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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139
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0159
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LIBER PRIMVS.
"/>
mediet ates harum rectarum compoſitarum æquales erunt. </
s
>
<
s
xml:id
="
echoid-s8989
"
xml:space
="
preserve
">Vt in duob{us} tropicis mediet as rectæ compo-
<
lb
/>
ſię ex ſinu altitudinis meridianæ ♋, & </
s
>
<
s
xml:id
="
echoid-s8990
"
xml:space
="
preserve
">ſinu depreſſionis meridianę ♋, vel ex ſinu altitudinis meridia-
<
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/>
næ ♑, & </
s
>
<
s
xml:id
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echoid-s8991
"
xml:space
="
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">ſinu depreſſionis ♑, erit 68151. </
s
>
<
s
xml:id
="
echoid-s8992
"
xml:space
="
preserve
">eadem permanens, & </
s
>
<
s
xml:id
="
echoid-s8993
"
xml:space
="
preserve
">vtilis ad omnium horarum altitudines,
<
lb
/>
Sole in principio ♋, vel ♑, exiſtente, inuestigandas.</
s
>
<
s
xml:id
="
echoid-s8994
"
xml:space
="
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"/>
</
p
>
<
p
style
="
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">
<
s
xml:id
="
echoid-s8995
"
xml:space
="
preserve
">RVRVS in omnibus parallelis ſemper vſurpatur idem ſinus totus 100000. </
s
>
<
s
xml:id
="
echoid-s8996
"
xml:space
="
preserve
">in Solis altitudini-
<
lb
/>
bus perquirendis.</
s
>
<
s
xml:id
="
echoid-s8997
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s8998
"
xml:space
="
preserve
">POSTREMO recta λ N, hoc eſt, differentia inter ſinum altitudinis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s8999
"
xml:space
="
preserve
">medietatem
<
lb
/>
prædictam K λ, nunquam mutatur in duobus parallelis oppoſitis: </
s
>
<
s
xml:id
="
echoid-s9000
"
xml:space
="
preserve
">quia eadem differentia est omnino in-
<
lb
/>
ter ſinum depreſſionis meridianæ, & </
s
>
<
s
xml:id
="
echoid-s9001
"
xml:space
="
preserve
">medietatem alteram θ λ, vt ex figuris manifeſtum eſt. </
s
>
<
s
xml:id
="
echoid-s9002
"
xml:space
="
preserve
">Conſtat autẽ
<
lb
/>
ex demonſtratis, ſinum depreſſionis meridianę paralleli borealis æqualem eſſe ſinui altitudinis meridianæ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0159-01
"
xlink:href
="
note-0159-01a
"
xml:space
="
preserve
">10</
note
>
paralleli auſtralis oppoſiti: </
s
>
<
s
xml:id
="
echoid-s9003
"
xml:space
="
preserve
">Vnde ſemper eadem differentia erit inter medietatem prædictam, & </
s
>
<
s
xml:id
="
echoid-s9004
"
xml:space
="
preserve
">ſinum
<
lb
/>
altitudinis meridianæ tam paralleli borealis, quàm oppoſiti auſtralis. </
s
>
<
s
xml:id
="
echoid-s9005
"
xml:space
="
preserve
">Vt in duobus tropicis erit huiuſmo
<
lb
/>
di differentia hic numerus ferè 26681. </
s
>
<
s
xml:id
="
echoid-s9006
"
xml:space
="
preserve
">qui nunquam mutãdus erit, donec omnes altitudines inuentæ ſint
<
lb
/>
in duobus tropicis, & </
s
>
<
s
xml:id
