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.
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uentus k T, maior fuerit ſinu toto, vt contingit in prioribus duabus figuris, detrahemus ex eo ſi-
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xlink:label
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xlink:href
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xml:space
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">Quando. finus
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ve ſus inuen@us
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fuent maior ſi-
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nu toto, quom o
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do per eum in-
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veniatur @epu-
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@@ulum.</
note
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num totum K M, & </
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<
s
xml:id
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xml:space
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">reliqui ſinus T M, arcum P R, accipiemus. </
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<
s
xml:id
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xml:space
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">Hic enim arcus P R, additus
<
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quadranti k P, conficiet arcum k R, compoſitum ex arcu ſemidiurno, & </
s
>
<
s
xml:id
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echoid-s7197
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xml:space
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">arcu crepuſculi. </
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>
<
s
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xml:space
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">Quare
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fig-0139-01
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<
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0139-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0139-01
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<
note
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xlink:href
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xml:space
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">10</
note
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<
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note-0139-03
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note-0139-03a
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xml:space
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">20</
note
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<
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note-0139-04
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xml:space
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">30</
note
>
<
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xlink:label
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note-0139-05
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xlink:href
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note-0139-05a
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xml:space
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preserve
">Quando ſinus
<
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/>
uer us inuen tus
<
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/>
fuerit mi
<
unsure
/>
nor ſi-
<
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/>
nu to@o, qua ta-
<
lb
/>
@one ex eo cre-
<
lb
/>
puſculum elicia
<
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/>
@ur.</
note
>
ablato arcu ſemidiurno k Q, reliquus erit arcus crepuſculi Q R. </
s
>
<
s
xml:id
="
echoid-s7199
"
xml:space
="
preserve
">Si verò dictus ſinus verſus K T,
<
lb
/>
fuerit minor ſinu toto, vt in tertia figura accidit, auferemus eum ex ſinu toto K M, & </
s
>
<
s
xml:id
="
echoid-s7200
"
xml:space
="
preserve
">reliqui ſinus
<
lb
/>
T M, arcum P R, accipiemus. </
s
>
<
s
xml:id
="
echoid-s7201
"
xml:space
="
preserve
">Hic enim arcus P R, ex quadrante K P, ablatus reliquum faciet ar-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0139-06
"
xlink:href
="
note-0139-06a
"
xml:space
="
preserve
">Quando ſinus
<
lb
/>
uerſus inuẽrus
<
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/>
fuerit æqualis
<
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/>
ſinui toti, quo
<
lb
/>
pacto ex eo in
<
lb
/>
cognitionẽ
<
unsure
/>
cre-
<
lb
/>
puſculi uen@a-
<
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/>
mus.</
note
>
cum k R, ex arcu ſemidiurno, & </
s
>
<
s
xml:id
="
echoid-s7202
"
xml:space
="
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">arcu crepuſculi compoſitum. </
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>
<
s
xml:id
="
echoid-s7203
"
xml:space
="
preserve
">Si igitur ex hoc rurſum detraha-
<
lb
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mus arcum ſemidiurnum K Q, remanebit arcus crepuſculi Q R. </
s
>
<
s
xml:id
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xml:space
="
preserve
">Si denique ſinus verſus prædi-
<
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ctus k T, inuentus æqualis fuerit ſinui toti, vt in quarta figura euenit, erit ipſemet quadrans k P,
<
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/>
<
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position
="
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xlink:label
="
note-0139-07
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xlink:href
="
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xml:space
="
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">40</
note
>
arcus ex arcu ſemidiurno, & </
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>
<
s
xml:id
="
echoid-s7205
"
xml:space
="
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">arcu crepuſculi compoſitus. </
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>
<
s
xml:id
="
echoid-s7206
"
xml:space
="
preserve
">Ab hoc ergo quadrante ſi ſubtrahamus
<
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/>
arcum ſemidiutnum K Q, reliquus erit arcus crepuſculi Q R, vel Q P.</
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
="
preserve
">Crepuſculum
<
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/>
quo modo ali-
<
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/>
ter explorandũ
<
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/>
ſit.</
note
>
<
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>
<
s
xml:id
="
echoid-s7208
"
xml:space
="
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">IDEM obtinebimus quoque hac ratione. </
s
>
<
s
xml:id
="
echoid-s7209
"
xml:space
="
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">Quoniam in eiſdem figuris eſt, vt K N, ſinus alti-
<
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/>
tudinis meridianæ ad N O, ſinum occultationis Solis ſub Horizonte in principio crepuſculi ma-
<
