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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LIBER PRIMVS.
"/>
oſtendimus: </
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>
<
s
xml:id
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echoid-s7069
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xml:space
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preserve
">Si ſiat vt E k, ſinus complementi altitudinis poli ad E L, ſinum totum, ita E k, ſinus
<
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declinationis paralleli dati reſpectu ſinus totius E F, ad aliud, inuenietur E L, ſinus amplitudinis
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ortiuę, occiduæue, reſpectu eiuſdem
<
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<
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fig-0137-01
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99
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01
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ſinus totius E F. </
s
>
<
s
xml:id
="
echoid-s7070
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xml:space
="
preserve
">Ex ſinu autem E L,
<
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/>
amplitudo ipſa ortiua, occiduaue no-
<
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/>
ta fiet.</
s
>
<
s
xml:id
="
echoid-s7071
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xml:space
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"/>
</
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<
p
>
<
s
xml:id
="
echoid-s7072
"
xml:space
="
preserve
">RVRSVS quia in eodem trian-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0137-01
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xlink:href
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note-0137-01a
"
xml:space
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">Arcus ſemidiur
<
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nus, qua uia per
<
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/>
ſinus eliciatur
<
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ex Analẽmate.</
note
>
gulo E K L, ſi E L, ponatur ſinus to-
<
lb
/>
tus, recta k L, eſt ſinus anguli k E L,
<
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/>
altitudinis poli, vt ex eadem tracta-
<
lb
/>
<
note
position
="
left
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xlink:label
="
note-0137-02
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xlink:href
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note-0137-02a
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xml:space
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">10</
note
>
tione ſinuum conſtat: </
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>
<
s
xml:id
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echoid-s7073
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xml:space
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">ſi fiat vt E K,
<
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/>
ſinus complementi altitudinis poli
<
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/>
ad K L, ſinum altitudinis poli, ita E K,
<
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/>
ſinus declinationis reſpectu ſinus to-
<
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/>
tius E F, ad aliud, cognita erit K L, in
<
lb
/>
partibus eiuſdem ſinus totius E F.
<
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/>
</
s
>
<
s
xml:id
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echoid-s7074
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xml:space
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">Deinde quoniam H K, eſt ſinus com-
<
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plemẽti declinationis reſpectu ſinus
<
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totius E F: </
s
>
<
s
xml:id
="
echoid-s7075
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xml:space
="
preserve
">Si fiat, vt H K, ſinus com-
<
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/>
plementi declinationis reſpectu ſi-
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0137-03
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xlink:href
="
note-0137-03a
"
xml:space
="
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">20</
note
>
nus totius E F, ad K L, quatenus nota
<
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facta eſt in partibus eiuſdem ſinus to
<
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/>
rius E F, ita H k, quatenus ſinus to-
<
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/>
rus in parallelo Solis, ad aliud, efficie
<
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tur K L, nota in partibus eiuſdem ſi-
<
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nus totius H k; </
s
>
<
s
xml:id
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echoid-s7076
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xml:space
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">ac propterea eius arcus M N, notus erit, qui in parallelo boreali additus quadran
<
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ti H M, complet arcum ſemidiurnum H N, in auſtrali vero ex quadrante H M, deductus relinquit
<
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arcum ſemidiurnum H N. </
s
>
<
s
xml:id
="
echoid-s7077
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xml:space
="
preserve
">Itaque ſi fiat, vt ſinus complementi altitudinis poli ad ſinum altitudi-
<
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nis poli, ita ſinus declinationis propoſiti paralleliad aliud, reperietur ſinus quidam, quem Pri-
<
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/>
mum Inuẽtum nominemus. </
s
>
<
s
xml:id
="
echoid-s7078
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xml:space
="
preserve
">Deinde ſi fiat, vt ſinus cõplementi declinationis ad ſinum, quem ap-
<
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<
note
position
="
left
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xlink:label
="
note-0137-04
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xlink:href
="
note-0137-04a
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xml:space
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">30</
note
>
pellaumus Primum Inuẽntum, ita ſinus totus ad aliud, inuentus erit ſinus cuiuſdam arcus, qui
<
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/>
Sole in ſignis borealibus commorante, adiectus ad quadrantem, vel Sole auſtralia percurrente ſi-
<
