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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vt in ſecunda figura apparet. </
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<
s
xml:id
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xml:space
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">Sumantur autem arcus A F, C G, grad. </
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<
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xml:space
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">25 {3/4}. </
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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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">puncta F, G, con-
<
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nectantur recta linea ipſam B D, ſecante in H, puncto, è quo, vt centro, ar cus deſcribatur I K, ſit{q́ue} ar-
<
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cus I K, æqualis altitudini poli; </
s
>
<
s
xml:id
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"
xml:space
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">& </
s
>
<
s
xml:id
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echoid-s12174
"
xml:space
="
preserve
">ex H, per K, recta ducatur ſecans A C, in L, puncto, e quo circu-
<
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lus deſcriptus diuidatur in partes 12. </
s
>
<
s
xml:id
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"
xml:space
="
preserve
">æquales, initio facto à recta A C, & </
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>
<
s
xml:id
="
echoid-s12176
"
xml:space
="
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">per diuiſionum puncta, ac
<
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centrum L, rectæ ducantur ſecantes circulum A B C D, in 12. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">punctis, ad quæ ex E, rectæ emiſſæ da-
<
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bunt initia ſignorum. </
s
>
<
s
xml:id
="
echoid-s12178
"
xml:space
="
preserve
">Nam C, erit initium ♈; </
s
>
<
s
xml:id
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echoid-s12179
"
xml:space
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">primum deinde punctum verſus G, initium ♉; </
s
>
<
s
xml:id
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xml:space
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">ſe-
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quens, initium ♊, & </
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<
s
xml:id
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xml:space
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">c. </
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>
<
s
xml:id
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"
xml:space
="
preserve
">Per hanc autem figuram inueſtigabimus in æquinoctiali linea puncta, per quæ
<
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/>
lineæ ſignorum aſcendentium debent duci, vt mox trademus. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Cæterum non eſt neceſſe hic, vt lineæ ſu-
<
lb
/>
pra rectam B D, reſpondeant lineis infra eandem B D, ſecundum lineam rectam, quemadmodum in ſu-
<
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/>
periori figura; </
s
>
<
s
xml:id
="
echoid-s12184
"
xml:space
="
preserve
">licet aliquando reſpondeant, vt in hac figura ad latitudinem grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">42. </
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>
<
s
xml:id
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"
xml:space
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">conſtructa ac-
<
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<
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position
="
left
"
xlink:label
="
note-0207-01
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xlink:href
="
note-0207-01a
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xml:space
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">10</
note
>
cidit in lineis ♍, & </
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>
<
s
xml:id
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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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">Hæ enim rectas lineas conſtituunt cum lineis ♒, & </
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>
<
s
xml:id
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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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">ſunt tamen om-
<
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nes aliæ vltra centrum producendæ, & </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">productæ punctis diſtinguendæ, ne cum alijs confundantur, at-
<
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/>
que eadem illis ſigna aſcribenda. </
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>
<
s
xml:id
="
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xml:space
="
preserve
">Vnde fit vt linea ♒, habeat etiam ſignum ♍; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">linea ♊, ſignum
<
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♏; </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſimiliter linea ♍, ſignum ♒; </
s
>
<
s
xml:id
="
echoid-s12196
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12197
"
xml:space
="
preserve
">linea ♏, ſignum ♊; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12199
"
xml:space
="
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">linea ♈, ſignum ♎; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">linea ♎,
<
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/>
ſignum ♈; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">atque ita quælibet linea habebit ſuum proprium ſignum ex deſcriptione, & </
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>
<
s
xml:id
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xml:space
="
preserve
">adhuc ſignum il-
<
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/>
lius lineę, quæ producta rectam cum ea lineam conſtituit. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Quæres, quoniam ad deſcriptionem ſignorum
<
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aſcendentium magnam affert vtilitatem, diligenter notanda eſt.</
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<
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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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">IT AQVE in recta linea E D, prioris figuræ ſumatur recta E O, æqualis meridianæ lineæ E I,
<
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<
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position
="
right
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xlink:label
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note-0207-02
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xlink:href
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note-0207-02a
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xml:space
="
preserve
">Deſcriptio aſcẽ
<
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dentium ſigno-
<
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rum in horolo
<
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/>
gio per proxi-
<
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/>
mas duas figu-
<
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/>
@as, ſ
<
unsure
/>
ecundum
<
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/>
praxim Andre@
<
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/>
Schoneri.</
note
>
horologij interceptæ inter E, centrum Aequatoris, & </
s
>
<
s
xml:id
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"
xml:space
="
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">lineam æquinoctialem, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">per O, ipſi A C, pa-
<
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/>
rallela agatur ſecans lineas ſignorum ex E, emiſſas in P, Q, R, S; </
s
>
<
s
xml:id
="
echoid-s12209
"
xml:space
="
preserve
">adeò vt poſito centro E, huius
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0207-03
"
xlink:href
="
note-0207-03a
"
xml:space
="
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">20</
note
>
figurę in centro E, Aequatoris horologij, & </
s
>
<
s
xml:id
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xml:space
="
