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 PRIMVS.
"/>
V Y, pars eſt ſinus totius A E, circuli maximi) ad V Y, quatenus ſinus totus eſt in ſu
<
unsure
/>
o parallelo,
<
lb
/>
ita β Z, quatenus pars eſt eiuſdem ſinus totius A E, maximi circuli (quæ quidem ęqualis eſt ſi-
<
lb
/>
nui μ Z, complementi altitudinis Solis in Verticali, vt demõſtrauimus) ad β Z, quatenus pars eſt
<
lb
/>
ſinus totius V Y. </
s
>
<
s
xml:id
="
echoid-s8018
"
xml:space
="
preserve
">Quapropter ſi fiat, ut ſinus complementi declinationis paralleli propoſiti ad
<
lb
/>
ſinum totum, ita ſinus complementi altitudinis Solis in Verticali exiſtentis ad aliud, cognita fiet
<
lb
/>
Z β, nempe ſinus diſtantię Solis à meridie. </
s
>
<
s
xml:id
="
echoid-s8019
"
xml:space
="
preserve
">Hac arte, Sole parallelum ♋, percurrente, inuenimus
<
lb
/>
hor. </
s
>
<
s
xml:id
="
echoid-s8020
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s8021
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8022
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s8023
"
xml:space
="
preserve
">paulo amplius ante, & </
s
>
<
s
xml:id
="
echoid-s8024
"
xml:space
="
preserve
">poſt meridiem, dum in Verticali circulo exiſtit, ad latitudi-
<
lb
/>
nem grad. </
s
>
<
s
xml:id
="
echoid-s8025
"
xml:space
="
preserve
">42. </
s
>
<
s
xml:id
="
echoid-s8026
"
xml:space
="
preserve
">Ex quibus horis facile conijcies, quota hora ſit poſt mediam noctem, uel ab occa-
<
lb
/>
ſu, aut ortu Solis, cum Sol Verticalem obtinet, ſi prius tempus meridiei cognoſcatur more Italo-
<
lb
/>
rum, & </
s
>
<
s
xml:id
="
echoid-s8027
"
xml:space
="
preserve
">Babyloniorum. </
s
>
<
s
xml:id
="
echoid-s8028
"
xml:space
="
preserve
">Rurſus colliges ex hora cognita ante, uel p
<
unsure
/>
oſt meridiem quolibet die,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0149-01
"
xlink:href
="
note-0149-01a
"
xml:space
="
preserve
">Num Sol in fi-
<
lb
/>
gnis borealibus
<
lb
/>
exiſtens Verti-
<
lb
/>
calem at@@gerit,
<
lb
/>
necne, quo pa-
<
lb
/>
cto cognoſcat
<
unsure
/>
.</
note
>
<
note
position
="
left
"
xlink:label
="
note-0149-02
"
xlink:href
="
note-0149-02a
"
xml:space
="
preserve
">10</
note
>
Sole in ſignis borealibus exiſtente, an Sol attigerit Verticalem circulum, an uerò nondum ad eum
<
lb
/>
peruenerit, uel certe
<
unsure
/>
num eundem pertranſierit. </
s
>
<
s
xml:id
="
echoid-s8029
"
xml:space
="
preserve
">Quando enim antemeridiano tempore hora co-
<
lb
/>
gnita indicauerit maiorem diſtantiam à meridie, quàm inuenta eſt in Verticali circulo (ut ſi in
<
lb
/>
noſtro exemplo maiorem indicet, quàm hor. </
s
>
<
s
xml:id
="
echoid-s8030
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s8031
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8032
"
xml:space
="
preserve
">4.) </
s
>
<
s
xml:id
="
echoid-s8033
"
xml:space
="
preserve
">perſpicuum eſt, eum nondum ad Vertica-
<
lb
/>
lem motu primi mobilis perueniſſe, quando autem ęqualem diſtantiam monſtrauerit, in Verticali
