indicant; </
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<
s
xml:id
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"
xml:space
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">nempe N M, communis ſectio Aequatoris, & </
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>
<
s
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">circuli horę 12.
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</
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<
s
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xml:space
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">hoc eſt, Meridiani; </
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<
s
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xml:space
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">O P, Aequatoris, & </
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<
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">circuli horę primę à meridie, vel media nocte; </
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<
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xml:space
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">Q R, Aequa
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toris, & </
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<
s
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">circuli horę 2. </
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>
<
s
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">à meridie vel media nocte; </
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<
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">S T, Aequatoris, & </
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<
s
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">circuli horę 3. </
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>
<
s
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xml:space
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">à meridie,
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vel media nocte, &</
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<
s
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">c. </
s
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<
s
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xml:space
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">vt patet, ſi circulus ex E, deſcriptus in propria poſitione intelligatur. </
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<
s
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xml:space
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">Vergent
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enim puncta O, Q, S, in hemiſphærio ſupero ad partes occidentales, ſeu pomeridianas, &</
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<
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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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">QVARE circuli horarij à meridie, vel media nocte ſecant in plano horologii rectam F K,
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in punctis I, A, B, &</
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<
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<
s
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xml:space
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">(quæ quidem puncta non variantur, etiamſi planum circuli circa E, deſcri
<
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pti aliam poſitionem habeat, nempe in plano horologii, in quo ipſum deſcripſimus, exiſtat. </
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<
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xml:space
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">Nam
<
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ſi planum huius circuli circumuertatur circa rectam F K, tanguam cardinem immobilem, ita vt
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recta I E, ſemper perpendicularis ſit ad F K, occurrent recte N E, O E, Q E, & </
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<
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<
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xml:space
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">in eiſdem ſemper
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punctis ęquinoctiali lineę F K, vt perſpicuum eſt) ac idcirco per hęc puncta incedent communes
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ſectiones illorum circulorum horariorum, & </
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<
s
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">plani horologij, quæ quidem ſunt lineę horarię à
<
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meridie, vel media nocte; </
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<
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">Atqui per corollar. </
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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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">eędem communes ſe-
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ctiones, ſeu lineæ horarię, ſecant ſe mutuo in horologij centro H, in quo axis D H, plano horolo-
<
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gij occurrit. </
s
>
<
s
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="
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"
xml:space
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">Igitur rectę per puncta I, A, B, &</
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>
<
s
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">c. </
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>
<
s
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">æquinoctialis lineę F k, & </
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>
<
s
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="
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xml:space
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">per punctum H, ſeu cen
<
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trum horologij, emiſſę ſunt lineę horarũ à meridie, vel media nocte, ita vt meridiana linea H I E,
<
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<
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">20</
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indicet horam 12. </
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<
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">meridiei, & </
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<
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">lineę ad ſiniſtram illius monſtrent horas à meridie; </
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<
s
xml:id
="
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xml:space
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">lineę verò ad
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dexteram horas à media nocte, vt in ſigura apparet, & </
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>
<
s
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">in ſcholio ſequenti declarabimus.</
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<
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</
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<
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<
s
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">SOLA linea horę 6. </
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>
<
s
xml:id
="
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xml:space
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">ducenda eſt per H, perpendicularis ad H I, vel ęquidiſtans ipſi F k, qua-
<
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lis eſt C L. </
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<
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">Cum enim, vt in ſcholio propoſ. </
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<
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">22. </
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<
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<
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xml:space
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">docuimus, in horologio horizon-
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tali parallelæ ſint linea ęquinoctialis, & </
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<
s
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xml:space
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">linea horę ſextę à meridie, vel media nocte, perſpicuum
<
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eſt, rectam C L, lineam eſſe horę ſextę à meridie, vel media nocte, quandoquidem parallela eſt
<
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ęquinoctiali lineę F K, tranſitq́; </
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<
s
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xml:space
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">per punctum H, vbi omnes horarię lineę à meridie, vel media
<
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nocte ſe interſecant. </
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>
<
s
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xml:space
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">Horologium igitur Aſtronomicum horizontale conſtituimus, &</
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<
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<
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faciendum erat.</
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</
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</
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<
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<
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horologii Aſtro
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nomici horizõ-
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talis, commodiſ
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ſima pro horis
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deli@eãdis, quæ
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propinquæ ſunt
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hotæ 6. à mer.
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vel med. noc.</
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<
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<
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">ANDREAS Schonerus proponit aliam rationem horarum à meridie, vel media nocte deſcriben-
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darum, quæ per commoda eſt pro illis horis delineandis, quæ æquinoctialem lineam in punctis valde remo
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tis ſecant, quales ſunt horæ, quæ propinquæ ſunt horæ ſextæ à mer. </
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<
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<
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<
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xml:space
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">Ea autem est huiuſmodi.
