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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æquales lineas abſcindant M α, N β, perpendicularesq́; </
s
>
<
s
xml:id
="
echoid-s12882
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xml:space
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">ſint ad M N) eumq́ue in partes 24. </
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<
s
xml:id
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"
xml:space
="
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">æqua-
<
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les diſtribuamus, initio facto à puncto e, occidentali; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">reperiemus in arcu ♑, puncta, per quæ horæ
<
lb
/>
ab occaſu ducendæ erunt. </
s
>
<
s
xml:id
="
echoid-s12885
"
xml:space
="
preserve
">Vt ſi ex puncto δ, horæ 23. </
s
>
<
s
xml:id
="
echoid-s12886
"
xml:space
="
preserve
">tropici ♑, per centrum E, rectã ducamus,
<
lb
/>
quæ æquinoctialem lineam ſecet in ε, inueniemus per rectam H ε, productam in arcu ♑, punctũ
<
lb
/>
λ, pro hora 23. </
s
>
<
s
xml:id
="
echoid-s12887
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12888
"
xml:space
="
preserve
">ſic de cæteris.</
s
>
<
s
xml:id
="
echoid-s12889
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12890
"
xml:space
="
preserve
">QVOD ſi non lubeat circulum M a N b, ex E, deſcriptum ſecare in duas portiones, quarum
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0215-01
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xlink:href
="
note-0215-01a
"
xml:space
="
preserve
">Quo pacto cir-
<
lb
/>
culus M a N b,
<
lb
/>
aliter diuida-
<
lb
/>
tur in arcum
<
lb
/>
diuinum tropi
<
lb
/>
ci Cancri, vel
<
lb
/>
Capricorni.</
note
>
vna ſimilis ſit arcui diurno tropici ♋, vel ♑, & </
s
>
<
s
xml:id
="
echoid-s12891
"
xml:space
="
preserve
">nocturno altera, ea ratione, quam in ſcholio pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s12892
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s12893
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s12894
"
xml:space
="
preserve
">antecedentis tradidimus; </
s
>
<
s
xml:id
="
echoid-s12895
"
xml:space
="
preserve
">abſoluen dum erit negorium hoc modo. </
s
>
<
s
xml:id
="
echoid-s12896
"
xml:space
="
preserve
">Ex puncto N, numere
<
lb
/>
tur vtrinque arcus ſemidiurnus, tropici quidem ♋, vſque ad puncta a, & </
s
>
<
s
xml:id
="
echoid-s12897
"
xml:space
="
preserve
">b, tropici vero ♑, vſque
<
lb
/>
ad puncta d, & </
s
>
<
s
xml:id
="
echoid-s12898
"
xml:space
="
preserve
">e. </
s
>
<
s
xml:id
="
echoid-s12899
"
xml:space
="
preserve
">Quod quidem facile fiet, ſi circulus occulte diuidatur in 24. </
s
>
<
s
xml:id
="
echoid-s12900
"
xml:space
="
preserve
">horas æquales, ini-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0215-02
"
xlink:href
="
note-0215-02a
"
xml:space
="
preserve
">10</
note
>
tio facto à puncto N, & </
s
>
<
s
xml:id
="
echoid-s12901
"
xml:space
="
preserve
">ex vtraquè parte numerentur horæ in arcu ſemidiurno contentæ, &</
s
>
<
s
xml:id
="
echoid-s12902
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12903
"
xml:space
="
preserve
">Du-
<
lb
/>
ctis enim rectis a b, d e, habebimus eaſdem portiones, quas prius, reſpondentes arcui diurno tro-
<
lb
/>
pici ♋, vel ♑. </
s
>
<
s
xml:id
="
echoid-s12904
