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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ad centrum H, inſiſtunt, æquales ſunt arcubus, quibus hi inſiſtunt ad idem centrum H.</
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<
s
xml:id
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</
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<
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<
s
xml:id
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"
xml:space
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">POST hæc in ſemicirculo ex D, deſcripto ſupputentur declinationes ſignorum, initio facto
<
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à recta D C, ad vtramque partem ipſius rectæ D C; </
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>
<
s
xml:id
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xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s10354
"
xml:space
="
preserve
">per fines ſupputationum ex D, egrediantur
<
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/>
rectæ, quę radij erunt ſignorum, Sole in principijs ipſorum exiſtente, ita vt recta D C, in medio
<
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/>
omnium aliarum rectarum ſit radius Aequatoris, ſiue ♈, & </
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>
<
s
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xml:space
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">♎, vt perſpicuum eſt ex ijs, quæ in
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Analemmate diximus 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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>
<
s
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"
xml:space
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">ſuperioris lib. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Erunt autem arcus ſemicirculi ex D, deſcripti, in-
<
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/>
ter radium Aequatoris D C, & </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">radios aliorum ſignorum poſiti, vel æquales omnino arcubus Ana-
<
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/>
lemmatis inter diametrum Aequatoris, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">communes ſectiones Eclipticæ, & </
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>
<
s
xml:id
="
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xml:space
="
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">Meridiani poſitis,
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quando nimirum ſemicirculus ex D, deſcriptus ęqualis fuerit circulo Analemmatis, vel certè ipſis
<
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ſimiles exiſtent, quando ſcilicet dictus ſemicirculus circulo Analemmatis fuerit inæqualis. </
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>
<
s
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="
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"
xml:space
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">Vnde
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<
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">10</
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vt ſacilius deſcribantur radij ſignorum per eorum declinationes in Analemmate inuentas, e re fo-
<
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ret, ſi ſemicirculus ex D, deſcriptus haberet ſemidiametrum æqualem ſemidiametro Analemma-
<
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tis, vt arcus declinationũ ex Analemmate in hunc ſemicirculũ beneficio circini poſſint transferri.</
s
>
<
s
xml:id
="
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xml:space
="
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</
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<
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>
<
s
xml:id
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"
xml:space
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">EX hac itaque figura in hunc modum conſtructa, quam in ſequentibus figuram radiorum Zo
<
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diaci appellabimus, deſcribentur in horologio arcus ſignorum hac ratione. </
s
>
<
s
xml:id
="
echoid-s10365
"
xml:space
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">Transferatur ex figu-
<
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ra iam confecta linea H μ, horæ 12. </
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>
<
s
xml:id
="
echoid-s10366
"
xml:space
="
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">inter punctum H, & </
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>
<
s
xml:id
="
echoid-s10367
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xml:space
="
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">radium ♋, in lineam meridianam horo-
<
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/>
logij ex H, vel linea I μ, inter Aequatoris radium, & </
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>
<
s
xml:id
="
echoid-s10368
"
xml:space
="
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">radium ♋, ex puncto I, æquinoctialis lineę
<
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in horologio in lineam meridianam, punctum notando K. </
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>
<
s
xml:id
="
echoid-s10369
"
xml:space
="
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">Similiter linea horę primę, & </
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>
<
s
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="
echoid-s10370
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xml:space
="
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">11. </
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>
<
s
xml:id
="
echoid-s10371
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xml:space
="
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">eiuſ-
<
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dem figuræ inter H, & </
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>
<
s
xml:id
="
echoid-s10372
"
xml:space
="
preserve
">eundem radium ♋, vel inter ęquinoctialem radium, & </
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>
<
s
xml:id
="
echoid-s10373
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xml:space
="
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">radium ♋, transfe-
<
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ratur in lineas horę primæ, & </
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>
<
s
xml:id
="
echoid-s10374
"
xml:space
="
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">11. </
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>
<
s
xml:id
="
echoid-s10375
"
xml:space
="
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">horologij ex H, vel ex ξ, π, punctis æquinoctialis lineæ, pun-
<
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<
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position
="
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xlink:label
="
note-0181-02
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xlink:href
="
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xml:space
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">20</
note
>
ctum quoque in qualibet notando: </
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>
<
s
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="
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xml:space
="
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">Et ſic reliqua ſpatia inter H, & </
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>
<
s
xml:id
="
echoid-s10377
"
xml:space
="
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">radium ♋, vel inter æquino-
<
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ctialem radium, & </
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>
<
s
xml:id
="
echoid-s10378
"
xml:space
="
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">radium ♋, transferantur in horologium in lineas horarum correſpondẽtium,
<
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/>
puncta notando in illis. </
s
>
<
s
xml:id
="
echoid-s10379
"
xml:space
="
preserve
">Deinde hæc puncta in horariis lineis horologii notata coniungantur ap-
<
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poſitè linea quadam curua, & </
s
>
<
s
xml:id
="
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xml:space
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">inflexa. </
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>
<
s
xml:id
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xml:space
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">Hæc enim erit ſectio conica ♋, in horologio deſcripta. </