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">puncto O, in puncto I, parallela per O@, ducta congruat li-
<
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/>
neæ æquinoctiali. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Si igitur hæc puncta ex O, ſumpta in lineam æquinoctialem horologij ab I, hincinde
<
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/>
transferantur, per quæ ipſi lineæ meridianæ ducantur parallelæ, ſecabuntur tropici in punctis, per quę
<
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/>
lineæ ſignorum aſcendentium tranſeunt. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Nam per puncta tropici ♑, incedunt lineę ſignorum ſemi-
<
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/>
circuli A D C, nempe ♒, & </
s
>
<
s
xml:id
="
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xml:space
="
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">♓, in horis ante meridiem, & </
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>
<
s
xml:id
="
echoid-s12214
"
xml:space
="
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">♈, in ipſa hora meridiei, at ♉, & </
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>
<
s
xml:id
="
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xml:space
="
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">♊, in
<
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horis poſt meridiem: </
s
>
<
s
xml:id
="
echoid-s12216
"
xml:space
="
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">per puncta vero tropici ♋, lineæ ſignorum reliquorum his oppoſitorum, vt ♏, & </
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>
<
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xml:id
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xml:space
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">
<
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♐, in horis post meridiem, & </
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>
<
s
xml:id
="
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xml:space
="
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">♎, in ipſa hora meridiei, at ♌, & </
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>
<
s
xml:id
="
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xml:space
="
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">♍, in horis ante meridiem.</
s
>
<
s
xml:id
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xml:space
="
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"/>
</
p
>
<
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style
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<
s
xml:id
="
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"
xml:space
="
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">RVRSVS in recta E D, poſterioris figuræ ſumatur E M, eidem meridianæ E I, in horologio in-
<
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terceptæ inter E, centrum Aequatoris, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">lineam æquinoctialem, æqualis, & </
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>
<
s
xml:id
="
echoid-s12223
"
xml:space
="
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">per M, ipſi A C, paralle-
<
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la agatur; </
s
>
<
s
xml:id
="
echoid-s12224
"
xml:space
="
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">adeo vt rurſus poſito centro E, huius figuræ in centro E, Aequatoris horologij, & </
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>
<
s
xml:id
="
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xml:space
="
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">puncto M,
<
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<
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position
="
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xlink:label
="
note-0207-04
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xlink:href
="
note-0207-04a
"
xml:space
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">30</
note
>
in puncto I, parallela per M, ducta æquinoctiali lineæ congruat. </
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>
<
s
xml:id
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"
xml:space
="
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">ſecabit en
<
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/>
im hæc parallela lineas ſigno-
<
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rum ex E, emiſſas in punctis, quæ accepta ex M, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">in lineam æquinoctialem horologij translata ex I, da-
<
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bunt puncta, per quę lineæ aſcendentium ſignorum in linea æquinoctiali duci debent: </
s
>
<
s
xml:id
="
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"
xml:space
="
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">hac tamen lege, vt
<
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puncta ſignorum ♉, ♊, ♋, ♏, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">♐, transferantur in horas ante meridiem, puncta verò reliquorum
<
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ſignorum in horas pomeridianas, eo nimirum ordine, quem habent ſigna in parallela per M, ducta, ſi ęqui
<
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/>
noctiali lineę horologij ſuperponeretur, ita vt centrum E, caderet ſurſum verſus, (quod contingeret,
<
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/>
ſi E, centrum Aequatoris in horologio acceptum fuiſſet verſus punctum H) & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">linea ♉, vel punctum A,
<
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huius figuræ, ad partem dextram horologij, & </
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>
<
s
xml:id
="
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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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"/>
</
p
>
<
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style
="
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<
s
xml:id
="
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"
xml:space
="
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">IAM ſi hæc puncta æquinoctialis lineæ cum punctis reſpondentibus in tropicis per lineas rectas
<
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coniungantur, habebuntur lineæ ſignorum aſcendentium, vt prius. </
s
>
<
s
xml:id
="
echoid-s12234
"
xml:space
="
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">Lineæ autem ♈, ♎, ♋, & </
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>
<
s
xml:id
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"
xml:space
="
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">♑, ducen-
<
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<
note
position
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xlink:label
="
note-0207-05
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xlink:href
="
note-0207-05a
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xml:space
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">40</
note
>
tur, vt ante diximus. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Huius operationis demonſtratio nulla adducitur ab Andrea Schonero, ſed ſola
<
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/>
praxi contentus, quæ ſine dubio pulcherrima eſt, eam ſcriptis mandauit.</
s
>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
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style
="
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">
<
s
xml:id
="
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"
xml:space
="
preserve
">VTILITATEM porro habent ſigna aſcendentia in horologio deſcripta in ſignem valde, ac il-
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0207-06
"
xlink:href
="
note-0207-06a
"
xml:space
="
preserve
">Per ſigna aſcẽ
<
unsure
/>
-
<
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/>
dentia in horo
<
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/>
logio deſcripta
<
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/>
exploratur ſitus
<
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/>
totius cœli quo
<
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/>
libet momento
<
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/>
temporis.</
note
>
luſtrem: </
s
>
<
s
xml:id
="
echoid-s12239
"
xml:space
="
preserve
">quippe cum exipſis quolibet momento temporis totum propemodum cœli ſitum exploremus.