"
xml:space
="
preserve
">Vnde diuiſio circuli rurſus inchoanda erit à puncto b, vel à puncto e.</
s
>
<
s
xml:id
="
echoid-s12905
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12906
"
xml:space
="
preserve
">POSSVMVS quoque initium huius diuiſionis ſtatuere in qualibet hora ab occaſu, etiamſi
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0215-03
"
xlink:href
="
note-0215-03a
"
xml:space
="
preserve
">Quomodo à
<
lb
/>
qualibet hora
<
lb
/>
ab occ. initium
<
lb
/>
diuiſionis habe
<
lb
/>
re poteſt circu-
<
lb
/>
lus M a N b, e-
<
lb
/>
tiamſi non diui
<
lb
/>
dat
<
unsure
/>
ur in arcum
<
lb
/>
diurnum tropi
<
lb
/>
ci Cancri, vel
<
lb
/>
Capricorni. Itẽ
<
lb
/>
qua ratione in
<
lb
/>
eodem circulo
<
lb
/>
inuenienda ſit
<
lb
/>
quęcunque ho-
<
lb
/>
ra propoſita ab
<
lb
/>
or. vel occ. in
<
lb
/>
quocunque pa-
<
lb
/>
rallelo.</
note
>
circulum non ſecemus in arcum diurnum tropici ♋, vel ♑, hac ratione. </
s
>
<
s
xml:id
="
echoid-s12907
"
xml:space
="
preserve
">Arcus ſemidiurnus au-
<
lb
/>
ferantur ex horis 24. </
s
>
<
s
xml:id
="
echoid-s12908
"
xml:space
="
preserve
">vt habeatur tempus meridiei more Italorũ. </
s
>
<
s
xml:id
="
echoid-s12909
"
xml:space
="
preserve
">Ex hoc tempore cognoſcemus,
<
lb
/>
quantum hora quælibet ab occ. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">propoſita diſtet à meridie. </
s
>
<
s
xml:id
="
echoid-s12911
"
xml:space
="
preserve
">Vnde ſi à puncto N, numeretur hæc
<
lb
/>
diſtantia verſus b, ſi hora propoſita eſt pomeridiana, aut verſus a, ſi antemeridiana, habebimus
<
lb
/>
punctum propoſitæ horæ, à qua diuiſio circuli in 24. </
s
>
<
s
xml:id
="
echoid-s12912
"
xml:space
="
preserve
">partes æquales inchoanda erit. </
s
>
<
s
xml:id
="
echoid-s12913
"
xml:space
="
preserve
">Exempli
<
lb
/>
gratia, Sole exiſtente in principio ♋, arcus ſemidiurnus, ad latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s12914
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s12915
"
xml:space
="
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">continet hor. </
s
>
<
s
xml:id
="
echoid-s12916
"
xml:space
="
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">7.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12917
"
xml:space
="
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">
<
note
position
="
left
"
xlink:label
="
note-0215-04
"
xlink:href
="
note-0215-04a
"
xml:space
="
preserve
">20</
note
>
Min. </
s
>
<
s
xml:id
="
echoid-s12918
"
xml:space
="
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">32. </
s
>
<
s
xml:id
="
echoid-s12919
"
xml:space
="
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">quo ſublato ex horis 24. </
s
>
<
s
xml:id
="
echoid-s12920
"
xml:space
="
preserve
">remanent hor. </
s
>
<
s
xml:id
="
echoid-s12921
"
xml:space
="
preserve
">16. </
s
>
<
s
xml:id
="
echoid-s12922
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s12923
"
xml:space
="
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">28. </
s
>
<
s
xml:id
="
echoid-s12924
"
xml:space
="
preserve
">pro tempore meridiei: </
s
>
<
s
xml:id
="
echoid-s12925
"
xml:space
="
preserve
">ac proin-
<
lb
/>
de hora 18. </
s
>
<
s
xml:id
="
echoid-s12926
"
xml:space
="
preserve
">ab occaſu diſtabit à meridie verſus partes occidentales hora 1. </
s
>
<
s
xml:id
="
echoid-s12927
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s12928
