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 PRIMVS.
"/>
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<
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xml:space
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">THEOREMA 19. PROPOSITIO 21.</
head
>
<
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xml:space
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">@ Omnes lineæ
<
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horaiũ à mer.
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vel med. noc.
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in quocunque
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horologio axẽ
<
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mundi ſecante
<
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ſe mutuo inter.
<
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ſecant in illo
<
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puncto axis, in
<
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quo axis plano
<
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horologii occur
<
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@it.</
note
>
<
p
>
<
s
xml:id
="
echoid-s4114
"
xml:space
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">LINEAE omnium horarum à meridie vel media nocte in quo-
<
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cunque horologio, cuius planum axem mundi ſecat, ſe mutuo interſe-
<
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/>
cant in illo puncto axis, in quo horologii plano ipſe axis occurrit.</
s
>
<
s
xml:id
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xml:space
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</
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<
p
>
<
s
xml:id
="
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"
xml:space
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">CVM enim omnes circuli horas à meridie vel media nocte monſtrantes incedant per mun-
<
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/>
di polos, ex propoſ. </
s
>
<
s
xml:id
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"
xml:space
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">9. </
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>
<
s
xml:id
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echoid-s4118
"
xml:space
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">huius lib. </
s
>
<
s
xml:id
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echoid-s4119
"
xml:space
="
preserve
">vbi ſe mutuo eorum circunferentiæ interſecant, erit axis mundi
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0097-02
"
xlink:href
="
note-0097-02a
"
xml:space
="
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">Lineæ horarú
<
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/>
à mer uel med.
<
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/>
noc. in horolo-
<
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gio Aequino-
<
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/>
ctiali, Horizon-
<
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/>
ta’i, Verticaliq́
<
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/>
ſphærę obliquę,
<
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/>
conueniunt om
<
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/>
nes in @ pun-
<
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/>
cto, in quo axis
<
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/>
mundi planum
<
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/>
horologij ſecat,
<
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/>
excepto Vertica
<
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/>
li horologio il-
<
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/>
lius ſphærę ob-
<
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/>
liquæ, vbi po-
<
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/>
lus eſt in verti-
<
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/>
ce capitis.</
note
>
<
note
position
="
left
"
xlink:label
="
note-0097-03
"
xlink:href
="
note-0097-03a
"
xml:space
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">10</
note
>
eorum planorum communis ſectio. </
s
>
<
s
xml:id
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echoid-s4120
"
xml:space
="
preserve
">In quo igitur puncto occurrit axis plano horologii, in eo-
<
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/>
dem coibunt, per propoſ. </
s
>
<
s
xml:id
="
echoid-s4121
"
xml:space
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">18. </
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>
<
s
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="
echoid-s4122
"
xml:space
="
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">huius lib. </
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>
<
s
xml:id
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"
xml:space
="
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">omnium illorum, & </
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>
<
s
xml:id
="
echoid-s4124
"
xml:space
="
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">plani horologii communes ſectio-
<
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/>
nes, hoc eſt, lineæ horariæ à meridie vel media nocte. </
s
>
<
s
xml:id
="
echoid-s4125
"
xml:space
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preserve
">Quapropter lineæ omnium horarum à
<
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/>
meridie, vel media nocte, &</
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>
<
s
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echoid-s4126
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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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">Quod erat demonſtrandum.</
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<
s
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="
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xml:space
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</