="
echoid-s9007
"
xml:space
="
preserve
">ad quem numerum modo adijcienda eſt recta T λ, inuenta, modo ex eodem detra-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0159-02
"
xlink:href
="
note-0159-02a
"
xml:space
="
preserve
">
<
gap
/>
</
note
>
henda in ſignis borealibus, vel certè in australibus ſignis ipſemet numerus 26681. </
s
>
<
s
xml:id
="
echoid-s9008
"
xml:space
="
preserve
">ſubducendus eſt ex re-
<
lb
/>
cta T λ, inuenta, vt habeatur ſinus T N, altitudinis Solis, vt ex ſuperioribus patet.</
s
>
<
s
xml:id
="
echoid-s9009
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9010
"
xml:space
="
preserve
">QVOD ſi per alterum modum altitudines Solis inueſtigare placuerit in duobus oppoſitis parallelis,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0159-03
"
xlink:href
="
note-0159-03a
"
xml:space
="
preserve
">Qui numeri ij-
<
lb
/>
dẽ permaneãt, ſi
<
lb
/>
altitudines So-
<
lb
/>
lis indagen tur
<
lb
/>
per ſecundum
<
lb
/>
modũ pro ſingu
<
lb
/>
lis horis cuiuſ-
<
lb
/>
uis paralleli.</
note
>
permanebit quidem in vno eodem parallelo & </
s
>
<
s
xml:id
="
echoid-s9011
"
xml:space
="
preserve
">ſinus verſus arcus ſemidiurni, et ſinus rectus altitudinis
<
lb
/>
meridianæ ſmeper idẽ ſed ad altitudi@es inquir endas in altero parallelo, qui ei opponitur, proprius ſinus
<
lb
/>
tam verſus arcus ſemidiurni, quàm rectus altitudinis meridianę accipiendus crit. </
s
>
<
s
xml:id
="
echoid-s9012
"
xml:space
="
preserve
">Solum id commodi ha-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0159-04
"
xlink:href
="
note-0159-04a
"
xml:space
="
preserve
">20</
note
>
bebimus, quòd detr acto ſinu verſo arcus ſemidiurni vnius paralleli ex tota diametro, hoc eſt, ex 200000.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9013
"
xml:space
="
preserve
">ſtatim habeamus ſinum verſam arcus ſemidiurni paralleli oppoſiti: </
s
>
<
s
xml:id
="
echoid-s9014
"
xml:space
="
preserve
">quia ſinus verſus arcus ſemidiurni
<
lb
/>
vnius paralleli eſt æqualis ſinui verſo arcus ſeminocturni alterius paralleli oppoſiti: </
s
>
<
s
xml:id
="
echoid-s9015
"
xml:space
="
preserve
">Perſpicuum autem
<
lb
/>
eſt, ſinum verſum arcus ſeminocturni ex tota diametro ſubductum relinq@ere arcum verſum arcus ſemi-
<
lb
/>
diurni, & </
s
>
<
s
xml:id
="
echoid-s9016
"
xml:space
="
preserve
">contra. </
s
>
<
s
xml:id
="
echoid-s9017
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0159-05
"
xlink:href
="
note-0159-05a
"
xml:space
="
preserve
">Qui numeri nũ
<
lb
/>
quam mutẽtur,
<
lb
/>
ſi per vltimam
<
lb
/>
viam, quam an-
<
lb
/>
te rationẽ trian
<
lb
/>
gulorũ ſphæri-
<
lb
/>
corum tradidi-
<
lb
/>
mus, @nueſtigen
<
lb
/>
tur altitudines
<
lb
/>
Solis pro ſingu
<
lb
/>
lis hotis duorũ
<
lb
/>
parallelorũ op-
<
lb
/>
poſitorum.</
note
>
</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9018
"
xml:space
="
preserve
">AT vero in vltimailla via, quam proxime ante rationem ex triangulis ſphæricis depromptam ſcri-
<
lb
/>