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>
<
s
xml:id
="
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xml:space
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">Eo-
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dem modo conicæ ſectiones aliorum ſignorum deſcribentur, ſi rectæ inter H, & </
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>
<
s
xml:id
="
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xml:space
="
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">radios ſignorum,
<
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vel inter æquinoctialem radium, & </
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>
<
s
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="
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xml:space
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">radios ſignorum comprehenſæ in lineas horarias correſpon-
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dentes horologij ex H, centro horologij, vel ex linea æquinoctiali transferantur, &</
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>
<
s
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="
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xml:space
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">c. </
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>
<
s
xml:id
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xml:space
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">hac tamen cõ
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ditione, vt rectæ inter radium Aequatoris, & </
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>
<
s
xml:id
="
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xml:space
="
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">radios aliorum ſignorum verſus punctum H, exiſten
<
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tes, transferantur à linea æquinoctiali in reſpondentes lineas horarias verſus centrum H; </
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>
<
s
xml:id
="
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xml:space
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">aliæ autẽ
<
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in contrariam partem: </
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>
<
s
xml:id
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xml:space
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">Item interualla linearum ex H, cadentium verſus radium Aequatoris DC,
<
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<
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transferantur ex centro horologij H, in eas lineas horarias, quæ ex H, centro horologii verſus li-
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neam æquinoctialem tendunt; </
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>
<
s
xml:id
="
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xml:space
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">Interualla verò linearum ex H, ductarum in alteram partem rectæ
<
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H V, ita vt radium Aequatoris infra D, ſecare non poſſint, transferantur in lineas horarum horolo
<
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/>
gij ex centro H, in partem ſuperiorem, hoc eſt, in eas horas, quæ lineam æquinoctialem non ſecãt,
<
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/>
quales ſunt omnes horæ poſt horam ſextam à meridie vſque ad mediam noctem, & </
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>
<
s
xml:id
="
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xml:space
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">omnes horæ
<
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à media nocte, vſque ad horam ſextam.</
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>
<
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</
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<
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<
s
xml:id
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xml:space
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">COMMODVM etiam erit interdum in ſemiſſibus horarum, vel quadrantibus inquirere
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puncta arcuum ſignorum. </
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>
<
s
xml:id
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xml:space
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">Vt in propoſito exemplo, quia puncta in lineis horarum quintæ à me-
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dia nocte, & </
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<
s
xml:id
="
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xml:space
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">ſeptimæ à meridie, per quæ duci debet arcus ♋, nimium diſtant à centro H, inuenien
<
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da erunt huiuſmodi puncta in lineis horarum 5 {1/2}. </
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>
<
s
xml:id
="
echoid-s10396
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xml:space
="
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">à media nocte, & </
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>
<
s
xml:id
="
echoid-s10397
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xml:space
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">6 {1/2}. </
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>
<
s
xml:id
="
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xml:space
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">à meridie. </
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<
s
xml:id
="
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"
xml:space
="
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">Idem facien
<
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<
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="
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xml:space
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">40</
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>
dum eſſet in lineis horarum 8 {1/2}. </
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<
s
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xml:space
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">à media nocte, & </
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>
<
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xml:id
="
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xml:space
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">3 {1/2}. </
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>
<
s
xml:id
="
echoid-s10402
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xml:space
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">à meridie pro punctis arcus ♑, inueſtigan
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dis, &</
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>
<
s
xml:id
="
echoid-s10403
"
xml:space
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">c. </
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>
<
s
xml:id
="
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xml:space
="
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">In proxima figura linea ex H, cadens ad ſiniſtram rectæ H V, punctis diſtincta pertinet ad
<
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horas 5 {1/2}. </
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>
<
s
xml:id
="
echoid-s10405
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xml:space
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">à media nocte, & </
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<
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="
echoid-s10406
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xml:space
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">6 {1/2}. </
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>
<
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xml:id
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xml:space
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">à meridie, &</
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>
<
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="
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xml:space
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">c.</
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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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">SED demonſtremus iam Geometricè, rectè hac ratione deſcribi parallelos, arcusve ſignorũ.