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>
</
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<
head
xml:id
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xml:space
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">COROLLARIVM.</
head
>
<
p
>
<
s
xml:id
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echoid-s4129
"
xml:space
="
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">ITAQVE in horologio Aequinoctiali, & </
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>
<
s
xml:id
="
echoid-s4130
"
xml:space
="
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">Horizontali, Verticaliq́; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quocunq; </
s
>
<
s
xml:id
="
echoid-s4132
"
xml:space
="
preserve
">ſphæræ obliquæ ſecant
<
lb
/>
ſe mutuo lineæ oẽs horariæ à meridie vel media nocte in uno eodemq; </
s
>
<
s
xml:id
="
echoid-s4133
"
xml:space
="
preserve
">axis pũcto, in quo nimirũ axis ipſe
<
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/>
planis dictorum horologiorum occurrit: </
s
>
<
s
xml:id
="
echoid-s4134
"
xml:space
="
preserve
">quia plana horum horologiorum ſecant axem, quemadmodum
<
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/>
& </
s
>
<
s
xml:id
="
echoid-s4135
"
xml:space
="
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">circuli maximi, quibus ipſa æquidiſtant, videlicet Aequator, Horizon, Verticalisq́; </
s
>
<
s
xml:id
="
echoid-s4136
"
xml:space
="
preserve
">ſphærę obliquæ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0097-04
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xlink:href
="
note-0097-04a
"
xml:space
="
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">20</
note
>
cuiuſuis eundem interſecant, vt maniſeſtum eſt. </
s
>
<
s
xml:id
="
echoid-s4137
"
xml:space
="
preserve
">Excipe tamen Verticale horologium illius ſphæræ obli-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0097-05
"
xlink:href
="
note-0097-05a
"
xml:space
="
preserve
">In omni horo-
<
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/>
logio, quodæ-
<
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/>
quidiſta@ circu-
<
lb
/>
lo maximo per
<
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/>
polos mũ
<
unsure
/>
di nõ
<
lb
/>
ducto, lincæ ho-
<
lb
/>
rarum 2 mer.
<
lb
/>
vel med. noc. ſe
<
lb
/>
mutuo interſe-
<
lb
/>
cant in vno eo-
<
lb
/>
demq́; puncto,
<
lb
/>
in quo nimirũ
<
lb
/>
axis mundi ho
<
lb
/>
rologio occur-
<
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/>
rit.</
note
>
quæ, in qua vertex eſt polus mundi. </
s
>
<
s
xml:id
="
echoid-s4138
"
xml:space
="
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">Ibi enim Verticalis circulus per mundi polos, & </
s
>
<
s
xml:id
="
echoid-s4139
"
xml:space
="
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">axem incedit, atque
<
lb
/>
adeò axem non ſecat. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Igitur neque planum horologii ei æquidiſtans eundem ſecare poteſt.</
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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">DENIQVE, vt vno verbo omnia comprehendamus, lineæ horarię à meridie vel media nocte om-
<
lb
/>
nes in horologio quolibet, cuius planum non æquidiſtat alicui circulo per polos mundi tranſeunti, vel axi
<
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/>
mundi, (cuiuſmodi ſunt ferè omnia horologia declinantia, & </
s
>
<
s
xml:id
="
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"
xml:space
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">inclinata,) ſecant axem mundi in vno eo-
<
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/>
demq́; </
s
>
<
s
xml:id
="
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"
xml:space
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">puncto, in quo ſcilicet axis ipſe plano horologij occurrit: </
s
>
<
s
xml:id
="
echoid-s4145
"
xml:space
="
preserve
">quia horologium eiuſmodi quodcunque
<
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/>
axem mundi ſecat, cum circulus maximus, cui ęquidiſtat, non per polos mundi ponatur tranſire.</
s
>
<
s
xml:id
="
echoid-s4146
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xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4147
"
xml:space
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">APPELLATVR autem punctum illud, in quo axis mundi plano horologii occurrit, centrum
<
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/>
horologii.</
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>
<
s
xml:id
="
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xml:space
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</
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>
</
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>
<
div
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type
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n
="
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<
head
xml:id
="
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style
="
it
"
xml:space
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">SCHOLIVM.</
head
>
<
note
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="
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"
xml:space
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">30</
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>
<
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="
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"
xml:space
="
preserve
">Centrum horo
<
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/>
logii quid.</
note
>
<
p
style
="
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">
<
s
xml:id
="
echoid-s4149
"
xml:space
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preserve
">PARI ratione, lineæ quælibet horariæ tam à meridie vel media nocte, quàm ab ortu vel occaſu,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0097-08
"
xlink:href
="
note-0097-08a
"
xml:space
="
preserve
">Quænam horæ
<
lb
/>
ab or. vel occ. &
<
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/>
à mer. vel med.