"
xml:space
="
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">32. </
s
>
<
s
xml:id
="
echoid-s12929
"
xml:space
="
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">hoc eſt, gra-
<
lb
/>
dibus 23. </
s
>
<
s
xml:id
="
echoid-s12930
"
xml:space
="
preserve
">Si igitur ex N, verſus b, numerentur grad. </
s
>
<
s
xml:id
="
echoid-s12931
"
xml:space
="
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">23. </
s
>
<
s
xml:id
="
echoid-s12932
"
xml:space
="
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">vel hor. </
s
>
<
s
xml:id
="
echoid-s12933
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s12934
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s12935
"
xml:space
="
preserve
">32. </
s
>
<
s
xml:id
="
echoid-s12936
"
xml:space
="
preserve
">reperietur punctum
<
lb
/>
f, horæ 18. </
s
>
<
s
xml:id
="
echoid-s12937
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s12938
"
xml:space
="
preserve
">in tropico ♋, à quo diuiſio circuli principium habere poteſt, vt aliæ horæ ab
<
lb
/>
occ. </
s
>
<
s
xml:id
="
echoid-s12939
"
xml:space
="
preserve
">habeantut. </
s
>
<
s
xml:id
="
echoid-s12940
"
xml:space
="
preserve
">Rurſus ab eodem meridie diſtabit hora vndecima ab occ. </
s
>
<
s
xml:id
="
echoid-s12941
"
xml:space
="
preserve
">horis 5. </
s
>
<
s
xml:id
="
echoid-s12942
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s12943
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s12944
"
xml:space
="
preserve
">hoc
<
lb
/>
eſt, gradibus 82. </
s
>
<
s
xml:id
="
echoid-s12945
"
xml:space
="
preserve
">quæ diſtantia ſi numeretur ex N, verſus a, quia hora vndecima eſt antemeridia-
<
lb
/>
na, inuenietur punctum m, horæ vndecimæ ab occ. </
s
>
<
s
xml:id
="
echoid-s12946
"
xml:space
="
preserve
">in tropico ♋, à quo etiam diuiſio circuli ini-
<
lb
/>
tium poteſt habere. </
s
>
<
s
xml:id
="
echoid-s12947
"
xml:space
="
preserve
">Poſtremo, Sole exiſtente in principio ♑, arcus ſemidiurnus comprehendit
<
lb
/>
hor. </
s
>
<
s
xml:id
="
echoid-s12948
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s12949
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s12950
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s12951
"
xml:space
="
preserve
">ad eandem latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s12952
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s12953
"
xml:space
="
preserve
">quo detracto ex 24. </
s
>
<
s
xml:id
="
echoid-s12954
"
xml:space
="
preserve
">remanent hor. </
s
>
<
s
xml:id
="
echoid-s12955
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s12956
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s12957
"
xml:space
="
preserve
">32.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12958
"
xml:space
="
preserve
">pro tempore meridiei: </
s
>
<
s
xml:id
="
echoid-s12959
"
xml:space
="
preserve
">atque adeo hora 23. </
s
>
<
s
xml:id
="
echoid-s12960
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s12961
"
xml:space
="
preserve
">diſtabit à meridie verſus occidentem horis 3. </
s
>
<
s
xml:id
="
echoid-s12962
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0215-05
"
xlink:href
="
note-0215-05a
"
xml:space
="
preserve
">30</
note
>
Min. </
s
>
<
s
xml:id
="
echoid-s12963
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s12964
"
xml:space
="
preserve
">id eſt, grad. </
s
>
<
s
xml:id