<
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</
s
>
<
s
xml:id
="
echoid-s12240
"
xml:space
="
preserve
">Nam ex vmbra gnomonis cadente in lineam aliquam ſignorum aſcendentium, confestim cognoſcimus,
<
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/>
quodnam ſignum tunc temporis ſupra Horizontem emergat, ac proinde, quodnam occidat, cùm neceſſe
<
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/>
ſit, oppoſitum tunc ſignum occidere. </
s
>
<
s
xml:id
="
echoid-s12241
"
xml:space
="
preserve
">Ex ſigno rurſus aſcendente facile in cognitionem ſigni, quod cœlum
<
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/>
tunc mediat, atque adeò & </
s
>
<
s
xml:id
="
echoid-s12242
"
xml:space
="
preserve
">oppoſiti, quod angulum terræ oecupat, perueniemus ex ijs, quæ paulo ante in
<
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hac propoſ. </
s
>
<
s
xml:id
="
echoid-s12243
"
xml:space
="
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">tradidimus. </
s
>
<
s
xml:id
="
echoid-s12244
"
xml:space
="
preserve
">Quod vt facilius aſſequamur, deſcribendæ erunt duæ tabellæ, vna ad ſiniſtram
<
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/>
partem horologij, & </
s
>
<
s
xml:id
="
echoid-s12245
"
xml:space
="
preserve
">ad dextram altera, in quarum priore contineantur hæc ſex ſigna aſcendentia ♈, ♉,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0207-07
"
xlink:href
="
note-0207-07a
"
xml:space
="
preserve
">50</
note
>
♊, ♋, ♌, & </
s
>
<
s
xml:id
="
echoid-s12246
"
xml:space
="
preserve
">♍, vna cum ſex ſignis oppoſitis, quæ tunc ſub Horizontem deſcendunt, & </
s
>
<
s
xml:id
="
echoid-s12247
"
xml:space
="
preserve
">cum alijs ſex,
<
lb
/>
quæin Meridiano ſupra Horizontem reperiuntur illo tempore, & </
s
>
<
s
xml:id
="
echoid-s12248
"
xml:space
="
preserve
">denique cum ſex, quæ hiſce vltimis op-
<
lb
/>
ponuntur, & </
s
>
<
s
xml:id
="
echoid-s12249
"
xml:space
="
preserve
">in Meridiano infra Horizontem exiſtunt: </
s
>
<
s
xml:id
="
echoid-s12250
"
xml:space
="
preserve
">In poſteriore verò alia ſex ſigna aſcendentia ♎,
<
lb
/>
♏, ♐, ♑, ♒, & </
s
>
<
s
xml:id
="
echoid-s12251
"
xml:space
="
preserve
">♓, vnà cum deſcendentibus, cœlum mediantibus, atque in angulo terræ exiſtentibus
<
lb
/>
collocentur, cuiuſm
<
unsure
/>
odi ſunt ſequentes duæ tabellæ ad latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s12252
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s12253
"
xml:space
="
preserve
">fabricatæ.</
s
>
<
s
xml:id
="
echoid-s12254
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div659
"
type
="
section
"
level
="
1
"
n
="
170
">
<
head
xml:id
="
echoid-head173
"
xml:space
="
preserve
">SEQVVNTVR TABELLÆ.</
head
>
</
div
>
</
text
>
</
echo
>