<
lb
/>
noc. in quouis
<
lb
/>
horologio pa-
<
lb
/>
rallelæ ſint.</
note
>
quarum circuli horarij eandem habent communem ſectionem, in quouis horologio, cuius planum commu-
<
lb
/>
ni illi ſectioni non æquidiſtat, ſed ipſam ſecat, quamuis communis illa ſectio non ſit axis mundi, ſe mutuo
<
lb
/>
ſecant in illo puncto communis ſectionis, in quo ipſa plano horologij occurrit. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Eadem enim prorſus eſt
<
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/>
demonſtr atio, ex propoſ. </
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>
<
s
xml:id
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xml:space
="
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">18. </
s
>
<
s
xml:id
="
echoid-s4152
"
xml:space
="
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">huius lib. </
s
>
<
s
xml:id
="
echoid-s4153
"
xml:space
="
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">deſumpta. </
s
>
<
s
xml:id
="
echoid-s4154
"
xml:space
="
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">Huiuſmodi ſunt ternæ quælibet horæ poſitæ in tabula
<
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/>
<
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="
right
"
xlink:label
="
note-0097-09
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xlink:href
="
note-0097-09a
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xml:space
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">Quælibet horæ
<
lb
/>
in tabulis præ-
<
lb
/>
cedentium dua
<
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/>
rum propoſ. de-
<
lb
/>
ſcriptæ, vna cũ
<
lb
/>
hora, vel linea,
<
lb
/>
quæ in titulo
<
lb
/>
tabulæ eſt poſi-
<
lb
/>
@a, ſe mutuo ſe-
<
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/>
cant in vno pũ-
<
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/>
cto.</
note
>
propoſ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">19. </
s
>
<
s
xml:id
="
echoid-s4156
"
xml:space
="
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">huius lib. </
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>
<
s
xml:id
="
echoid-s4157
"
xml:space
="
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">vnà cum linea æquinoctiali; </
s
>
<
s
xml:id
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"
xml:space
="
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">nec non & </
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>
<
s
xml:id
="
echoid-s4159
"
xml:space
="
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">binæ quæuis in tabulis triginta ſex præ-
<
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/>
cedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s4160
"
xml:space
="
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">poſitæ, vnà cum hora, quæ in tit@lo cuiuſque tabulæ deſcripta eſt.</
s
>
<
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xml:id
="
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"
xml:space
="
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"/>
</
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>
</
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>
<
div
xml:id
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type
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1
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n
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<
head
xml:id
="
echoid-head114
"
xml:space
="
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">THEOREMA 20. PROPOSITIO 22.</
head
>
<
note
position
="
left
"
xml:space
="
preserve
">40</
note
>
<
p
>
<
s
xml:id
="
echoid-s4162
"
xml:space
="
preserve
">LINEAE omnium horarum à meridie vel media nocte in quo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0097-11
"
xlink:href
="
note-0097-11a
"
xml:space
="
preserve
">Lineæ horarũ
<
lb
/>
à mer. vel med.
<
lb
/>
nocte oẽs ſunt
<
lb
/>
parallelę in ho-
<
lb
/>
@ologio, q@ cir-
<
lb
/>
culo maximo p@
<
lb
/>
polos mũdi du-
<
lb
/>
cto æquidiſtat.</
note
>
cunque horologio, cuius planum circulo cuipiam per polos mundi de-
<
lb
/>
ſcripto, vel axi mundi æquidiſtat, ſunt parallelæ.</
s
>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4164
"
xml:space
="
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">NAM cum omnes circuli horarii à meridie vel media nocte deſcribantur, ex propoſ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">9. </
s
>
<
s
xml:id
="
echoid-s4166
"
xml:space
="
preserve
">hu-
<
lb
/>
ius lib. </
s
>
<
s
xml:id
="
echoid-s4167
"
xml:space
="
preserve
">per polos mundi, vbi eorum circunferentiæ mutuo ſe interſecant, erit axis mundi commu
<
lb
/>
nis eorum planorum ſectio. </
s
>
<
s
xml:id
="
echoid-s4168
"
xml:space
="
preserve
">Quare, ſi planum horologii ipſos circulos horarios ſecans æquidi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0097-12
"
xlink:href
="
note-0097-12a
"
xml:space
="
preserve
">Lineæ horarũ à
<
lb
/>
mer. vel med.