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0149-03
"
xlink:href
="
note-0149-03a
"
xml:space
="
preserve
">Altitudo Soli@
<
lb
/>
ſupra Horizon-
<
lb
/>
tem ex hora co
<
lb
/>
gnita quomodo
<
lb
/>
aliter, quàm ſu-
<
lb
/>
pra, inueſtige-
<
lb
/>
tur.</
note
>
eum exiſtere, quando denique minorem ſignificauerit, eundem iam pertranſiiſſe Verticalẽ, atque
<
lb
/>
inter Verticalem, & </
s
>
<
s
xml:id
="
echoid-s8034
"
xml:space
="
preserve
">Meridianum ex parte auſtrali eſſe poſitum. </
s
>
<
s
xml:id
="
echoid-s8035
"
xml:space
="
preserve
">Contrarium intelligas tempore
<
lb
/>
pomeridiano.</
s
>
<
s
xml:id
="
echoid-s8036
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8037
"
xml:space
="
preserve
">TOTVM hoc problema expedire poſſumus hoc etiam modo. </
s
>
<
s
xml:id
="
echoid-s8038
"
xml:space
="
preserve
">Quia in eiſdem figuris om-
<
lb
/>
nibus ſuprapoſitis eſt, ut K S, ſinus verſus arcus ſemidiurni ad R S, differentiam inter ſinum
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0149-04
"
xlink:href
="
note-0149-04a
"
xml:space
="
preserve
">20</
note
>
uerſum arcus ſemidiurni, & </
s
>
<
s
xml:id
="
echoid-s8039
"
xml:space
="
preserve
">ſinum verſum diſtantię Solis à meridie, ita K N, ſinus altitudinis me
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0149-05
"
xlink:href
="
note-0149-05a
"
xml:space
="
preserve
">2. vel 4. ſexti</
note
>
ridianę ad T N, ſinum altitudinis Solis: </
s
>
<
s
xml:id
="
echoid-s8040
"
xml:space
="
preserve
">Si fiat, vt ſinus uerſus arcus ſemidiurni ad differentiam
<
lb
/>
inter ſinum uerſum ſemidiurni arcus, & </
s
>
<
s
xml:id
="
echoid-s8041
"
xml:space
="
preserve
">ſinum uerſum diſtantię Solis à meridie, ita ſinus al-
<
lb
/>
titudinis meridianę ad aliud, inuenietur finus altitudinis Solis quæſitę, atque adeò altitudo ipſa
<
lb
/>
maniſeſta erit.</
s
>
<
s
xml:id
="
echoid-s8042
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
right
"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
in æquinoctiis
<
lb
/>
quo modo ex
<
lb
/>
hora nota co-
<
lb
/>
gnoſcatur.</
note
>
<
p
>
<
s
xml:id
="
echoid-s8043
"
xml:space
="
preserve
">IN Aequatore autem, vt ex ſexta figura apparet, ſinus uerſus arcus ſemidiurni eſt ſinus totus
<
lb
/>
H E, & </
s
>
<
s
xml:id
="
echoid-s8044
"
xml:space
="
preserve
">differentia inter ipſum, & </
s
>
<
s
xml:id
="
echoid-s8045
"
xml:space
="
preserve
">ſinum uerſum diſtantię Solis à meridie eſt R E, ſinus cõplemen-
<
lb
/>
ti diſtantię Solis à meridie, & </
s
>
<
s
xml:id
="
echoid-s8046
"
xml:space
="
preserve
">ſinus altitudinis meridianę eſt ſinus complementi altitudinis po-
<
lb
/>
li. </
s
>
<
s
xml:id
="
echoid-s8047
"
xml:space
="
preserve
">Vnde ſi tunc fiat, vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſinus
<
lb
/>
complementi altitudinis poli ad aliud, habebitur ſinus altitudinis Solis tempore obſeruationis,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0149-07
"
xlink:href
="
note-0149-07a
"
