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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Table of Notes
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0151
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LIBER PRIMVS.
"/>
<
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>
<
s
xml:id
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echoid-s8164
"
xml:space
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">SED inter omnes modos fortaſſe commodiſſimus hic erit. </
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>
<
s
xml:id
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echoid-s8165
"
xml:space
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">Quoniam in prioribus quinque
<
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figuris ad initiũ huius propoſ. </
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>
<
s
xml:id
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echoid-s8166
"
xml:space
="
preserve
">poſitis eſt, vt k M, ſinus totus in parallelo Solis ad K R, ita K λ, me-
<
lb
/>
<
note
position
="
right
"
xlink:label
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note-0151-01
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xlink:href
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note-0151-01a
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xml:space
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">2. vel 4. ſexti</
note
>
dietas rectę compoſitę ex ſinu altitudinis meridianę, & </
s
>
<
s
xml:id
="
echoid-s8167
"
xml:space
="
preserve
">ſinu depreſſionis meridianæ ad
<
emph
style
="
sc
">K</
emph
>
T: </
s
>
<
s
xml:id
="
echoid-s8168
"
xml:space
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">Et
<
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/>
vt k R, ad R S, differentiam inter K S, ſinum verſum arcus ſemidiurni, & </
s
>
<
s
xml:id
="
echoid-s8169
"
xml:space
="
preserve
">K R, ſinum verſum di-
<
lb
/>
<
note
position
="
right
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xlink:label
="
note-0151-02
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xlink:href
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note-0151-02a
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xml:space
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">2. ſexti.</
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>
ſtantię Solis à meridie, ita K T, ad T N, ſinum rectum altitudinis Solis; </
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>
<
s
xml:id
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echoid-s8170
"
xml:space
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">Erit ex æquo, vt
<
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style
="
sc
">K</
emph
>
M, ſinus
<
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/>
totus in parallelo Solis ad R S, differentiam inter ſinum verſum arcus ſemidiurni, & </
s
>
<
s
xml:id
="
echoid-s8171
"
xml:space
="
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">ſinũ verſum
<
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diſtantię Solis à meridie, ita K λ, medietas rectę compoſitę ex ſinu altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s8172
"
xml:space
="
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">ſinu
<
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depreſſionis meridianę ad T N, ſinum rectum altitudinis Solis. </
s
>
<
s
xml:id
="
echoid-s8173
"
xml:space
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preserve
">Quapropter ſi fiat, vt ſinus totus
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0151-03
"
xlink:href
="
note-0151-03a
"
xml:space
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">Altitudo Solis
<
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quo pacto ex ho
<
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/>
ra aliter inue-
<
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nienda.</
note
>
ad differentiam inter ſinum verſum arcus ſemidiurni, & </
s
>
<
s
xml:id
="
echoid-s8174
"
xml:space
="
preserve
">ſinum verſum diſtantiæ Solis à meridie,
<
lb
/>
ita medietas rectæ compoſitę ex ſinu altitudinis meridianę, & </
s
>
<
s
xml:id
="
echoid-s8175
"
xml:space
="
preserve
">ſinu depreſſionis meridianę, ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0151-04
"
xlink:href
="
note-0151-04a
"
xml:space
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">10</
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>
aliud, inuentus erit ſinus rectus altitudinis Solis, qui inquiritur; </
s
>
<
s
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="
echoid-s8176
"
xml:space
="
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">atque adeo altitudo ipſa no-
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ta euadet.</
s
>
<
s
xml:id
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echoid-s8177
"
xml:space
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8178
"
xml:space
="
preserve
">QVOD ſi viciſſim fiat, vt K λ, medietas prędicta ad T N, ſinum altitudinis Solis, ita
<
emph
style
="
sc
">K</
emph
>
M, ſinus
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0151-05
"
xlink:href
="
note-0151-05a
"
xml:space
="
preserve
">Quomodo ho-
<
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ra ex altitudine
<
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/>
Solis ſupputan
<
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/>
da ſit aliter ꝗ̃
<
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/>
ſupra traditum
<
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/>
eſt.</
note
>
totus ad aliud, inuenietur R S, differentia inter ſinum verſum arcus ſemidiurni, & </
s
>
<
s
xml:id
="
echoid-s8179
"
xml:space
="
preserve
">ſinum verſum
<
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/>
diſtantię Solis à meridie; </
s
>
<
s
xml:id
="
echoid-s8180
"
xml:space
="
preserve
">qua differentia ſublata à ſinu verſo arcus ſemidiurni, reliquus erit k R,
<
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/>
ſinus verſus diſtantię Solis à meridie, &</
s
>
<
s
xml:id
="
echoid-s8181
"
xml:space
="
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">c.</
s
>
<
s
xml:id
="
echoid-s8182
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8183
"
xml:space
="
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">AVT certe hoc modo (qui mihi magis probatur) idem negotium conficiemus. </
