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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GNOMONICES
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<
s
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xml:space
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">QVOD ſi murus in meridiem ſpectet, ſed obſeruatio fiat pomeridiano tempore, & </
s
>
<
s
xml:id
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"
xml:space
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">punctum qui-
<
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<
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left
"
xlink:label
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note-0108-01
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xlink:href
="
note-0108-01a
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xml:space
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">Quãdo murus
<
lb
/>
in meridiẽ ſpe-
<
lb
/>
ctat, & Sol au-
<
lb
/>
ſtralior eſt, quã
<
lb
/>
Verticalis pro-
<
lb
/>
priè dictus, ob-
<
lb
/>
ſeruatioq́ue fit
<
lb
/>
poſt meridiem.</
note
>
dem S, inter Q, & </
s
>
<
s
xml:id
="
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xml:space
="
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">R, extiterit, ita vt Sol & </
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>
<
s
xml:id
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"
xml:space
="
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">murum, & </
s
>
<
s
xml:id
="
echoid-s4839
"
xml:space
="
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">Verticalem primarium ex auſtrali parteil-
<
lb
/>
luminet, angulus{q́ue} T R H, angulo C D G, deprehenſus fuerit æqualis, carebit rurſum murus declina-
<
lb
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tione. </
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>
<
s
xml:id
="
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xml:space
="
preserve
">Si verò angulus T R H, maior inueniatur angulo C D G, erit murus ex parte occidentis inter
<
lb
/>
Verticalem primarium, & </
s
>
<
s
xml:id
="
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xml:space
="
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">Verticalem per centrum Solis ductum poſitus. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Quocirca dempto angulo
<
lb
/>
C D G, ex angulo T R H, remane
<
unsure
/>
bit angulus declinationis muri à Verticali primario, & </
s
>
<
s
xml:id
="
echoid-s4843
"
xml:space
="
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">à meridie in
<
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/>
ortum. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Si denique angulus T R H, minor angulo C D G, fuerit, exiſtet Verticalis primarius ex parte oc-
<
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cidentis inter murum, & </
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>
<
s
xml:id
="
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"
xml:space
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">verticalem, qui per Solem ducitur. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Ablato ergo illo ex hoc, reliquus erit an-
<
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gulus declinationis muri à Verticali primario, & </
s
>
<
s
xml:id
="
echoid-s4847
"
xml:space
="
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">à meridie in occaſum.</
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<
s
xml:id
="
echoid-s4848
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xml:space
="
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"/>
</
p
>
<
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<
s
xml:id
="
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"
xml:space
="
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">PVNCTO autem S, cadente in R, ita vt Sol illuminet quidem murum ex parte auſtrali, Vertica
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-02
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xlink:href
="
note-0108-02a
"
xml:space
="
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">Quãdo murus
<
lb
/>
in meridiẽ ſpe-
<
lb
/>
ctat, & Sol in
<
lb
/>
Verticali pro-
<
lb
/>
priè dicto exi-
<
lb
/>
ſtit, vel borea-
<
lb
/>
lior eſt, quàm
<
lb
/>
Verticalis pro-
<
lb
/>
ptiè dictus, ob-
<
lb
/>
ſeruati@q́ue fit
<
lb
/>
poſt meridiem.</
note
>
<
note
position
="
left
"
xlink:label
="
note-0108-03