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</
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<
s
xml:id
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xml:space
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">Non enim deſunt, qui vel omnino negent, inter quos eſt Ioan. </
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>
<
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">B@ptiſta Benedictus in ſua Gnomo
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nica cap. </
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<
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">70. </
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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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">vbi alia, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">multo longiore ratione conatur arcus ſignorum deſcribere, vel certè
<
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dubitent, hoc modo rectè poſſe deſcribi arcus ſignorum, cùm rationem non videant, qua hæc no-
<
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<
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xlink:label
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xml:space
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">Demonſtratio
<
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poſterioris de-
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ſcriptionis pa-
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rallelorum, ſiue
<
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arcuum ſigno-
<
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rum. Vnde li-
<
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quet, Ioan. Ba-
<
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ptiſtam Benedi
<
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ctum immerito
<
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huiuſmodi de-
<
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ſcriptionẽ dam
<
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nare.</
note
>
ſtra deſcriptio, quam quidem omnes ſcriptores ſine vlla demonſtratione tradunt, nitatur. </
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>
<
s
xml:id
="
echoid-s10418
"
xml:space
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">Intelli-
<
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gatur ergo triangulum D H I, portionis Analemmatis præcedentis propoſ. </
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>
<
s
xml:id
="
echoid-s10419
"
xml:space
="
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">vel horologij in ſcho-
<
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lio eiuſdem propoſ. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſine por@ione Analemmatis deſcripti, rectum ad planum horologii, ac lineæ
<
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<
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="
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xlink:label
="
note-0181-06
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xlink:href
="
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xml:space
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">50</
note
>
meridianæ inſiſtens, ita vt punctum H, in centro horologii, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">I, in linea æquinoctiali ſtatuatur, vt
<
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in horologio huius propoſ. </
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>
<
s
xml:id
="
echoid-s10422
"
xml:space
="
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">apparet. </
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>
<
s
xml:id
="
echoid-s10423
"
xml:space
="
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">Si igitur figura continens lineas horarias, & </
s
>
<
s
xml:id
="
echoid-s10424
"
xml:space
="
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">ſignorum ra-
<
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dios proxime conſtructa axi H D, dicti trianguli ad horologium recti applicetur, & </
s
>
<
s
xml:id
="
echoid-s10425
"
xml:space
="
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">hinc inde cir-
<
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/>
cunducatur, ita tamen vt D C, radius Aequatoris rectum ſemper angulum in D, cum axe D H, con
<
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/>
ſtituat; </
s
>
<
s
xml:id
="
echoid-s10426
"
xml:space
="
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">perſpicuum eſt, radios ſignorum, ſi eos planum horologii penetrare concipiamus animo,
<
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/>
in horologio deſcribere ſectiones conicas ſignorum, in quas nimirum ad motum diurnum ipſi
<
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/>
radii à Sole proiiciuntur; </
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>
<
s
xml:id
="
echoid-s10427
"
xml:space
="
preserve
">quia in illa circunductione radii ſignorum efficientes cum radio Aequa
<
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toris angulos declinationum, & </
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>
<
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xml:id
="
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xml:space
="
preserve
">cum axe angulos complementorum declinationum, à conicis ſu-
<
lb
/>
perficiebus à radiis Solis deſcriptis non recedunt, ſed producti ad cœlum vſque ad ipſos paralle-
<
lb
/>
los perueniunt. </
s
>
<
s
xml:id
="
echoid-s10429
"
xml:space
="
preserve
">Q
<
unsure
/>
uoniam verò latera H D, D C, trianguli H D C, proximè antecedentis figuræ
<
lb
/>
(vt à quinta hora à meridie, vel à ſeptima à med. </
s
>
<
s
xml:id
="
echoid-s10430
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s10431
"
xml:space
="
preserve
">cui reſpondet linea H C@ incipiamus) </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>