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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rhead
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GNOMONICES
"/>
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xlink:label
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note-0228-01
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xlink:href
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note-0228-01a
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xml:space
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">Quando altitu
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do poli ſupra
<
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Horizõtem tan
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ta eſt, vt parum
<
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à vert@ce capitis
<
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polus recedat,
<
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quid agendum
<
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in horologii de
<
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ſcri ptione.</
note
>
exiguus, in remotiſſimo puncto cum eo conueniat in H, acutiſſimum{q́ue} angulum efficiat; </
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>
<
s
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echoid-s14240
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xml:space
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">deſcribemus
<
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nihilominus horologium, etiamſi centrum H, non habeamus, vt in ſcholio propoſ. </
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>
<
s
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="
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"
xml:space
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">1. </
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<
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xml:space
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">huius lib. </
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>
<
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"
xml:space
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">horizontale
<
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horologium conſtruximus, licet in eo centrum H, non haberemus, (quod quidem contingit, cum perexi-
<
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gua eſt altitudo poli ſupra Horizontem.) </
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>
<
s
xml:id
="
echoid-s14244
"
xml:space
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">hoc excepto, quòd loco anguli altitudinis poli D E F, conſtituen
<
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dus eſt in V erticali horologio angulus complementi altitudinis poli: </
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<
s
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="
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xml:space
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">Reliqua omnia abſoluenda ſunt, vt
<
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in dicto ſcholio.</
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>
<
s
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="
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xml:space
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</
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<
s
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xml:space
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">RVRSVS quando altitudo politam exigua eſt, vt Aequatoris diameter F D, acutiſſimum angu
<
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<
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xlink:label
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note-0228-02
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xlink:href
="
note-0228-02a
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xml:space
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">Quando altitu-
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do poli ſupra
<
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Horizontẽ per
<
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exigua el
<
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/>
t, quid
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in deſcriptione
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horologii agen-
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dum.</
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lum cum H I, & </
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>
<
s
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="
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"
xml:space
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">in remotiſſimo puncto I, conſtituat; </
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<
s
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xml:space
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">ac proinde difficile ſit punctum illud, in quo dictus
<
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angulus conſtituitur, dignoſcere, vtemur eodem remedio, quod in dicto ſcholio propoſ. </
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>
<
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xml:space
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">1. </
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<
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xml:space
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">huius lihri tradi
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dimus pro horologio horizontali, cum altitudo poli tanta ponebatur, vt polus parum à vertice capitis
<
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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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">10</
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>
abeſſet; </
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>
<
s
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xml:space
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">dummodo ad Verticale horologium conſtruendum pro angulo altitudinis poli B A N, conſtitua-
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mus angulum complementi altitudinis poli.</
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<
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</
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<
s
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xml:space
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">CAETERVM horologium verticale auſtrale hactenus deſcriptum indicabit quoque horas in op-
<
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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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">Si horologium
<
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auſtrale inuer-
<
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tatur, vt ex ſupe
<
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riore parte fiat
<
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/>
inferior, & quæ
<
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/>
poſt hanc inuer
<
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/>
ſionem dextra
<
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/>
eſt, fiat ſiniſtra,
<
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/>
& contra, ma-
<
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/>
nentibus @iſdẽ
<
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/>
numeris hora-
<
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/>
rum, conſtructũ
<
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erit horologiũ
<
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boreale Sed ho
<
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ræ, quæ prius à
<
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meridie nume-
<
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rabantur, nunc
<
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à med. noc. nu
<
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/>
merandæ erũ@
<
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& contra.</
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>
poſita parte plani horologij, quæ ad boream ſpectat, ſi omnes illius partes ita inuertantur, vt ex ſuperio-
<
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re fiat inferior, & </
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<
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="
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">quæ poſt hanc inuerſionem nobis ad horologium conuerſis dextra eſt, in ſiniſtram mute-
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tur, & </
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>
<
s
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="
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xml:space
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">contra, manentibus tamen ijſdem proſus horarum numeris. </
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>
<
s
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xml:space
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">Sed tunc portio lineæ meridianæ à
<
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centro horologij H, inchoata, et verſus lineam æquinoctialem procedens, quæ in horologio auſtrali indica-
<
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bat horam 12. </
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>
<
s
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xml:space
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">meridiei, in hoc boreali horologio horam 12. </
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<
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xml:space
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">mediæ noctis ſignificabit; </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">quæ in illo horã
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12. </
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>
<
s
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xml:space
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">mediæ noctis, in hoc horam 12. </
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>
<
s
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xml:space
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">meridiei monſtrabit: </
s
>
<
s
xml:id
="
echoid-s14264
"
xml:space
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">at que adeo horæ, quæ ibi à meridie computaban-
<
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tur, hic à media nocte, & </
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>
<
s
xml:id
="
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xml:space
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">quæ ibi à media nocte, hic à meridie numer andæ erunt. </
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<
s
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xml:space
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">Quod ex ijs, quæiam de
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<
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">20</
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<
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number
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158
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<
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="
0228-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0228-01
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</
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monſtrabimus, perſpicuum fiet. </
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<
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<
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in Auſtrali horologio linea meri-
<
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diana H I, centrum horologij H, li-
<
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nea æquinoctialis F K; </
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<
s
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="
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xml:space
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">ſtylus G D,
<
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eius{q́ue} locus punctum G; </
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<
s
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xml:space
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">linea, v. </
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<
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">g.