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xlink:href
="
note-0108-03a
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xml:space
="
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">10</
note
>
lem verò primarium nullo modo, declinabit murus à Verticali, & </
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>
<
s
xml:id
="
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xml:space
="
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">à meridie in occaſum, angulo inuento
<
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C D G; </
s
>
<
s
xml:id
="
echoid-s4851
"
xml:space
="
preserve
">quia tunc Sol in Verticali primario exiſtet, qui ex parte occidentis auſtralior eſt ipſo muro.</
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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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style
="
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<
s
xml:id
="
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xml:space
="
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">CADENTE denique puncto S, inter P, & </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">R, ita vt Sol murum quidem illuminet ex parte au-
<
lb
/>
ſtrali, Verticalem vero primarium ex parte boreali, conſtitutus erit Verticalis, in quo eſt Sol, inter mu-
<
lb
/>
rum, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Verticalem primarium ex parte occidentis. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Quapropter ſi angulus T R H, addatur angulo
<
lb
/>
C D G, componetur angulus, quo murus à Verticali primario, & </
s
>
<
s
xml:id
="
echoid-s4857
"
xml:space
="
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">à meridie in occaſum deflectit.</
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>
<
s
xml:id
="
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xml:space
="
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</
p
>
<
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<
s
xml:id
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xml:space
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">AT verò ſi murus in Septentrionem vergat, obſeruatio autem fiat ante meridiem, & </
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>
<
s
xml:id
="
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xml:space
="
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">punctum S,
<
lb
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<
note
position
="
left
"
xlink:label
="
note-0108-04
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xlink:href
="
note-0108-04a
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xml:space
="
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">Quãdo murus
<
lb
/>
ſpectat in bo-
<
lb
/>
ream, & Sol au-
<
lb
/>
ſtralior eſt, quã
<
lb
/>
Verticalis pro-
<
lb
/>
priè dictus, vel
<
lb
/>
in Verticali pro
<
lb
/>
priè dicto exi-
<
lb
/>
ſtit, obſerua-
<
lb
/>
tioq́ue fit ante
<
lb
/>
meridiem.</
note
>
inter Q, & </
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>
<
s
xml:id
="
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xml:space
="
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">R, extiterit, ita vt Sol illuminet murum ex parte Septentrionali, & </
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>
<
s
xml:id
="
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xml:space
="
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">Verticalem propriè
<
lb
/>
dictum ex parte auſtrali, poſitus erit Verticalis per Solem ductus inter murum, & </
s
>
<
s
xml:id
="
echoid-s4863
"
xml:space
="
preserve
">Verticalem prima-
<
lb
/>
rium, ex parte orientis. </
s
>
<
s
xml:id
="
echoid-s4864
"
xml:space
="
preserve
">Igitur ſi angulus T R H, angulo C D G, addatur, conficietur angulus declina-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-05
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xlink:href
="
note-0108-05a
"
xml:space
="
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">20</
note
>
tionis muri à Verticali primario, & </
s
>
<
s
xml:id
="
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xml:space
="
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">à Septentrione in ortum.</
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>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
p
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<
s
xml:id
="
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"
xml:space