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</
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<
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xml:space
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">In æquinoctiali linea F k, ſumatur recta I a, æqualis rectæ I E, vel I D, & </
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<
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xml:space
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">per a, ducatur ad ęquinoctia-
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lem lineam perpendicularis a b, vel ipſi H I, parallela ſecans lineam horæ ſextæ C L, (quæ ſemper ex
<
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H, centro horologij ducitur perpendicularis ad H I, vel parallela lineæ ęquinoctiali, vt oſtenſum eſt) in b. </
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Sumpta deinde b d, æquali ipſi a b, ducatur per d, ad b d, perpendicularis e f, vel parallela ipſi H I. </
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<
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<
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Poſtremo ex d, centro deſcripto circulo, eo{q́ue} in partes 24. </
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<
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xml:space
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">diuiſo, initio facto à recta b d, ducantur ex d,
<
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<
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xlink:label
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xml:space
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">Segmenta æqui
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noctialis lineæ
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in horologio ho
<
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rizontali inter
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lineam meridia
<
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nam, & binas
<
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horas vtrinque
<
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à meridie æqua
<
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li temporis ſpa-
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lio diſtãtes, ſunt
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æqualia.</
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centro per diuiſionum puncta lineæ occultæ. </
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>
<
s
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xml:space
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">Hæ enim rectam a b, ſecabunt in punctis, per quæ ſi ex H,
<
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<
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centro horologij rectæ emittantur, dabunt hæ, vt prius, horas à meridie, vel media nocte.</
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</
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<
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xml:space
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">IN horologio porrò quouis horizontali binæ lineæ quęcunque horariæ hinc inde à meridiana linea
<
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æquali temporis ſpatio remotæ auferunt ex linea ęquinoctiali F K, lineas æquales, illas nimirum, quæ in-
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ter lineas borarias, & </
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>
<
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">meridianam lineam interijciuntur. </
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<
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xml:space
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">Vt lineæ H F, H K, quarum vtraque quin-
<
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que horis à meridiana linea diſtat, auferunt lineas I F, I K, æquales. </
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>
<
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xml:space
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">Cum enim anguli I E F, I E k, qui
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continentur ſub linea meridiana, & </
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>
<
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xml:space
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">rectis occultis ex E, ad F, K, ductis, (licet enim E F, ducta non
<
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ſit, eam tamen ductam eſſe concipiendum eſt) æquales ſint, quòd in centro E, ab æqualibus arcubus circuli
<
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<
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xlink:label
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xml:space
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">27. tertij.</
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ex E, deſcripti ſubtendantur, & </
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<
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">anguli ad I, recti, erunt duo anguli I E F, E I F, trianguli E I F, æqua-
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les duobus angulis I E K, E I K, trianguli E I K; </
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>
<
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xml:space
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">ac propterea cum habeant latus I E, commune, erunt
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<
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">26. primi.</
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reliqua later a vnius æqualia reliquis lateribus alterius, nempe I F, ipſi I K, quod eſt propoſitũ. </
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>
<
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">Eadem
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<
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">50</
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>
<
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xlink:label
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xml:space
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">Arcus circuli ex
<
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H, centro horo
<
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logij horizon@a
<
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lis deſcripti, in-
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ter metidianã
<
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lineam & binas
<
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horas vtrinque
<
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à metidie æqua
<
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liter diſtantes
<
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interiecti ſunt
<
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æquales.</
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>
eſt ratio de cęteris. </
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>
<
s
xml:id
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xml:space
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">Itaque ſpatia horaria ante meridiem æqualia ſunt ſpatijs horarijs poſt meridiem, ſin-
<
lb
/>
gula ſingulis, in linea æquinoctiali horologij horizontalis.</
s
>
<
s
xml:id
="
echoid-s9392
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9393
"
xml:space
="
preserve
">EX hoc ſequitur, arcus circuli cuiuſuis ex H, deſcripti in horologio horizontali inter ceptos inter li-
<
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neam meridianam, & </
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>
<
s
xml:id
="
echoid-s9394
"
xml:space
="
preserve
">binas quaſcunque lineas horarias æquali ſpatio temporis à meridie diſtantes, qua-
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les ſunt v. </
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>
<
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xml:id
="
echoid-s9395
"
xml:space
="
preserve
">g. </
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<
s
xml:id
="
echoid-s9396
"
xml:space
="
preserve
">arcus circuli ex H, deſcripti inter meridianam lineam H I, & </
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>
<
s
xml:id
="
echoid-s9397
"
xml:space
="
preserve
">lineas H F, H K, interiecti,
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æquales eſſe. </
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<
s
xml:id
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echoid-s9398
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xml:space
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">Nam cum latera I H, I F, trianguli I H F, lateribus I H, I K, trianguli I H K, ęqualia
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ſint, angulos{q́ue} comprehendant æquales, nempe rectos, erunt & </
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<
s
xml:id
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echoid-s9399
"
xml:space
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preserve
">anguli I H F, I H K, æquales, ac propte-
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/>
<
note
position
="
right
"
xlink:label
="
note-0165-11
"
xlink:href
="
note-0165-11a
"
xml:space
="
preserve
">4. primi.</
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rea in circulo ex H, deſcripto ab arcubus ęqualibus ſubtendentur, & </
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>
<
s
xml:id
="
echoid-s9400
"
xml:space
="
preserve
">ſic de cęteris.
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/>
</
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>
<
s
xml:id
="
echoid-s9401
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0165-12
"
xlink:href
="
note-0165-12a
"
xml:space
="
preserve
">26. tertij.</
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>
</
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>
</
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>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9402
"
xml:space
="
preserve
">SEQVITVR rurſus, interualla inter centrum E, Aequatoris, & </
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>
<
s
xml:id
="
echoid-s9403
"
xml:space
="
preserve
">binas horas quaſcunque in ęqui
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/>
<
note
position
="
right
"
xlink:label
="
note-0165-13
"
xlink:href
="
note-0165-13a
"
xml:space
="
preserve
">Interualla in-
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ter E, centrum
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/>
Aequatoris &
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/>
binas horas v
<
unsure
/>
-</
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>
noctiali linea F K, ęquali temporis interuallo à linea meridiana diſtantes, qualia ſunt interualla E F,
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/>
E K, eſſe ę
<
unsure
/>
qualia. </
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>
<
s
xml:id
="
echoid-s9404
"
xml:space
="
preserve
">Cum enim ęqualia ſint latera I E, I F, trianguli I E F, lateribus I E, I K, </
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</
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>
</
text
>
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>