xml:space
="
preserve
">30</
note
>
<
note
position
="
right
"
xlink:label
="
note-0149-08
"
xlink:href
="
note-0149-08a
"
xml:space
="
preserve
">Qua ratio ne. ex
<
lb
/>
altitudine Solis
<
lb
/>
ſupra Horizon-
<
lb
/>
tem cognita in-
<
lb
/>
ueſtige. u@ ho-
<
lb
/>
ra.</
note
>
ut & </
s
>
<
s
xml:id
="
echoid-s8048
"
xml:space
="
preserve
">ſupra demonſtratum eſt.</
s
>
<
s
xml:id
="
echoid-s8049
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8050
"
xml:space
="
preserve
">RVRSVS quia eſt, ut k N, ſinus altitud nis meridianę ad T N, ſinum altitudinis Solis,
<
lb
/>
ita K S, ſinus uerſus arcus ſemidiurni ad R S, differentiam inter ſinum uerſum arcus ſemidiur-
<
lb
/>
ni, & </
s
>
<
s
xml:id
="
echoid-s8051
"
xml:space
="
preserve
">ſinum uerſum diſtantiæ Solis à meridie: </
s
>
<
s
xml:id
="
echoid-s8052
"
xml:space
="
preserve
">Si ſiat, ut ſinus altitudinis meridianę ad ſinum
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0149-09
"
xlink:href
="
note-0149-09a
"
xml:space
="
preserve
">2. vel 4. ſexti</
note
>
altitudinis Solis tempore obſeruationis inuentę, ita ſinus uerſus arcus ſemidiurni ad aliud, re-
<
lb
/>
perietur numerus, qui ex ſinu uerſo arcus ſemidiurni ſublatus relinquit ſinum uerſum diſtan-
<
lb
/>
tiæ Solis à meridie. </
s
>
<
s
xml:id
="
echoid-s8053
"
xml:space
="
preserve
">Ex hoc autem ſinu uerſo diſtantiam Solis à meridie, atque adeò horam in-
<
lb
/>
ueniemus hac ratione. </
s
>
<
s
xml:id
="
echoid-s8054
"
xml:space
="
preserve
">Quando ſinus uerſus diſtantiæ Solis à meridie inuentus minor fuerit ſi-
<
lb
/>
nu toto, vt contingit ſemper in ſignis auſtralibus, & </
s
>
<
s
xml:id
="
echoid-s8055
"
xml:space
="
preserve
">in ſignis etiam borealibus, cum diſtantia So-
<
lb
/>
lis à meridie minor eſt quadrante, auferemus @um ex ſinu toto, & </
s
>
<
s
xml:id
="
echoid-s8056
"
xml:space
="
preserve
">reſidui ſinus recti arcum ex
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0149-10
"
xlink:href
="
note-0149-10a
"
xml:space
="
preserve
">40</
note
>
quadrante auferemus, remanebitq́ue diſtantia Solis à meridie. </
s
>
<
s
xml:id
="
echoid-s8057
"
xml:space
="
preserve
">Si autem dictus ſinus verſus
<
lb
/>
ęqualis fuerit ſinui toti, quod bis duntaxat in quolibet arcu diurno parallelorum borealium eue-
<
lb
/>
nire poteſt, erit diſtantia Solis à meridie quadrans complectens ſex horas. </
s
>
<
s
xml:id
="
echoid-s8058
"
xml:space
="
preserve
">Si denique ſinus ver-
<
lb
/>
ſus inuentus extiterit maior ſinu toto, auferemus ex eo ſinum totum, & </
s
>
<
s
xml:id
="
echoid-s8059
"
xml:space
="
preserve
">reſidui ſinus recti arcum
<
lb
/>
ad quadrantem adijciemus, conficiemusq́; </
s
>
<
s
xml:id
="
echoid-s8060
"
xml:space
="
preserve
">diſtantiam Solis à meridie.</
s
>
<
s
xml:id
="
echoid-s8061
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
right
"
xml:space
="
preserve
">Quota hora ſi@,
<
lb
/>
quo modo in
<
lb
/>
æquinoctiis ex
<
lb
/>
data altitudine
<
lb
/>
Solis cognoſce@.
