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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59
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0079
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LIBER PRIMVS.
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contactum oppoſitum, atque adeo per polos circulorum C F, D F, per propoſ. </
s
>
<
s
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xml:space
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">5. </
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<
s
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<
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<
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xml:space
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">Theodoſii. </
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<
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xml:space
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">Quo-
<
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<
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xlink:label
="
note-0079-01
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xlink:href
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note-0079-01a
"
xml:space
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">Aequinoctialis
<
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circulus, &
<
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duo circuli ho-
<
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rarum ab or.
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vel occ. tangen-
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tes maximum
<
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parallelorũ ſem
<
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per apparentiũ
<
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in punctis op-
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poſitis, & circu-
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lus horæ à mer.
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vel med. noc. ſe
<
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cans eundẽ pa-
<
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rallelũ in pun-
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cto æqualiter à
<
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punctis conta-
<
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ctuum diſtan-
<
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te ſe mutuo
<
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interſecant in
<
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vno eodemq́ue
<
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puncto.</
note
>
niam igitur duo circuli A B, C F, ſe mutuo ſecant, ſecabit maximus circulus E C, per eorum polos du-
<
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ctus, ſegmenta ipſorum bifariam, per propoſ. </
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>
<
s
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="
echoid-s3800
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<
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xml:space
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</
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<
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<
figure
xlink:label
="
fig-0079-01
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xlink:href
="
fig-0079-01a
"
number
="
59
">
<
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file
="
0079-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-01
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</
figure
>
2. </
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>
<
s
xml:id
="
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xml:space
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">Theodoſii. </
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>
<
s
xml:id
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"
xml:space
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">Quare cum ſegmenta ipſorum ſint ſe-
<
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/>
micirculi, quòd per propoſ. </
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>
<
s
xml:id
="
echoid-s3805
"
xml:space
="
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">11. </
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>
<
s
xml:id
="
echoid-s3806
"
xml:space
="
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">lib. </
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>
<
s
xml:id
="
echoid-s3807
"
xml:space
="
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">1. </
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>
<
s
xml:id
="
echoid-s3808
"
xml:space
="
preserve
">Theodoſii, ma-
<
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/>
ximi
<
unsure
/>
circuli cum ſint, ſe mutuo bifariam ſecent, erit
<
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/>
tam arcus circuli C F, inter punctum C, & </
s
>
<
s
xml:id
="
echoid-s3809
"
xml:space
="
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">Aequa-
<
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/>
torem poſitus, quàm arcus Aequatoris inter circu-
<
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/>
lum E C, & </
s
>
<
s
xml:id
="
echoid-s3810
"
xml:space
="
preserve
">circulum C F, poſitus quadrans, vtpote
<
lb
/>
dimidium ſemicirculi. </
s
>
<
s
xml:id
="
echoid-s3811
"
xml:space
="
preserve
">Eadem ratione erit tam arcus
<
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<
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position
="
left
"
xlink:label
="
note-0079-02
"
xlink:href
="
note-0079-02a
"
xml:space
="
preserve
">10</
note
>
circuli D F, inter punctum D, & </