<
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</
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<
s
xml:id
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xml:space
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">horæ 5. </
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<
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xml:space
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">à meridie H K; </
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<
s
xml:id
="
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"
xml:space
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">linea horæ
<
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octauæ à media nocte H R, et axis
<
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mundi H D. </
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>
<
s
xml:id
="
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"
xml:space
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">Quoniam igitur axis
<
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D H, plano horologij auſtralis oc-
<
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currit in H, & </
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<
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xml:space
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">productus planum
<
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<
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xlink:label
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">30</
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>
ſecat, faciens angulum A H B, in
<
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facie oppoſita & </
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>
<
s
xml:id
="
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"
xml:space
="
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">boreali cũ linea
<
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/>
meridiana, quæ eadem est in vtra-
<
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/>
que facie plani, (cum ſit communis
<
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/>
ſectio Meridiani circuli, & </
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>
<
s
xml:id
="
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"
xml:space
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">pla-
<
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ni horologij.) </
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>
<
s
xml:id
="
echoid-s14278
"
xml:space
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">æqualem angulo D H I, in facie auſtrali cõprehenſo ſub eadem linea meridiana, & </
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<
s
xml:id
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">axe; </
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>
<
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xml:id
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">fit,
<
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<
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xlink:label
="
note-0228-07
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xlink:href
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xml:space
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">15. primi.</
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vt ſi accipiatur recta H C, in parte plani oppoſita, æqualis rectæ H G, in facie auſtrali, & </
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<
s
xml:id
="
echoid-s14281
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xml:space
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">ex C, eriga-
<
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tur ſtylus ad planum horologij borealis, atque adeò & </
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>
<
s
xml:id
="
echoid-s14282
"
xml:space
="
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">ad rectam H C, perpendicularis, ſecans axem in
<
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A; </
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<
s
xml:id
="
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"
xml:space
="
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">ſtylus C A, ſtylo G D, & </
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<
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xml:id
="
echoid-s14284
"
xml:space
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">axis H A, axi H D, ſit æqualis. </
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<
s
xml:id
="
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"
xml:space
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">Quoniã enim intriangulo A H C, duo
<
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anguli H, C, duobus angulis H, G, trianguli D H G, æquales ſunt; </
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>
<
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="
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">latus H C, lateri H G, ſumptum
<
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<
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æqualc; </
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<
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">erit & </
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>
<
s
xml:id
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xml:space
="
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">latus C A, lateri G D, æquale, & </
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>
<
s
xml:id
="
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"
xml:space
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">latus A H, lateri D H. </
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>
<
s
xml:id
="
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xml:space
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">Quòd ſi ex A, ducatur ad axẽ
<
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<
note
position
="
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"
xlink:label
="
note-0228-09
"
xlink:href
="
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xml:space
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">26. primi.</
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>
H A, perpendicularis A B, occurrens lineæ meridianæ in B, erit A B, exiſtens in plano Meridiani per
<
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rectas A H, H B, ducto, communis ſectio Aequatoris ac Meridiani. </
s
>
<
s
xml:id
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xml:space
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">Nam quoniam axis H A, per pro-
<
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<
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xlink:label
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">2. vndec.</
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>
poſ. </
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<
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">10. </
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<
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">lib. </
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<
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">1. </