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/>
tutini, vel fine veſpertini, quam occultationem ponimus grad. </
s
>
<
s
xml:id
="
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xml:space
="
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">18. </
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>
<
s
xml:id
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xml:space
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">ita K S, ſinus verſus arcus ſemi-
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<
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xlink:label
="
note-0139-09
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xlink:href
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xml:space
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">2. ſexti.</
note
>
diurni ad S T; </
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>
<
s
xml:id
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xml:space
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">Si fiat, ut ſinus altitudinis meridianæ ad ſinum grad. </
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>
<
s
xml:id
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echoid-s7213
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xml:space
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">18. </
s
>
<
s
xml:id
="
echoid-s7214
"
xml:space
="
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">ita ſinus verſus arcus ſemi
<
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/>
diurni ad aliud, inuenietur numerus rectę S T, qui additus ſinui verſo arcus ſemidiurni conficit
<
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/>
ſinum uerſum arcus compoſiti ex arcu ſemidiurno, & </
s
>
<
s
xml:id
="
echoid-s7215
"
xml:space
="
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">arcu crepuſculi. </
s
>
<
s
xml:id
="
echoid-s7216
"
xml:space
="
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">Ex quo ſinu verſo inuenie-
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niemus, vt prius, crepuſculi longitudinem. </
s
>
<
s
xml:id
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echoid-s7217
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xml:space
="
preserve
">Exemplum nullum ponimus, quia ex figuris ipſis res
<
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manifeſta per ſe exiſtit.</
s
>
<
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</
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<
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">50</
note
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<
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xml:space
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">Crepuſculum
<
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qua tatione in
<
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/>
æquinoctus in-
<
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ueſtigetur.</
note
>
<
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>
<
s
xml:id
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xml:space
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">SOLE æquinoctialia puncta, ideſt, principium ♈, uel ♎, poſſidente, multo facilius crepu-
<
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ſculorum magnitudines inuenientur hac ratione. </
s
>
<
s
xml:id
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echoid-s7220
"
xml:space
="
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">Ducta in prima figura ex H, ad A C, & </
s
>
<
s
xml:id
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echoid-s7221
"
xml:space
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">X Y,
<
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perpendiculari H α β, erit ut H α, ſinus altitudinis Aequatoris, ſiue complementi altitudinis po-
<
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<
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xlink:label
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xlink:href
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xml:space
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">2. ſexti.</
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li, ad α β, ſinum grad. </
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<
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">18. </
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<
s
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xml:space
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">(quot nimirum graduum poſuimus arcum A X) ita H E, ſinus totus
<
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ad E γ, ſinum rectum arcus crepuſculi δ G. </
s
>
<
s
xml:id
="
echoid-s7224
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xml:space
="
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">Si igitur fiat, ut ſinus complementi altitudinis poli
<
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ad ſinum grad. </
s
>
<
s
xml:id
="
echoid-s7225
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xml:space
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">18. </
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>
<
s
xml:id
="
echoid-s7226
"
xml:space
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">ita ſinus totus ad aliud, proueniet ſinus, cuius arcus dabit crepuſculum, Sole
<
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in ęquinoctijs exiſtente.</
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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xml:space
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">Crepuſcula om
<
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nia, qua ratione
<
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/>
facilime ſuppu-
<
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te@tur.</
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>
<
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<
s
xml:id
="
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xml:space
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">CAETERVM inuenta hac ratione, quam proxime expoſuimus, quantitate rectæ E γ, inue-
<
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niemus per eam crepuſcula omnium parallelorum, ſiue punctorum Eclipticæ, hoc modo. </
s
>
<
s
xml:id
="
echoid-s7229
"
xml:space
="
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">Quo-
<
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niam E γ, æqualis eſt ſingulis ſegmentis S T, diametrorum parallelorum in@er A C, X Y, interce-
<
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/>
<
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xlink:label
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xlink:href
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xml:space
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">34. primi.</
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ptis, cognita erunt huiuſmodi ſegmenta in partibus ſinus totius maximi circuli in ſphæra. </
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