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>
<
s
xml:id
="
echoid-s3812
"
xml:space
="
preserve
">Aequatorem po-
<
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/>
ſitus, quàm arcus Aequatoris inter circulos E B,
<
lb
/>
D F, poſitus, quadrans. </
s
>
<
s
xml:id
="
echoid-s3813
"
xml:space
="
preserve
">Rurſus quia duo circuli C F,
<
lb
/>
D F, ſe mutuo ſecant, ſecabit maximus circulus C D,
<
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/>
per eorum polos ductus ſegmenta ipſorũ bifariam, per
<
lb
/>
propoſ. </
s
>
<
s
xml:id
="
echoid-s3814
"
xml:space
="
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">9. </
s
>
<
s
xml:id
="
echoid-s3815
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s3816
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s3817
"
xml:space
="
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">Theodoſii. </
s
>
<
s
xml:id
="
echoid-s3818
"
xml:space
="
preserve
">Cum ergo ſegmenta ipſo-
<
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/>
rum ſint, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3819
"
xml:space
="
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">11. </
s
>
<
s
xml:id
="
echoid-s3820
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3821
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s3822
"
xml:space
="
preserve
">Theodoſii, ſemicirculi,
<
lb
/>
erunt arcus circulorum C F, D F, inter puncta C,
<
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/>
D, & </
s
>
<
s
xml:id
="
echoid-s3823
"
xml:space
="
preserve
">punctum ſectionis poſiti, quadrantes: </
s
>
<
s
xml:id
="
echoid-s3824
"
xml:space
="
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">atque adeò cum oſtenſum ſit, & </
s
>
<
s
xml:id
="
echoid-s3825
"
xml:space
="
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">arcus eorundem inter pun-
<
lb
/>
cta C, D, & </
s
>
<
s
xml:id
="
echoid-s3826
"
xml:space
="
preserve
">Aequatorem poſitos eſſe quadrantes, mutuo ſe ſecabunt in Aequatore, vt in puncto F, ita
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0079-03
"
xlink:href
="
note-0079-03a
"
xml:space
="
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">20</
note
>
vt arcus C F, D F, A F, B F, ſint quadrantes. </
s
>
<
s
xml:id
="
echoid-s3827
"
xml:space
="
preserve
">Rurſus quoniam ci@culi maximi E G, C D, per polos
<
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/>
parallelorum C D, A B, ducti, parallelos ſecant, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3828
"
xml:space
="
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">10. </
s
>
<
s
xml:id
="
echoid-s3829
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s3830
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s3831
"
xml:space
="
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">Theodoſii, in arcus ſimiles; </
s
>
<
s
xml:id
="
echoid-s3832
"
xml:space
="
preserve
">Eſt
<
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/>
autem arcus C G, inter E C, E G, quadrans, ex hypotheſi, erit quoque arcus Aequatoris A B, inter eoſ-
<
lb
/>
dem circulos maximos E C, E G, poſitus, quadrans: </
s
>
<
s
xml:id
="
echoid-s3833
"
xml:space
="
preserve
">Ac proinde cum arcus A F, oſtenſus ſit quadrans,
<
lb
/>
tranſibit circulus maximus E G, per punctum F. </
s
>
<
s
xml:id
="
echoid-s3834
"
xml:space
="
preserve
">Quamobrem quatuor circuli maximi A B, C F, D F,
<
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/>
E F, vnam eandemq́, communem habent ſectionem, quod eſt propoſitum: </
s
>
<
s
xml:id
="
echoid-s3835
"
xml:space
="
preserve
">Atque idcirco, in quo puncto
<
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/>
planum horologij communi huic ſectioni occurrit, per idem communes ſectiones eorundem circulorum, & </
s
>
<
s
xml:id
="
echoid-s3836
"
xml:space
="
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">
<
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/>
plani horologij tranſibunt, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3837
"
xml:space
="
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">18. </
s
>
<
s
xml:id
="
echoid-s3838
"
xml:space
="
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">huius libri: </
s
>
<
s
xml:id
="
echoid-s3839
"
xml:space
="
preserve
">adeo vt in eodem puncto ſe interſecent in horolo-
<
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gio communes illæ ſectiones, hoc eſt, linea æquinoctialis, & </
s
>
<
s
xml:id
="
echoid-s3840
"
xml:space
="
preserve
">lineæ horariæ circulorum C F, D F, E F.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s3841
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0079-04
"
xlink:href
="
note-0079-04a
"
xml:space
="
preserve
">Quænam horæ
<
lb
/>
ab or. vel occ.
<
lb
/>
& à mer. vel
<
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/>
med. noc. ſe mu
<
lb
/>
tuo ſecent in li-
<
lb
/>
nea ęquinoctia
<
lb
/>
li in vno pun-
<
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/>
cto.</
note
>
Quocircain quo puncto horaria linea circuli E F, æquinoctialem lineam ſecat, per idem ducendæ erunt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0079-05
"
xlink:href
="
note-0079-05a
"
xml:space
="
preserve
">30</
note
>
lineæ horariæ circulorum C F, D F. </
s
>
<
s
xml:id
="
echoid-s3842
"
xml:space
="
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">Vt autem ſciamus, quarumnam hor arum ſint circuli C F, D F, E F,
<
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/>
contemplabimur diligenter figuram propoſ. </
s
>
<
s
xml:id
="
echoid-s3843
"
xml:space
="
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">9. </
s
>
<
s
xml:id
="
echoid-s3844
"
xml:space
="
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">huius libri, quæ parallelum ſemper apparentium maximũ