pſimus, habebimus in oppoſitis parallelis non ſolum eandem ſemper medietatem rectę compoſitæ ex ſinu
<
lb
/>
altitudinis meridianę, & </
s
>
<
s
xml:id
="
echoid-s9019
"
xml:space
="
preserve
">ſinu meridianę depreſſionis, atque ſinum totum, verum etiam eoſaem ſinus ver
<
lb
/>
ſos diſtantiarum Solis à meridie in horis ęqualiter à Meridiano diſtantibus, vt ſunt horæ prima, & </
s
>
<
s
xml:id
="
echoid-s9020
"
xml:space
="
preserve
">vnde-
<
lb
/>
cima. </
s
>
<
s
xml:id
="
echoid-s9021
"
xml:space
="
preserve
">Item ſecunda & </
s
>
<
s
xml:id
="
echoid-s9022
"
xml:space
="
preserve
">decima, & </
s
>
<
s
xml:id
="
echoid-s9023
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s9024
"
xml:space
="
preserve
">tam in parallelo ♋, quàm in parallelo ♑. </
s
>
<
s
xml:id
="
echoid-s9025
"
xml:space
="
preserve
">Vnde in eiſdem horis ea-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0159-06
"
xlink:href
="
note-0159-06a
"
xml:space
="
preserve
">30</
note
>
dem recta K T, inuenictur, adeo vt in parallelo oppoſito non opus ſit inueſtigare rurſus rectam K T, pro
<
lb
/>
illa hora, pro qua inuenta eſt eadem K T, in altero parallelo, ſed eadem omnino aſſumenda, vt detraha-
<
lb
/>
tur à ſinu altitudinis meridianæ propoſiti paralleli, & </
s
>
<
s
xml:id
="
echoid-s9026
"
xml:space
="
preserve
">c.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9027
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0159-07
"
xlink:href
="
note-0159-07a
"
xml:space
="
preserve
">Qui ſinus ijdẽ
<
lb
/>
ſemper maneãt,
<
lb
/>
ſi per triangula
<
lb
/>
ſphærica altitu-
<
lb
/>
dines Solis in-
<
lb
/>
quirantur pro
<
lb
/>
ſingulis horis
<
lb
/>
duorum paral-
<
lb
/>
lelorum oppoſi
<
lb
/>
torum,</
note
>
</
s
>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9028
"
xml:space
="
preserve
">DENIQVE ſi quis altitudines Solis in duobus oppoſitis parallelis maluerit per triangula ſphęri
<
lb
/>
ca indagare, negotium etiam perfacile reddetur, quia idem ſemper ſinus totus, idemq́, ſinus declinationis
<
lb
/>
vtriuſq; </
s
>
<
s
xml:id
="
echoid-s9029
"
xml:space
="
preserve
">paralleli in omniũ horarũ altitudinibus perueſtigandis ret inendus eſt, vt ex dictis liquido cõſtat.</
s
>
<
s
xml:id
="
echoid-s9030
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9031
"
xml:space
="
preserve
">CÆTERVM vbi tanta eſt poli altitudo, vt totus parallelus aliquis borealis ſupra Horizontem
<
lb
/>
extet, ſiue illum tangat, vt in prima hac figura ſubiecta, ſiue non, vt in ſecunda, nihilo ſecius per priorem
<
lb
/>
modum in hac propoſ. </
s
>
<
s
xml:id
="
echoid-s9032
"
xml:space
="
preserve
">traditum altitudo Solis ex hora cognita, & </
s
>
<
s
xml:id
="
echoid-s9033
"
xml:space
="
preserve
">viciſſim ex altitudine Solis hora inue-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0159-08
"
xlink:href
="
note-0159-08a
"
xml:space
="
preserve
">Quando paral-
<
lb
/>
lelus borealis to
<
lb
/>
tus eſt ſupra Ho
<
lb
/>
rizontem, qua
<
lb
/>
ratio ne altitu-
<
lb
/>
do Solis ex no-
<
lb
/>
ta hora, & uiciſ-
<
lb
/>
ſim ex altitudi-