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/>
gna, ex quadrante detractus, dabit arcum ſemidiurnum. </
s
>
<
s
xml:id
="
echoid-s7079
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xml:space
="
preserve
">Amplitudinẽ ergo ortiuam, occiduamve,
<
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& </
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>
<
s
xml:id
="
echoid-s7080
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xml:space
="
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">arcnm ſemidiurnum cuiuſuis paralleli, ad datam poli altitudinem inueſtigauimus. </
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>
<
s
xml:id
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xml:space
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">Quod fa-
<
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ciendum erat.</
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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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<
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style
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xml:space
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">SCHOLIVM.</
head
>
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<
s
xml:id
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xml:space
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">DVOS alios modos inueniendi arcus ſemidiurni ſine triangulis quoque ſphæricis, Sole in quocunque
<
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parallelo exiſtente, trademus in ſcholio propoſ. </
s
>
<
s
xml:id
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xml:space
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preserve
">ſequentis, quos lectori non ingratos fore confidimus.</
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<
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xml:space
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</
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<
s
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xml:space
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">CAETERM arcus ſemidiurni parallelorum auftr alium, vt ex demonstratis conſtat, æquales
<
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<
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xlink:label
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xml:space
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">40</
note
>
<
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="
right
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xlink:label
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note-0137-06
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xlink:href
="
note-0137-06a
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xml:space
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">Arcus ſemidiu@
<
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ni parallelorũ
<
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auſtraliũ æqua-
<
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les ſunt arcu-
<
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bus ſeminoctur
<
lb
/>
nis parallelorũ
<
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/>
borealium op-
<
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poſitorum.</
note
>
ſunt ſeminocturnis arcubus parallelorum borealium oppoſitorum. </
s
>
<
s
xml:id
="
echoid-s7087
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xml:space
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">Eadem enim operatione in priori mo-
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do inuentus eſt & </
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>
<
s
xml:id
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xml:space
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">arcus ſemidiurnus auſtr alis paralleli, & </
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>
<
s
xml:id
="
echoid-s7089
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xml:space
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">ſeminocturnus paralleli borealis oppoſiti.
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</
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<
s
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xml:space
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">Quod etiarn non obſcure ex propoſ. </
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>
<
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">19. </
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<
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">lib. </
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<
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">2. </
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<
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">Theod. </
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<
s
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">elicitur. </
s
>
<
s
xml:id
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echoid-s7096
"
xml:space
="
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">Cùm enim ibi demonstretur, alterna ſeg-
<
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menta oppoſitorum & </
s
>
<
s
xml:id
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echoid-s7097
"
xml:space
="
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">æqualium parallelorum, in quæ ab Horizonte diuiduntur, & </
s
>
<
s
xml:id
="
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"
xml:space
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">cuiuſmodi ſunt ar-
<
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cus diurnus vnius paralleli, & </
s
>
<
s
xml:id
="
echoid-s7099
"
xml:space
="
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">arcus nocturnus alterius paralleli oppoſiti & </
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>
<
s
xml:id
="
echoid-s7100
"
xml:space
="
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">æqualis, eſſe æqualia inter
<
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ſe, erunt quoque eorum dimidia inter ſe æqualia, nempe arcus ſemidiurnus paralleli vnius, & </
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>
<
s
xml:id
="
echoid-s7101
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xml:space
="
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">ſemino-
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cturnus alterius. </
s
>
<
s
xml:id
="
echoid-s7102
"
xml:space
="