<
lb
/>
dum.</
note
>
<
p
>
<
s
xml:id
="
echoid-s8062
"
xml:space
="
preserve
">SOLE in æquinoctiis exiſtente, vt ex ſexta figura eſt manifeſtum, ſinus altitudinis meri-
<
lb
/>
dianæ eſt ſinus complementi altitudinis poli, & </
s
>
<
s
xml:id
="
echoid-s8063
"
xml:space
="
preserve
">ſinus uerſus arcus ſemidiurni eſt ſinus totus
<
lb
/>
H E, & </
s
>
<
s
xml:id
="
echoid-s8064
"
xml:space
="
preserve
">differentia inter ſinum uerſum arcus ſemidiurni, & </
s
>
<
s
xml:id
="
echoid-s8065
"
xml:space
="
preserve
">ſinum verſum diſtantiæ Solis à me-
<
lb
/>
ridie, eſt ſinus complementi diſtantiæ Solis à meridie. </
s
>
<
s
xml:id
="
echoid-s8066
"
xml:space
="
preserve
">Quamobrem, ſi tunc ſiat, vt ſinus com-
<
lb
/>
plementi altitudinis poli ad ſinum altitudinis Solis tempore obſeruationis, ita ſinus totus ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0149-12
"
xlink:href
="
note-0149-12a
"
xml:space
="
preserve
">50</
note
>
aliud, habebitur ſinus complementi diſtantiæ Solis à meridie. </
s
>
<
s
xml:id
="
echoid-s8067
"
xml:space
="
preserve
">Id quod ſupra quoque demon-
<
lb
/>
ſtratum eſt.</
s
>
<
s
xml:id
="
echoid-s8068
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8069
"
xml:space
="
preserve
">EXEMPLVM. </
s
>
<
s
xml:id
="
echoid-s8070
"
xml:space
="
preserve
">Ponamus Solem in parallelo ♐, uel ♒, habere poſt meridiem altitudinẽ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0149-13
"
xlink:href
="
note-0149-13a
"
xml:space
="
preserve
">Exemplum.</
note
>
ſupra Horizontem grad. </
s
>
<
s
xml:id
="
echoid-s8071
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s8072
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8073
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s8074
"
xml:space
="
preserve
">Fiat ut 46638. </
s
>
<
s
xml:id
="
echoid-s8075
"
xml:space
="
preserve
">ſinus altitudinis meridianę ad 11753. </
s
>
<
s
xml:id
="
echoid-s8076
"
xml:space
="
preserve
">ſinum
<
lb
/>
altitudinis Solis inuentę
<
unsure
/>
, ita 66867. </
s
>
<
s
xml:id
="
echoid-s8077
"
xml:space
="
preserve
">ſinus uerſus arcus ſemidiurni ad aliud, prodibitq́; </
s
>
<
s
xml:id
="
echoid-s8078
"
xml:space
="
preserve
">hic fermè
<
lb
/>
numerus 16851. </
s
>
<
s
xml:id
="
echoid-s8079
"
xml:space
="
preserve
">qui ex 66867. </
s
>
<
s
xml:id
="
echoid-s8080
"
xml:space
="
preserve
">ſinu uerfo arcus ſemidiurni ſubtractus relinquet 50016. </
s
>
<
s
xml:id
="
echoid-s8081
"
xml:space
="
preserve
">ſinum
<
lb
/>
uerſum diſtantię Solis à meridie. </
s
>
<
s
xml:id
="
echoid-s8082
"
xml:space
="
preserve
">Hunc ergo quia minor eſt ſinu toto, ex 100000. </
s
>
<
s
xml:id
="
echoid-s8083
"
xml:space
="
preserve
">ſinu toto ſubdu-
<
lb
/>
cemus, & </
s
>
<
s
xml:id
="
echoid-s8084
"
xml:space
="
preserve
">reſidui ſinus recti 49984. </
s
>
<
s
xml:id
="
echoid-s8085
"
xml:space
="
preserve
">arcũ grad. </
s
>
<
s
xml:id
="
echoid-s8086
"
xml:space
="
preserve
">29. </
s
>
<
s
xml:id
="
echoid-s8087
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8088
"
xml:space
="
preserve
">59. </
s
>
<
s
xml:id
="
echoid-s8089
"
xml:space
="
preserve
">ex quadrante dememus, habebimusq́;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8090
"
xml:space
="
preserve
">diſtantiam Solis à meridie grad. </
s
>
<
s
xml:id
="
echoid-s8091
"
xml:space
="
preserve
">60. </
s
>
<
s
xml:id
="
echoid-s8092
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8093
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s8094
"
xml:space
="
preserve
">hoc eſt, hor. </
s
>
<
s
xml:id
="
echoid-s8095
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s8096
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8097
"
xml:space
="
preserve
">o, poſt meridiẽ, quia obſeruatio
<
lb
/>
ponitur facta poſt meridiem. </
s
>
<
s
xml:id
="
echoid-s8098
"
xml:space
="
preserve
">Ante meridiem eſſet hora 8. </
s
>
<
s
xml:id
="
echoid-s8099
"
xml:space
="
preserve
">poſt med. </
s
>
<
s
xml:id
="
echoid-s8100
"
xml:space
="
preserve
">noct. </
s
>
<
s
xml:id
="
echoid-s8101
"
xml:space
="
preserve
">Cognita autem hora
<
lb
/>
meridiei more Italorũ, & </
s
>
<
s
xml:id
="
echoid-s8102
"
xml:space
="
preserve
">Babyloniorum ex quantitate diei, facile comperiemus, quęnam hora </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>