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<
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">Theod. </
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<
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">ad planum Aequatoris est perpendicularis, tranſit{q́ue} per centrum eius; </
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>
<
s
xml:id
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xml:space
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">erit quoque
<
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idem axis, per def. </
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<
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">3. </
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<
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">lib. </
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<
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">11. </
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<
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="
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xml:space
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">Euclidis, ad communem ſectionem Aequatoris, & </
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>
<
s
xml:id
="
echoid-s14303
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xml:space
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">Meridiani per idem cen-
<
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trum ductam perpendicularis. </
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>
<
s
xml:id
="
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xml:space
="
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">Quare poſito A, centro Aequatoris, ſeu mundi, erit A B, in plano Meri
<
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diani exiſtens, & </
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>
<
s
xml:id
="
echoid-s14305
"
xml:space
="
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">ad axem H A, perpendicularis, communis ſectio Aequatoris, ac Meridiani. </
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>
<
s
xml:id
="
echoid-s14306
"
xml:space
="
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">Erit autẽ
<
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recta A B, ipſi D I, & </
s
>
<
s
xml:id
="
echoid-s14307
"
xml:space
="
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">H B, ipſi H I, æqualis; </
s
>
<
s
xml:id
="
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xml:space
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">propterea quòd in triangulo A H B, duo anguli A, H,
<
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/>
<
note
position
="
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xlink:label
="
note-0228-11
"
xlink:href
="
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xml:space
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">26. primi.</
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>
duobus angulis D, I, trianguli D H I, ſunt æquales, & </
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>
<
s
xml:id
="
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xml:space
="
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">latus A H, lateri D H, oſtenſum æquale, & </
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>
<
s
xml:id
="
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">c.
<
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</
s
>
<
s
xml:id
="
echoid-s14311
"
xml:space
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">Igitur ſi per B, ducatur in horologio boreali linea æquinoctialis B L, ad lineam meridianam perpendicu-
<
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<
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xlink:label
="
note-0228-12
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xlink:href
="
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xml:space
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">50</
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>
laris, diſtabit ea tantum à centro H, ſurſum verſus, quantum æquinoctialis linea F K, ab eodem centro
<
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H, abeſt deorſum verſus in horologio auſtrali. </
s
>
<
s
xml:id
="
echoid-s14312
"
xml:space
="
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">Quamobrem ſi in linea meridiana H B, producta ſumatur
<
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/>
recta B M, rectæ B A, æqualis, & </
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>
<
s
xml:id
="
echoid-s14313
"
xml:space
="
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">ex M, circulus deſcribatur, & </
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>
<
s
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="
echoid-s14314
"
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="
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">in partes 24. </
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>
<
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">ſecetur, & </
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>
<
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="
echoid-s14316
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xml:space
="
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">c. </
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>
<
s
xml:id
="
echoid-s14317
"
xml:space
="
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">deſcribetur
<
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/>
in facie plani oppoſita, & </
s
>
<
s
xml:id
="
echoid-s14318
"
xml:space
="
preserve
">boreali horologium boreale, quemadmodum in facie auſtr ali deſcriptum eſt au-
<
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/>
ſtrale, cum ſumpſimus rectam I E, æqualem rectæ I D, & </
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>
<
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xml:id
="
echoid-s14319
"
xml:space
="
preserve
">ex E, circulum deſcripſimus, & </
s
>
<
s
xml:id
="
echoid-s14320
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s14321
"
xml:space
="
preserve
">vt ſupra
<
lb
/>
demonſtratum eſt. </
s
>
<
s
xml:id
="
echoid-s14322
"
xml:space
="
preserve
">Eadem enim prorſus hic demonſtratio erit.</
s
>
<
s
xml:id
="
echoid-s14323
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s14324
"
xml:space
="
preserve
">HOC autem horologium boreale habetur quoque, ſi omnes lineæ auſtralis horologij per centrum H,
<
lb
/>
producantur. </
s
>
<
s
xml:id
="
echoid-s14325
"
xml:space
="
preserve
">Cum enim omnes circuli horarij à meridie, vel media nocte incedant per axem D H A,
<
lb
/>
ita vt ſecent planum horologij in H, erunt communes ſectiones ipſorum, & </
s
>
<
s
xml:id
="
echoid-s14326
"
xml:space
="
preserve
">plani horologij tam in facie
<
lb
/>
auſtrali, quàm in boreali, eædem rectæ lineę per H, trãſeuntes; </
s
>
<
s
xml:id
="
echoid-s14327
"
xml:space
="
preserve
">ita tamen, vt hę ſectiones, hoc eſt, lineę ho-
<
lb
/>
rarię, in boreali horologio intelligantur in parte plani oppoſita, quandoquidem & </
s
>
<
s
xml:id
="
echoid-s14328
"
xml:space
="
preserve
">axis mundi D H, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>