preserve
">Igitur ſi omnium punctorum Eclipticæ arcus ſemidiurni deſiderentur, ſatis erit, vt ar-
<
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<
note
position
="
right
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xlink:label
="
note-0137-07
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xlink:href
="
note-0137-07a
"
xml:space
="
preserve
">Satis eſt, ſi inne
<
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ſtigentur arcus
<
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ſemidiurni pa-
<
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rallelorum au-
<
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/>
ſtralium. Ex his
<
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/>
enim facili ne-
<
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gotio elicientur
<
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/>
quoque arcus ſe
<
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/>
midiurni paral
<
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lelorũ borealiũ
<
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oppoſitorum.</
note
>
cus ſemidiurni inueſtigentur in par allelis auſtr alibus: </
s
>
<
s
xml:id
="
echoid-s7103
"
xml:space
="
preserve
">hienim, cũ æquales ſint arcubus ſeminocturnis pa-
<
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rallelorum borealium oppoſitorum, vt dictum eſt, ſubducti ex ſemicirculo relinquent arcus etiam ſemi-
<
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/>
diurnos parallelorum borealium oppoſitorum.</
s
>
<
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xml:id
="
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xml:space
="
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"/>
</
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<
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="
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xml:space
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">50</
note
>
<
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="
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<
s
xml:id
="
echoid-s7105
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xml:space
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">HOC etiam ex poſteriori modo liquido conſtat. </
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>
<
s
xml:id
="
echoid-s7106
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xml:space
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">Quoniam enim in Analemmate eadem operatione
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inuentus est & </
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>
<
s
xml:id
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echoid-s7107
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xml:space
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">arcus M N, in parallelo boreali, & </
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>
<
s
xml:id
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echoid-s7108
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xml:space
="
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">in auſtrali, quo quidem & </
s
>
<
s
xml:id
="
echoid-s7109
"
xml:space
="
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">quadrans M I, arcum ſe-
<
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/>
minocturnum N I, paralleli borealis, & </
s
>
<
s
xml:id
="
echoid-s7110
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xml:space
="
preserve
">quadrans M H, arcum ſemidiurnum H N, paralleli auſtr alis
<
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/>
ſuperat, perſpicuum eſt, arcum ſeminocturnum N I, paralleli borealis æqualem eſſe ſemidiurno arcui
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0137-09
"
xlink:href
="
note-0137-09a
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xml:space
="
preserve
">Satis eſt, ſi ſup-
<
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/>
putcn@ur arcus
<
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ſemidiutni v-
<
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/>
nius quadrãtis
<
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/>
auſtralis Eclipti
<
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/>
cæ: quia ex his
<
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/>
arcus ſcmidiur
<
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/>
ni aliorũ pun-
<
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ctorũ Eclipticæ
<
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/>
facile colligun-
<
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tur.</
note
>
N H, paralleli auſtralis. </
s
>
<
s
xml:id
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echoid-s7111
"
xml:space
="
preserve
">Et ſic de cæteris. </
s
>
<
s
xml:id
="
echoid-s7112
"
xml:space
="
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">Vbi etiam manifeſte cernis, arcum ſeminocturnum N I, ex
<
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/>
ſemicirculo H N I, ſubtractum relinquere arcum ſemidiurnum H N.</
s
>
<
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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
="
echoid-s7114
"
xml:space
="
preserve
">IMMO quia arcus ſemidiurni vnius quadrantis Eclipticæ auſtralis, qui interijcitur inter Aequato-
<
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rem, & </
s
>
<
s
xml:id
="
echoid-s7115
"
xml:space
="
preserve
">colurum Solſtitiorum, æquales ſunt ſemidiurnis arcubus alterius quadrantis auſtralis, ſuppu-
<
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/>
tandi erunt duntaxat arcus ſemidiurni vnius quadrantis Eclipticæ auſtralis, nempe eius, qui inter prin
<
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/>
c
<
unsure
/>
ipium ♎, & </
s
>
<
s
xml:id
="
echoid-s7116
"
xml:space
="
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">principium ♑, interijeitur. </
s
>
<
s
xml:id
="
echoid-s7117
"
xml:space
="
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">Nam hi æquales erunt ſemidiurnis arcubus alterius quadran
<
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tis auſiralis inter principium ♈, & </
s
>
<
s
xml:id
="
echoid-s7118
"
xml:space
="
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">principium ♑, intercepti. </
s
>
<
s
xml:id
="
echoid-s7119
"
xml:space
="
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">Iidem verò ex ſemicir culo detracti </
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>
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