s
>
<
s
xml:id
="
echoid-s8184
"
xml:space
="
preserve
">Quoniam eſt
<
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/>
vt K M, ſinus totus in parallelo Solis, ad K R, ſinum verſum diſtantię Solis à meridie, ita K λ, me-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0151-06
"
xlink:href
="
note-0151-06a
"
xml:space
="
preserve
">2. vel 4. ſexti</
note
>
dietas rectę compoſitę ex ſinu altitudinis meridianę, & </
s
>
<
s
xml:id
="
echoid-s8185
"
xml:space
="
preserve
">ſinu depreſſionis meridianę ad K T, diffe-
<
lb
/>
rentiam inter k N, ſinum altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s8186
"
xml:space
="
preserve
">T N, ſinum altitudinis Solis tempore obſerua-
<
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/>
<
note
position
="
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xlink:label
="
note-0151-07
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="
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xml:space
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">20</
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>
tionis: </
s
>
<
s
xml:id
="
echoid-s8187
"
xml:space
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">Si fiat vt ſinus totus ad ſinum verſum diſtantię Solis à meridie, ita medietas rectæ compo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0151-08
"
xlink:href
="
note-0151-08a
"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
qua ratione ex
<
lb
/>
hora aliter inue
<
lb
/>
nienda.</
note
>
ſitę ex ſinu altitudinis meridianę, & </
s
>
<
s
xml:id
="
echoid-s8188
"
xml:space
="
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">ſinu depreſſionis meridianæ ad aliud, reperietur numerus
<
lb
/>
rectę k T, qui ex ſinu altitudinis meridianæ detractus relinquet ſinum altitudinis Solis.</
s
>
<
s
xml:id
="
echoid-s8189
"
xml:space
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8190
"
xml:space
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">ITEM, ſi viciſſim fiat, vt k λ, medietas prædicta ad K T, differentiam inter ſinum altitudinis
<
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/>
<
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="
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"
xlink:label
="
note-0151-09
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xlink:href
="
note-0151-09a
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xml:space
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">Hora qua ratio
<
lb
/>
ne aliter ex alti
<
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/>
tudine Solis nu
<
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/>
meranda.</
note
>
meridianę, & </
s
>
<
s
xml:id
="
echoid-s8191
"
xml:space
="
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">ſinum altitudinis Solis, quę nota ponitur, ita k M, ſinus totus ad aliud, cognitus erit
<
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K R, ſinus verſus diſtantiæ Solis à meridie, &</
s
>
<
s
xml:id
="
echoid-s8192
"
xml:space
="
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">c.</
s
>
<
s
xml:id
="
echoid-s8193
"
xml:space
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8194
"
xml:space
="
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">HIC modus poſtremus latiſſime patet. </
s
>
<
s
xml:id
="
echoid-s8195
"
xml:space
="
preserve
">Pertinet enim etiam ad illum parallelum Solis, qui
<
lb
/>
<
note
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="
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"
xlink:label
="
note-0151-10
"
xlink:href
="
note-0151-10a
"
xml:space
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">Quis modus
<
lb
/>
inuenieudæ al-
<
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titudinis Solis
<
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/>
ſit præſtantior.</
note
>
vel Horizontem tangit, vel totus ſupra eundem extat, vt ad finem ſcholij huius propoſ. </
s
>
<
s
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="
echoid-s8196
"
xml:space
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">dicemus.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s8197
"
xml:space
="
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">Adde quòd conuenit non ſolum in Horizontem, ſed in alia etiã omnia plana, quæ vel recta ſint ad
<
lb
/>
Horizontem, vel inclinata, vt ex propoſ. </
s
>
<
s
xml:id
="
echoid-s8198
"
xml:space
="
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">1. </
s
>
<
s
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="
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xml:space
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">lib. </
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>
<
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="
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xml:space
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">4. </
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>
<
s
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="
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"
xml:space
="
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">perſpicuum erit. </
s
>
<
s
xml:id
="
echoid-s8202
"
xml:space
="
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">Ibi enim eadem hac rationealti-
<
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/>
<
note
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="
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xlink:label
="
note-0151-11
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xlink:href
="
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xml:space
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">30</
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>
iudinem Solis ſupra quodcunque planum ex data hora inueſtigabimus. </
s
>
<
s
xml:id
="
echoid-s8203
"
xml:space
="
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">Quare præ cæter is omni-
<
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/>
bus modus hic memorię commendandus erit.</
s
>
<
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="
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xml:space
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8205
"
xml:space
="
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">LIBET iam per triangula ſphęrica idem hoc problema explicare. </