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">SI verò punctum S, idem fuerit, quod R, ita vt Sol adhuc murum illuminet ex parte boreali, Ver-
<
lb
/>
ticalem autem propriè dictum nullo modo, erit angulus inuentus C D G, angulus declinationis muri à
<
lb
/>
Verticali propriè dicto, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">à Septentrione in ortum.</
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>
<
s
xml:id
="
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xml:space
="
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"/>
</
p
>
<
p
style
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<
s
xml:id
="
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xml:space
="
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">SI denique fuerit punctum S, inter P, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">R, ita vt Sol & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">murum, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Verticalem propriè dictum ex
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-06
"
xlink:href
="
note-0108-06a
"
xml:space
="
preserve
">Quando murus
<
lb
/>
in boream ſpe-
<
lb
/>
ctat, & Sol bo-
<
lb
/>
realior eſt, quã
<
lb
/>
Verticalis pro-
<
lb
/>
priè dictus, ob-
<
lb
/>
ſeruatioq́ue fit
<
lb
/>
ante meridiem.</
note
>
parte boreali illuminet, cõferendus erit angulus T R H, cum angulo C D G. </
s
>
<
s
xml:id
="
echoid-s4874
"
xml:space
="
preserve
">Si enim ille huic fuerit ęqua-
<
lb
/>
lis, nullam habebit murus declinationem, propter cauſam ante dictam. </
s
>
<
s
xml:id
="
echoid-s4875
"
xml:space
="
preserve
">Si verò angulus T R H, angulũ
<
lb
/>
C D G, ſuperauerit, ſi hic ab illo ſubducatur, relinquetur angulus, quo murus à Verticali primario decli-
<
lb
/>
nat, & </
s
>
<
s
xml:id
="
echoid-s4876
"
xml:space
="
preserve
">à Septentrione in occaſum; </
s
>
<
s
xml:id
="
echoid-s4877
"
xml:space
="
preserve
">propterea quòd tunc murus ex parte orientis collocatus erit inter
<
lb
/>
Verticalem primarium, & </
s
>
<
s
xml:id
="
echoid-s4878
"
xml:space
="
preserve
">illum, qui per Solem incedit. </
s
>
<
s
xml:id
="
echoid-s4879
"
xml:space
="
preserve
">Si denique angulus T R H, angulo C D G, fue-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-07
"
xlink:href
="
note-0108-07a
"
xml:space
="
preserve
">30</
note
>
rit minor, exiſtet Verticalis primarius inter murum, & </
s
>
<
s
xml:id
="
echoid-s4880
"
xml:space
="
preserve
">Verticalem, qui per Solem tranſit, ex parte
<
lb
/>
Orientis. </
s
>
<
s
xml:id
="
echoid-s4881
"
xml:space
="
preserve
">Quamobrem ſi illum ex hoc detrahamus, reliquum faciemus angulum, quo murus à Verticali
<
lb
/>
primario, & </
s
>
<
s
xml:id
="
echoid-s4882
"
xml:space
="
preserve
">à Septentrione in ortum declinat.</
s
>
<
s
xml:id
="
echoid-s4883
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
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"
xml:space
="
preserve
">MVRO autem in Septentrionem ſpectante, ſi obſeruatio tempore pomeridiano fiat, punctum{q́ue} S,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-08
"
xlink:href
="
note-0108-08a
"
xml:space
="
preserve
">Quando murus
<
lb
/>
in boream ſpe-
<
lb
/>
ctat, & Sol au-
<
lb
/>
ſtralior eſt, quã
<
lb
/>
Verticalis pro-
<
lb
/>
priè dict
<
emph
style
="
sub
">9</
emph
>
, vel in
<
lb
/>
Verticali ꝓpriè
<
lb
/>
dicto exiſtit, vel
<
lb
/>
borealior eſt,
<
lb
/>
quàm Vertica-
<
lb
/>
lis propriè di-
<
lb
/>
ctus, obſeruatio-
<
lb
/>
q́ue fit poſt me-
<
lb
/>
ridiem.</
note
>
existat inter Q, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">R, ita vt Sol murum quidem ex parte boreali, Verticalem autẽ propriè dictum ex
<
lb
/>
auſtrali illuminet, poſitus erit Verticalis per Solem ductus, ex parte occidentali, inter murum, & </
s
>
<
s
xml:id
="
echoid-s4886
"
xml:space
="
preserve
">Ver
<
lb
/>
ticalem primarium. </
s
>
<
s
xml:id
="
echoid-s4887
"
xml:space
="
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">Quare ſi addatur angulus T R H, angulo C D G, conficietur angulus declinationis
<
lb
/>
muri à Verticali propriè dicto, & </
s
>
<
s
xml:id
="
echoid-s4888
"
xml:space
="
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">à Septentrione in occaſum.</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
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">
<
s
xml:id
="
echoid-s4890
"
xml:space
="
preserve
">CADENTE autem puncto S, in punctum R, ita vt Sol illuminet quidem murum ex parte borea-