<
lb
/>
ne Solis cogni-
<
lb
/>
ta exploranda
<
lb
/>
ſit hora.</
note
>
nietur, dummodo in vtr aque figura meridies intelligatur eſſe in K, vbi Sol in Meridiano exiſtens maxi-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0159-09
"
xlink:href
="
note-0159-09a
"
xml:space
="
preserve
">40</
note
>
mam habet altitudinẽ, quæ ex decli-
<
lb
/>
<
figure
xlink:label
="
fig-0159-01
"
xlink:href
="
fig-0159-01a
"
number
="
116
">
<
image
file
="
0159-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0159-01
"/>
</
figure
>
natione paralleli inueſtiganda eſt, vt
<
lb
/>
ſupra in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s9034
"
xml:space
="
preserve
">præcedentis
<
lb
/>
declarauimus. </
s
>
<
s
xml:id
="
echoid-s9035
"
xml:space
="
preserve
">Verum nulla hic erit
<
lb
/>
depreſſio Meridiana, ſed in priori fi-
<
lb
/>
gura quidẽ recta K λ, erit medietas
<
lb
/>
ſinus altitudinis meridianę; </
s
>
<
s
xml:id
="
echoid-s9036
"
xml:space
="
preserve
">In poſte
<
lb
/>
riori verò eadem K λ, medietas erit
<
lb
/>
rectę K θ, quæ differentia eſt inter
<
lb
/>
K N, ſinum maioris altitudinis me-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0159-10
"
xlink:href
="
note-0159-10a
"
xml:space
="
preserve
">50</
note
>
ridianę K A, & </
s
>
<
s
xml:id
="
echoid-s9037
"
xml:space
="
preserve
">θ N, ſinum minoris
<
lb
/>
altitudinis meridianę L C: </
s
>
<
s
xml:id
="
echoid-s9038
"
xml:space
="
preserve
">quę qui-
<
lb
/>
dem minor altitudo C L, habebitur,
<
lb
/>
ſi ex arcu I L, declinationis detraha
<
lb
/>
tur arcus I C, complementi altitudi
<
lb
/>
nis poli. </
s
>
<
s
xml:id
="
echoid-s9039
"
xml:space
="
preserve
">Quòd ſi declinatio ęqualis fuerit complemento altitudinis poli, tanget parallelus Horizontem,
<
lb
/>
vt in priori figura accidit. </
s
>
<
s
xml:id
="
echoid-s9040
"
xml:space
="
preserve
">Quòd autem K λ, ſit medietas dictarum rectarum, ita probabitur. </
s
>
<
s
xml:id
="
echoid-s9041
"
xml:space
="
preserve
">Quoniam in
<
lb
/>
priori figur a eſt, vt k M, ad M C, ita K λ, ad λ N; </
s
>
<
s
xml:id
="
echoid-s9042
"
xml:space
="
preserve
">In poſteriori verò vt K M, ad M L, ita K λ, ad λ θ Eſt
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0159-11
"
xlink:href
="
note-0159-11a
"
xml:space
="
preserve
">2. ſex@@.</
note
>
autemtam K M, ipſi M C, quàm K M, ipſi M L, æqualis, quòd hæ rectę ſint ſemidiametri ipſius paralle-
<
lb
/>
li; </
s
>
<
s
xml:id
="
echoid-s9043
"
xml:space
="
preserve
">erit quoque K λ, ipſi λ N, in priori figura, & </
s
>
<
s
xml:id
="
echoid-s9044
"
xml:space
="
preserve
">ipſi λ θ, in poſteriori ęqualis.</
s
>
<
s
xml:id
="
echoid-s9045
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9046
"
xml:space
="
preserve
">ITAQVE quoniam in priori figura, vbi parallelus Horizontem tangit, eſt vt K M, ſinus totus ad
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0159-12
"
xlink:href
="
note-0159-12a
"
xml:space
="
preserve
">2. vel 4. ſexti</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>