s
>
<
s
xml:id
="
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"
xml:space
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">Sit ergo Horizon ABCD;
<
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/>
</
s
>
<
s
xml:id
="
echoid-s8207
"
xml:space
="
preserve
">
<
note
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="
right
"
xlink:label
="
note-0151-12
"
xlink:href
="
note-0151-12a
"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
qua uia ex co-
<
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/>
gn@a hora per
<
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/>
triangula ſphæ-
<
lb
/>
rica ſit explotã-
<
lb
/>
da, Sole in quo-
<
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/>
cunque pa@all@
<
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/>
lo exiſtente.</
note
>
Meridianus B E D; </
s
>
<
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="
echoid-s8208
"
xml:space
="
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">Aequator AFC; </
s
>
<
s
xml:id
="
echoid-s8209
"
xml:space
="
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">Verticalis A E C; </
s
>
<
s
xml:id
="
echoid-s8210
"
xml:space
="
preserve
">parallelus Solis ſiue borealis, ſiue auſtralis
<
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/>
G H I, ita vt borealis Verticalem ſecet in K; </
s
>
<
s
xml:id
="
echoid-s8211
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xml:space
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preserve
">quod quidem contingit, quando arcus F H, declina-
<
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<
figure
xlink:label
="
fig-0151-01
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xlink:href
="
fig-0151-01a
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number
="
110
">
<
image
file
="
0151-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0151-01
"/>
</
figure
>
<
note
position
="
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xlink:label
="
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xlink:href
="
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xml:space
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">40</
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>
tionis parallelli minor fuerit arcu E F, altitudinis poli, qui inter verticem, & </
s
>
<
s
xml:id
="
echoid-s8212
"
xml:space
="
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">Aequatorem interpo
<
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/>
<
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">50</
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>
nitur; </
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>
<
s
xml:id
="
echoid-s8213
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xml:space
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">ponaturq́; </
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>
<
s
xml:id
="
echoid-s8214
"
xml:space
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">Sol in puncto L, ſui paralleli, ita vt H L, ſit diſtantia Solis à meridie, cui ſimilis
<
lb
/>
erit arcus Aequatoris F M, per propoſ. </
s
>
<
s
xml:id
="
echoid-s8215
"
xml:space
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">10. </
s
>
<
s
xml:id
="
echoid-s8216
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xml:space
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">lib. </
s
>
<
s
xml:id
="
echoid-s8217
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s8218
"
xml:space
="
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">Theodoſii, quem aufert circulus declinationis ex
<
lb
/>
polo N, per centrum Solis L, ductus. </
s
>
<
s
xml:id
="
echoid-s8219
"
xml:space
="
preserve
">Ex vertice E, per Solem L, deſcendat Verticalis E L O, ita vt
<
lb
/>
arcus altitudinis Solis ſit L O, quem inueſtigare oportet, ſi diſtantia Solis à meridie ex hora data
<
lb
/>
cognita ſit, vt prior pars problematis pręcipit. </
s
>
<
s
xml:id
="
echoid-s8220
"
xml:space
="
preserve
">Deſcribatur alius circulus maximus per A, polum
<
lb
/>
Meridiani, & </
s
>
<
s
xml:id
="
echoid-s8221
"
xml:space
="
preserve
">per Solem in L, conſtitutum, ſecans Meridianum in P.</
s
>
<
s
xml:id
="
echoid-s8222
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8223
"
xml:space
="
preserve
">QVONIAM igitur in triangulo ſphęrico A L M, priorum quatuor figurarum, angulus M,
<
lb
/>
rectus eſt, per propoſ. </
s
>
<
s
xml:id
="
echoid-s8224
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s8225
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s8226
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s8227
"
xml:space
="
preserve
">Theodoſii, cum circulus maximus N M, per N, polum Aequatoris
<
lb
/>
A F C, ductus ſit; </
s
>
<
s
xml:id
="
echoid-s8228
"
xml:space
="
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">erit per propoſ. </
s
>
<
s
xml:id
="
echoid-s8229
"
xml:space
="
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">19. </
s
>
<
s
xml:id
="
echoid-s8230
"
xml:space
="
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">lib: </
s
>
<
s
xml:id
="
echoid-s8231
"
xml:space
="
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">4. </
s
>
<
s
xml:id
="
echoid-s8232
"
xml:space
="
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">Ioan. </
s
>
<
s
xml:id
="
echoid-s8233
"
xml:space
="
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">Regiom. </
s
>
<
s
xml:id
="
echoid-s8234
"
xml:space
="
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">de triangulis, uel per propoſ. </
s
>
<
s
xml:id
="
echoid-s8235
"
xml:space
="
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">15. </
s
>
<
s
xml:id
="
echoid-s8236
"
xml:space
="
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">lib. </
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>
<
s
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echoid-s8237
"
xml:space
="
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">1.
<
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</
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<
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xml:id
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A M, hoc eſt, ut ſinus diſtantię Solis à meridie (eſt enim F M, diſtantia Solis à meridie, </
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