="
echoid-s12965
"
xml:space
="
preserve
">52. </
s
>
<
s
xml:id
="
echoid-s12966
"
xml:space
="
preserve
">quæ diſtantia ſi ſupputetur ex N, verſus e, inuenietur punctum δ, pro ho
<
lb
/>
ra 23. </
s
>
<
s
xml:id
="
echoid-s12967
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s12968
"
xml:space
="
preserve
">in tropico ♑, &</
s
>
<
s
xml:id
="
echoid-s12969
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12970
"
xml:space
="
preserve
">Hac ratione, cognito tempore meridiei, reperiemus punctum cu-
<
lb
/>
iuſcunque horæ ab occ. </
s
>
<
s
xml:id
="
echoid-s12971
"
xml:space
="
preserve
">Quod etiam de horis ab ortu intelligi volo. </
s
>
<
s
xml:id
="
echoid-s12972
"
xml:space
="
preserve
">Atque hoc non ſolum in
<
lb
/>
tropico ♋, vel ♑, verumetiam in quocunque parallelo. </
s
>
<
s
xml:id
="
echoid-s12973
"
xml:space
="
preserve
">Vnde ſi à puncto propoſitæ horæ ab occ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12974
"
xml:space
="
preserve
">in circulo M a N b, per centrum E, ducatur recta linea occulta ſecans æquinoctialem lineam in
<
lb
/>
puncto, per quod ex H, centro horologii recta ducatur, ſecabitur parallelus ♋, vel ♑, vel alius qui-
<
lb
/>
cunque in puncto propoſitæ horæ ab occ. </
s
>
<
s
xml:id
="
echoid-s12975
"
xml:space
="
preserve
">prout illa hora ſumpta fuerit in parallelo ♋, vel ♑, aut
<
lb
/>
in alio quouis parallelo.</
s
>
<
s
xml:id
="
echoid-s12976
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12977
"
xml:space
="
preserve
">ITAQVE ſi puncta horarum correſpondentia, quæ in tropicis inuenta ſunt, connectantur li-
<
lb
/>
neis rectis, deſcriptum erit horologium Italicum. </
s
>
<
s
xml:id
="
echoid-s12978
"
xml:space
="
preserve
">Tranſibunt autem lineæ horarum ab occaſu per
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0215-06
"
xlink:href
="
note-0215-06a
"
xml:space
="
preserve
">40</
note
>
puncta lineæ æquinoctialis, per quæ lineæ horarum à meridie, vel media nocte incedunt; </
s
>
<
s
xml:id
="
echoid-s12979
"
xml:space
="
preserve
">nimirũ
<
lb
/>
linea horæ 23. </
s
>
<
s
xml:id
="
echoid-s12980
"
xml:space
="
preserve
">ab occaſu per punctum horæ quintæ à meridie, vel media nocte; </
s
>
<
s
xml:id
="
echoid-s12981
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12982
"
xml:space
="
preserve
">linea horæ 22.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12983
"
xml:space
="
preserve
">per punctum horæ quartæ, & </
s
>
<
s
xml:id
="
echoid-s12984
"
xml:space
="
preserve
">ſic deinceps, quemadmodum ex tabula propoſ. </
s
>
<
s
xml:id
="
echoid-s12985
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s12986
"
xml:space
="
preserve
">ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s12987
"
xml:space
="
preserve
">
<
lb
/>
cui titulus eſt, AEQVINOCTIALIS LINEA, vel ex tabula arcus diurni horarũ 12. </
s
>
<
s
xml:id
="
echoid-s12988
"
xml:space
="
preserve
">pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s12989
"
xml:space
="
preserve
">23. </
s
>
<
s
xml:id
="
echoid-s12990
"
xml:space
="
preserve
">eiuſdem ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s12991
"
xml:space
="
preserve
">manifeſtũ eſt. </
s
>
<
s
xml:id
="
echoid-s12992
"
xml:space
="
preserve
">Vnde ſatis erit inuenire tantummodo puncta hora-
<
lb
/>
rum in alterutro tropicorũ: </
s
>
<
s
xml:id
="
echoid-s12993
"
xml:space
="
preserve