<
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/>
refert, & </
s
>
<
s
xml:id
="
echoid-s3845
"
xml:space
="
preserve
">in qua numeri exteriores ad horas ab ortu, vel occaſu, interiores verò ad horas à meridie, vel
<
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/>
media nocte pertinent. </
s
>
<
s
xml:id
="
echoid-s3846
"
xml:space
="
preserve
">Nam ſi C F, ponatur v. </
s
>
<
s
xml:id
="
echoid-s3847
"
xml:space
="
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">g. </
s
>
<
s
xml:id
="
echoid-s3848
"
xml:space
="
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">eſſe circulus horæ 19. </
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>
<
s
xml:id
="
echoid-s3849
"
xml:space
="
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">ab ortu, vel occaſu, ac pro-
<
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/>
inde D F, circulus horæ ſeptimæ ab ortu, vel occaſu, quæ illi per diametrum opponitur, quemadmodum
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3850
"
xml:space
="
preserve
">punctum D, puncto C; </
s
>
<
s
xml:id
="
echoid-s3851
"
xml:space
="
preserve
">erit E F, circulus horæ primæ à meridie, vel media nocte, quòd hęc quad ante
<
lb
/>
abſit ab vtraque illarum, quemadmodum & </
s
>
<
s
xml:id
="
echoid-s3852
"
xml:space
="
preserve
">punctum G, quadr ante abeſt à puncto C, & </
s
>
<
s
xml:id
="
echoid-s3853
"
xml:space
="
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">à puncto D.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s3854
"
xml:space
="
preserve
">Sic etiam ſi C F, ponatur eſſe circulus horæ 21 {1/2} ab ortu, vel occaſu, atque adeò D F, circulus horæ
<
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/>
9 {1/2}. </
s
>
<
s
xml:id
="
echoid-s3855
"
xml:space
="
preserve
">ab ortu, vel occaſu, erit E F, circulus, horæ 3 {1/2}. </
s
>
<
s
xml:id
="
echoid-s3856
"
xml:space
="
preserve
">à meridie, vel media nocte, atque ita de cæteris,
<
lb
/>
vt ex figura propoſ. </
s
>
<
s
xml:id
="
echoid-s3857
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s3858
"
xml:space
="
preserve
">huius libri perſpicuum eſt. </
s
>
<
s
xml:id
="
echoid-s3859
"
xml:space
="
preserve
">Item ſi E F, ponatur circulus cuiuſcunque horæ à me-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0079-06
"
xlink:href
="
note-0079-06a
"
xml:space
="
preserve
">40</
note
>
ridie, vel media nocte, ſtatim cognoſcemus, ad quas horas ab ortu, vel occaſu pertineant circuli C F, D F.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s3860
"
xml:space
="
preserve
">Nam ſi E F, ponatur circulus horæ δ{1/4}. </
s
>
<
s
xml:id
="
echoid-s3861
"
xml:space
="
preserve
">à meridie, vel media nocte, erit alter reliquorum, nempe C F,
<
lb
/>
circulus horæ 14 {1/4}. </
s
>
<
s
xml:id
="
echoid-s3862
"
xml:space
="
preserve
">ab ortu, vel occaſu, alter verò D F, circulus horæ 2 {1/4}. </
s
>
<
s
xml:id
="
echoid-s3863
"
xml:space
="
preserve
">ab ortu, vel occaſu, cum
<
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/>
vtraque harum horarum ab illa abſit quadrante, hoc eſt, ſex horis, vt ex dicta figura conſtat, quemad-
<
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/>
modum & </
s
>
<
s
xml:id
="
echoid-s3864
"
xml:space
="
preserve
">punctũ G, quadrante abeſt à punctis C, & </
s
>
<
s
xml:id
="
echoid-s3865
"
xml:space
="
preserve
">D, &</
s
>
<
s
xml:id
="
echoid-s3866
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s3867
"
xml:space
="
preserve
">Ex his autem facile componemus tabulam
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0079-07
"
xlink:href
="
note-0079-07a
"
xml:space
="
preserve
">Conſtructio ta-
<
lb
/>
bulæ in propoſ.
<
lb
/>
19 deſcriptæ.</
note
>
æquinoctialis lineæ in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s3868
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s3869
"
xml:space
="
preserve
">huius libri poſitam.</
s
>
<
s
xml:id
="
echoid-s3870
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s3871
"
xml:space
="
preserve
">PRO conſtructione autem aliarum tabularum,
<
lb
/>
<
figure
xlink:label
="
fig-0079-02
"
xlink:href
="
fig-0079-02a
"
number
="
60
">
<
image
file
="
0079-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-02
"/>
</
figure
>
quæ lineis horarum tam ab ortu, vel occaſu, quàm à
<
lb
/>
meridie, vel media nocte ſunt dicatæ; </
s
>
<
s
xml:id
="
echoid-s3872
"
xml:space
="
preserve
">ſit rurſum Ae-
<
lb
/>
quator A B, & </
s
>
<
s
xml:id
="
echoid-s3873
"
xml:space
="
preserve
">parallelus eorum, qui ſemper ap-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0079-08
"
xlink:href
="
note-0079-08a
"
xml:space
="
preserve
">50</
note
>
parent, maximus C D, atque polus mundi, ſeu pa-
<
lb
/>
rallelorum, E. </
s
>
<
s
xml:id
="
echoid-s3874
"
xml:space
="
preserve
">Tangant autem parallelum C D, in
<
lb
/>
punctis C, & </
s
>
<
s
xml:id
="
echoid-s3875
"
xml:space
="
preserve
">D, duo circuli horarum ab ortu, vel
<
lb
/>
occaſu C B, D A, ſe mutuo quidem in F, Aequato-
<
lb
/>
rem autem ſecãtes in punctis B, A, & </
s
>
<
s
xml:id
="
echoid-s3876
"
xml:space
="
preserve
">circulus A D,
<
lb
/>
productus ſecet quoque Aequatorem in N. </
s
>
<
s
xml:id
="
echoid-s3877
"
xml:space
="
preserve
">Eundem
<
lb
/>
verò parallelum C D, ſecet per polum E, circulus ali-
<
lb
/>
cuius horæ à meridie, vel media nocte in puncto G,
<
lb
/>
quod æqualiter à punctis C, & </
s
>
<
s
xml:id
="
echoid-s3878
"
xml:space
="
preserve
">D, distet, ita vt ar-
<
lb
/>
cus C G, D G, ſint æquales. </
s
>
<
s
xml:id
="
echoid-s3879
"
xml:space
="
preserve
">Dico hunc circulum E G,
<
lb
/>
productum tranſire per punctum F, ita vt tres circuli horarij C B, D A, E G, ſe mutuo ſecent </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>