<
lb
/>
li, Verticalem vero primarium nullo modo, dabit angulus inuentus C D G, declinationem muri à Ver-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-09
"
xlink:href
="
note-0108-09a
"
xml:space
="
preserve
">40</
note
>
ticali primario, & </
s
>
<
s
xml:id
="
echoid-s4891
"
xml:space
="
preserve
">à Septentrione in occaſum; </
s
>
<
s
xml:id
="
echoid-s4892
"
xml:space
="
preserve
">quoniam tunc Verticalis primarius per Solem incedit,
<
lb
/>
eſt{q́ue} ipſo muro borealior.</
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s4894
"
xml:space
="
preserve
">PVNCTO denique S, inter P, & </
s
>
<
s
xml:id
="
echoid-s4895
"
xml:space
="
preserve
">R, exiſtente’, ita vt Sol tam murum, quàm Verticalem pro-
<
lb
/>
priè dictum ex parte boreali illuminet, ſi quidem angulus T R H, æqualis fuerit angulo C D G, æquidi-
<
lb
/>
ſtabit murus Verticali primario, nullam{q́ue} habebit declinationem. </
s
>
<
s
xml:id
="
echoid-s4896
"
xml:space
="
preserve
">Si vero ille maior hoc fuerit, exiſtet
<
lb
/>
murus ex parte occidentali inter Verticalem primarium, & </
s
>
<
s
xml:id
="
echoid-s4897
"
xml:space
="
preserve
">illum, qui per Solem tranſit. </
s
>
<
s
xml:id
="
echoid-s4898
"
xml:space
="
preserve
">Quocirca
<
lb
/>
dempto angulo C D G, ex angulo T R H, reliquus erit angulus declinationis muri à Verticali propriè di-
<
lb
/>
cto, & </
s
>
<
s
xml:id
="
echoid-s4899
"
xml:space
="
preserve
">à Septentrione in ortum. </
s
>
<
s
xml:id
="
echoid-s4900
"
xml:space
="
preserve
">Si denique angulus T R H, angulo C D G, fuerit minor, collocatus erit
<
lb
/>
Verticalis primarius inter murum, & </
s
>
<
s
xml:id
="
echoid-s4901
"
xml:space
="
preserve
">Verticalem, in quo Sol exiſtit, ex parte occidentali. </
s
>
<
s
xml:id
="
echoid-s4902
"
xml:space
="
preserve
">Quare dem-
<
lb
/>
pto illo ex hoc, remanebit angulus declinationis muri à Verticali primario, & </
s
>
<
s
xml:id
="
echoid-s4903
"
xml:space
="
preserve
">à Septentrione in occa-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0108-10
"
xlink:href
="
note-0108-10a
"
xml:space
="
preserve
">50</
note
>
ſum. </
s
>
<
s
xml:id
="
echoid-s4904
"
xml:space
="
preserve
">Quæ omnia perſpicua ſunt, ſi attentè diligenterq́, ſitus circulorum, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">muri perpendatur.</
s
>
<
s
xml:id
="
echoid-s4906
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">Quando altitu-
<
lb
/>
do Solis æqua-
<
lb
/>
lis fuerit altitu-
<
lb
/>
dini eiuſdem
<
lb
/>
meridianæ.</
note
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s4907
"
xml:space
="
preserve
">QVOD ſi quando recta P Q, in Analemmate ceciderit in punctum N, hoc eſt, ſi altitudo Solis in-
<
lb
/>
uenta fuerit æqualis altitudini Meridianę Solis illius diei, exiſtet Sol in Meridiano circulo; </
s
>
<
s
xml:id
="
echoid-s4908
"
xml:space
="
preserve
">ac propterea
<
lb
/>
recta F D, in muro communis ſectio erit Meridiani, & </
s
>
<
s
xml:id
="
echoid-s4909
"
xml:space
="
preserve
">muri; </
s
>
<
s
xml:id
="
echoid-s4910
"
xml:space
="
preserve
">cùm Meridianus tunc per E, centrũ mundi,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s4911
"
xml:space
="
preserve
">per radium Solis E F, ducatur, murus{q́ue} ipſe in meridiem verget. </
s
>
<
s
xml:id
="
echoid-s4912
"
xml:space
="
preserve
">Igitur angulus C D G, in muro in-
<
lb
/>
uentus dabit declinationem muri à Meridiano, ac propterea eius complementum declinationem muri à
<
lb
/>
Verticali propriè dicto oſtendet, à meridie quidem in ortum, ſi vmbra F, cadat nobis ad murum conuer-
<
lb
/>
ſis ad dexteram, à meridie verò in occaſum, ſi ad ſiniſtram cadat vmbra.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4913
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0108-12
"
xlink:href
="
note-0108-12a
"
xml:space
="
preserve
">Inuentio facili
<
lb
/>
ma declinatio-
<
lb
/>
nis muri in me
<
lb
/>
ridiem vergen-
<
lb
/>
tis in ipſo meri-
<
lb
/>
die.</
note
>
</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s4914
"
xml:space
="
preserve
">QVOCIRCA ſi in meridie fiat obſeruatio, qui in plano Horizonti parallelo ex vmbra ſtyli in li-
<
lb
/>
neam meridian
<
unsure
/>
am cadente cognoſcitur, (quod quidem tempus, ſi commode fieri poſſit, ego ſemper elige-
<
lb
/>
rem) dicto citius declinatio reperietur. </
s
>
<
s
xml:id
="
echoid-s4915
"
xml:space
="
preserve
">Nam complementum anguli C D G, in muro inuenti dabit </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>