">hæc enim cum punctis correſpõdentibus in linea ęquinoctiali cõnexa
<
lb
/>
lineis rectis, dabunt horarias lineas ab occaſu, vt prius. </
s
>
<
s
xml:id
="
echoid-s12994
"
xml:space
="
preserve
">Accuratius tamen has lineas ducemus, ſi in
<
lb
/>
vtroque tropico horaria puncta inueſtigentur, vt terna correſpondentia puncta habeantur, per quę
<
lb
/>
ſingulæ lineæ horariæ duci debeant. </
s
>
<
s
xml:id
="
echoid-s12995
"
xml:space
="
preserve
">Ita enim facilè omnis error, qui in lineis horariis ducendis
<
lb
/>
committi poteſt, vitabitur.</
s
>
<
s
xml:id
="
echoid-s12996
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">50</
note
>
<
p
>
<
s
xml:id
="
echoid-s12997
"
xml:space
="
preserve
">QVOD ſi puncta aliquarum horarum in tropico ♋, inuenta non habeant puncta reſponden
<
lb
/>
tia in tropico ♑, cuiuſmodi ſunt in noſtro exemplo omnes horæ ante 16. </
s
>
<
s
xml:id
="
echoid-s12998
"
xml:space
="
preserve
">horam, ducendæ erunt
<
lb
/>
lineæ horariæ per puncta illarum horarum in tropico ♋, inuenta, & </
s
>
<
s
xml:id
="
echoid-s12999
"
xml:space
="
preserve
">per puncta reſpondentia in
<
lb
/>
linea æquinoctiali, quæ quidem ex dicta tabula propoſ. </
s
>
<
s
xml:id
="
echoid-s13000
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s13001
"
xml:space
="
preserve
">præcedentis libri, vel ex tabula ſcho-
<
lb
/>
lii propoſ. </
s
>
<
s
xml:id
="
echoid-s13002
"
xml:space
="
preserve
">33. </
s
>
<
s
xml:id
="
echoid-s13003
"
xml:space
="
preserve
">eiuſdem libri reperiuntur. </
s
>
<
s
xml:id
="
echoid-s13004
"
xml:space
="
preserve
">Linea verò horæ duodecimæ ducenda erit per punctum
<
lb
/>
in tropico ♋, inuentum lineæ æquinoctiali, vel lineæ horæ ſextæ à meridie, vel media nocte ęqui
<
lb
/>
diſtans. </
s
>
<
s
xml:id
="
echoid-s13005
"
xml:space
="
preserve
">In omni enim horologio horizontali, linea æquinoctialis, linea horæ ſextæ à meridie,
<
lb
/>
vel media nocte, & </
s
>
<
s
xml:id
="
echoid-s13006
"
xml:space
="
preserve
">linea horæ duodecimæ ab occaſu, parallelæ ſunt, vt in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s13007
"
xml:space
="
preserve
">22 præ-
<
lb
/>
cedentis libri demonſtrauimus. </
s
>
<
s
xml:id
="
echoid-s13008
"
xml:space
="
preserve
">At vero hora 11. </
s
>
<
s
xml:id
="
echoid-s13009
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s13010
"
xml:space
="
preserve
">ſi produceretur, tranſiret per horam quin
<
lb
/>
tam à mer. </
s
>
<
s
xml:id
="
echoid-s13011
"
xml:space
="
preserve
">vel med. </
s
>
<
s
xml:id
="
echoid-s13012
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s13013
"
xml:space
="
preserve
">in linea æquinoctiali; </
s
>
<
s
xml:id
="
echoid-s13014
"
xml:space
="
preserve
">Hora autem 10. </
s
>
<
s
xml:id
="
echoid-s13015
"
xml:space
="
preserve
">ab occ. </
s
>
<
s
xml:id
="
echoid-s13016
"
xml:space
="
preserve
">per horam quartam à mer.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s13017
"
xml:space
="
preserve
">vel med. </
s
>
<
s
xml:id
="
echoid-s13018
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s13019
"
xml:space
="
preserve
">quemadmodum tabula propoſ. </
s
>
<
s
xml:id
="
echoid-s13020
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s13021
"
xml:space
="
preserve
">libri ſuperioris præcipit.</
s
>
<
s
xml:id
="
echoid-s13022
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>