<
lb
/>
noc. in hori@on
<
lb
/>
tali horologio
<
lb
/>
ſphęræ rectæ, &
<
lb
/>
in quolibet Me
<
lb
/>
ridiano a@que
<
lb
/>
Polari, ſunt oẽs
<
lb
/>
inter ſeæquidi-
<
lb
/>
ſtantes.</
note
>
ſtet alicui circulo per polos mundi, atque adeo per axem, communem eorum ſectionem, ducto,
<
lb
/>
vel ipſi axi, erunt per propoſ. </
s
>
<
s
xml:id
="
echoid-s4169
"
xml:space
="
preserve
">18. </
s
>
<
s
xml:id
="
echoid-s4170
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s4171
"
xml:space
="
preserve
">illorum omnium circulorum, & </
s
>
<
s
xml:id
="
echoid-s4172
"
xml:space
="
preserve
">plani horologii ipſos
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0097-13
"
xlink:href
="
note-0097-13a
"
xml:space
="
preserve
">50</
note
>
ſecantis, communes ſectiones, hoc eſt, lineæ horariæ à meridie vel media nocte, parallelæ. </
s
>
<
s
xml:id
="
echoid-s4173
"
xml:space
="
preserve
">Quo
<
lb
/>
circa lineæ omnium horarum à meridie, vel media nocte, &</
s
>
<
s
xml:id
="
echoid-s4174
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s4175
"
xml:space
="
preserve
">Quod demonſtrandum erat.</
s
>
<
s
xml:id
="
echoid-s4176
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div269
"
type
="
section
"
level
="
1
"
n
="
112
">
<
head
xml:id
="
echoid-head115
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">In omni horo-
<
lb
/>
logio, quod æ-
<
lb
/>
quidiſta: circu-
<
lb
/>
lo maximo per
<
lb
/>
polos mũdi du-
<
lb
/>
cto, lineæ hora
<
lb
/>
rum à mer. vel
<
lb
/>
med. noc. om-
<
lb
/>
nes ſunt paral-
<
lb
/>
lelę.</
note
>
<
p
>
<
s
xml:id
="
echoid-s4177
"
xml:space
="
preserve
">SEQVITVR ex his, in horologio Horizontali ſphæræ rectæ, Meridiano, atque polari quolibet, li-
<
lb
/>
neas omnes horarias à meridie vel media nocte parallelas eſſe: </
s
>
<
s
xml:id
="
echoid-s4178
"
xml:space
="
preserve
">quoniam horum horologiorum plana
<
lb
/>
ęquidiſtant circulis, nempe Horizonti recto, Meridiano, & </
s
>
<
s
xml:id
="
echoid-s4179
"
xml:space
="
preserve
">circulo horæ ſextæ à meridie vel media no-
<
lb
/>
cte, per polos, & </
s
>
<
s
xml:id
="
echoid-s4180
"
xml:space
="
preserve
">axem mundi ductis, vt conſtat.</
s
>
<
s
xml:id
="
echoid-s4181
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4182
"
xml:space
="
preserve
">VT denique paucis multa complectar, lineæ omnes horarię à meridie vel media nocte in horologio
<
lb
/>
quouis, cuius planum alicui circulo horario à meridie uel media nocte, vel certè axi muudi æquidiſtat,
<
lb
/>
per hanc propoſ. </
s
>
<
s
xml:id
="
echoid-s4183
"
xml:space
="
preserve
">parallelę ſunt.</
s
>
<
s
xml:id
="
echoid-s4184
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>