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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per E, & </
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>
<
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xml:space
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">puncta diuiſionum ductæ communes ſectiones circulorum horariorum à meridie, vel
<
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media nocte, ac Æquatoris; </
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<
s
xml:id
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xml:space
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">cum Æquator, & </
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>
<
s
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xml:space
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">circulus F G H I, circa idem centrum E, deſcripti
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in arcus ſimiles ſecentur à dictis rectis, vt conſtat ex iis, quæ ad finem cap. </
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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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">in ſphæram ſcripſi-
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<
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xlink:href
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number
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179
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<
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file
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0256-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0256-01
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</
figure
>
mus: </
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>
<
s
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xml:space
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">Nempe G I,
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pſi A C, parallela,
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cõmunis ſectio Æ-
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quatoris, & </
s
>
<
s
xml:id
="
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xml:space
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">circuli
<
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horæ 12. </
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>
<
s
xml:id
="
echoid-s16138
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xml:space
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">ſeu Meri-
<
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diani. </
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>
<
s
xml:id
="
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xml:space
="
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">Nam com-
<
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munes ſectiones Me
<
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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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">10</
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ridiani, hoc eſt cir-
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culi horæ 12. </
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>
<
s
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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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">pla-
<
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ni horologii factæ
<
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ab Aequatore paral-
<
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lelę ſunt, atque adeo
<
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/>
cum A C, ſit cõmu-
<
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/>
nis ſectio Æquato-
<
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/>
ris, ac plani horolo-
<
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/>
gii, vt oſtendimus,
<
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/>
erit G I, communis
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0256-02
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xlink:href
="
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xml:space
="
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">20</
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>
ſectio Æquatoris, & </
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>
<
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xml:space
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<
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/>
Meridiani, ſeu circu
<
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li horæ 12. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">K L, cõ-
<
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munis ſectio Æqua-
<
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/>
toris, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">circuli horę
<
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/>
11. </
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>
<
s
xml:id
="
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"
xml:space
="
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">in horologio ad
<
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/>
ortum ſpectante; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">at
<
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in eo quod in occa-
<
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/>
ſum vergit, commu-
<
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/>
nis ſectio Æquatoris, & </
s
>
<
s
xml:id
="
echoid-s16147
"
xml:space
="
preserve
">circuli horæ primæ, & </
s
>
<
s
xml:id
="
echoid-s16148
"
xml:space
="
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">ſic deinceps; </
s
>
<
s
xml:id
="
echoid-s16149
"
xml:space
="
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">vt cõſtat, ſi diligenter circuli F G H I,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0256-03
"
xlink:href
="
note-0256-03a
"
xml:space
="
preserve
">30</
note
>
vel Æquatoris propria poſitio conſideretur in vtriuſque horologii Meridiani plano. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quamobrem
<
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/>
circuli horarii à meridie, vel media nocte ſecabunt æquinoctialem lineam A C, in plano horolo-
<
lb
/>
gii in punctis, in quæ cadunt rectæ per centrum E, & </
s
>
<
s
xml:id
="
echoid-s16151
"
xml:space
="
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">puncta diuiſionum circuli F G H I, eductæ;
<
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/>
</
s
>
<
s
xml:id
="
echoid-s16152
"
xml:space
="
preserve
">ac proinde per hæc puncta ducentur communes ſectiones eorundem circulorum horariorum, & </
s
>
<
s
xml:id
="
echoid-s16153
"
xml:space
="
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">
<
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/>
plani horologii, quæ quidem ſunt horariæ lineæ à meridie, vel media nocte. </
s
>
<
s
xml:id
="
echoid-s16154
"
xml:space
="
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">Cum ergo ex coroll. </
s
>
<
s
xml:id
="
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xml:space
="
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">
<
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propoſ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">22. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſuperioris lib. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">hæ lineæ horariæ parallelæ ſint in Meridiano horologio, perſpicuum eſt
<
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/>
rectas, quæ per puncta lineæ A C, ipſi D E, parallelæ aguntur, lineas horarias eſſe à meridie, vel me
<
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/>
dia nocte. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Sed dubitabit fortaſſe quiſpiam, an lineæ horarum à mer. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">noc. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſint perpendi-
<
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/>
culares ad lineam æquinoctialem A C; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">atqueadeo parallelæ ipſi D E, quæ perpendicularis du-
<
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/>
cta eſt ad A C, quemadmodum eas nos duximus: </
s
>
<
s
xml:id
="
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"
xml:space
="
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">demonſtrabimus & </
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>
<
s
xml:id
="
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xml:space
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">hoc hac ratione. </
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>
<
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xml:id
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xml:space
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">Quo-
<
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<
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">40</
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niam tam planum horologii, quàm planum cuiuſuis circuli horarii à mer. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">noc. </
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>
<
s
xml:id
="
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"
xml:space
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">rectum
<
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eſtad Æquatorem, erit quoque communis illorum ſectio ad eundem Æquatorem perpendicula-
<
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<
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position
="
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xlink:label
="
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xlink:href
="
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xml:space
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">19. vndec.</
note
>
ris, atque adeo, 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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">lib. </
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<
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">11. </
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>
<
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xml:space
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">Eucl. </
s
>
<
s
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xml:space
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">& </
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>
<
s
xml:id
="
echoid-s16175
"
xml:space
="
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">ad rectam A C, in Æquatore exiſtentem. </
s
>
<
s
xml:id
="
echoid-s16176
"
xml:space
="
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">Igitur omnes
<
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/>
lineæ horariæ à mer. </
s
>
<
s
xml:id
="
echoid-s16177
"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
echoid-s16178
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s16179
"
xml:space
="
preserve
">nempe communes ſectiones circulorum horariorum & </
s
>
<
s
xml:id
="
echoid-s16180
"
xml:space
="
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">plani
<
lb
/>
horologii ad rectam A C, perpendiculares ſunt: </
s
>
<
s
xml:id
="
echoid-s16181
"
xml:space
="
preserve
">Ac proinde cum per puncta inuenta in recta A C,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0256-06
"
xlink:href
="
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"
xml:space
="
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">29. primi.</
note
>
ducendæ ſint, recte eas per illa puncta parallelas ipſi D E, quæ ad A C, perpẽdicularis eſt, duximus:
<
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/>
</
s
>
<
s
xml:id
="
echoid-s16182
"
xml:space
="
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">quia hac ratione omnes ad A C, perpendiculares erunt. </
s
>
<
s
xml:id
="
echoid-s16183
"
xml:space
="
preserve
">Quod idem hac ratione demonſtrabitur. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">
<
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/>
Quoniam ſectiones factæ in Meridiano & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">plano horologii ab Horizonte parallelæ ſunt; </
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>
<
s
xml:id
="
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"
xml:space
="
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">Item 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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">10. vndec.</
note
>
ctiones factæ in eiſdẽ planis à circulo horæ 6. </
s
>
<
s
xml:id
="
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xml:space
="
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">erit angulus ſub illis contentus in Meridiano æqua
<
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<
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position
="
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"
xlink:label
="
note-0256-08
"
xlink:href
="
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xml:space
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">16. vndec.</
note
>
lis angulo comprehenſo ſub his in plano horologii. </
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>
<
s
xml:id
="
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xml:space
="
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">Cum ergo ille ſit angulus altitudinis poli,
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<
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xlink:label
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">50</
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vt conſtat, erit quoque hic angulus altitudinis poli. </
s
>
<
s
xml:id
="
echoid-s16189
"
xml:space
="
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">Quocirca cum angulus B A D, ſit angulus al-
<
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titudinis poli, propterea quòd, per conſtructionem, reliquus ex recto B A C, æqualis eſt comple-
<
lb
/>
mento altitudinis poli; </
s
>
<
s
xml:id
="
echoid-s16190
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s16191
"
xml:space
="
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">A B, ſit communis ſectio plani horologii & </
s
>
<
s
xml:id
="
echoid-s16192
"
xml:space
="
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">Horizontis, erit A D, com-
<
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/>
munis ſectio eiuſdem plani horologii, & </
s
>
<
s
xml:id
="
echoid-s16193
"
xml:space
="
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">circuli horæ 6. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">à mer. </
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>
<
s
xml:id
="
echoid-s16195
"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
echoid-s16196
"
xml:space
="
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">noc. </
s
>
<
s
xml:id
="
echoid-s16197
"
xml:space
="
preserve
">Ac proinde cum om
<
lb
/>
nes lineæ horariæ ſint inter ſe parallelæ, ac idcirco & </
s
>
<
s
xml:id
="
echoid-s16198
"
xml:space
="
preserve
">ipſi A D, æquidiſtent, vt oſtendimus; </
s
>
<
s
xml:id
="
echoid-s16199
"
xml:space
="
preserve
">erunt
<
lb
/>
omnes ad A C, perpendiculares, quemadmodum & </
s
>
<
s
xml:id
="
echoid-s16200
"
xml:space
="
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">ipſa A D, ad A C, perpendicularis eſt. </
s
>
<
s
xml:id
="
echoid-s16201
"
xml:space
="
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">Sola li-
<
lb
/>
<
note
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="
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"
xlink:label
="
note-0256-10
"
xlink:href
="
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"
xml:space
="
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">29. primi.</
note
>
nea meridiana, vel horæ 12. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">à mer. </
s
>
<
s
xml:id
="
echoid-s16203
"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
echoid-s16204
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s16205
"
xml:space
="
preserve
">deſcribi in hoc horologio n
<
unsure
/>
on poteſt, ſed euane-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0256-11
"
xlink:href
="
note-0256-11a
"
xml:space
="
preserve
">Linea meridia-
<
lb
/>
na, ſeu horæ 12.
<
lb
/>
deſcribi nequit
<
lb
/>
in Meridiano
<
lb
/>
horologio.</
note
>
ſcit, vt liquido conſtat ex ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s16206
"
xml:space
="
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">11. </
s
>
<
s
xml:id
="
echoid-s16207
"
xml:space
="
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">primi libri, cum Meridianus circulus planum ho-
<
lb
/>
rologii non ſecet, ſed ei æquidiſtet. </
s
>
<
s
xml:id
="
echoid-s16208
"
xml:space
="
preserve
">Itaque horologium Aſtronomicum Meridianum conſtitui-
<
lb
/>
mus, &</
s
>
<
s
xml:id
="
echoid-s16209
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s16210
"
xml:space
="
preserve
">Quod erat faciendum.</
s
>
<
s
xml:id
="
echoid-s16211
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>