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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GNOMONICES
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per propoſ. </
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<
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<
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<
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xml:space
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">eiuſdem plani inclinatione ad Horizontem, inueniatur ex propoſ. </
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<
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<
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ius lib. </
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<
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xml:space
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">minor diameter Ellipſis, quam perpendiculares à circunferentia plani inclinati (quod in
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0114-01
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ſphæra circulũ facit, ex propoſ. </
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<
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<
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<
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<
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</
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<
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<
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<
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huius lib. </
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<
s
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xml:space
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">faciunt, quæ ſit HI, maiorem diame-
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trum F G, ſecans in centro E, ad angulos rectos. </
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<
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lam ex coroll. </
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<
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<
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<
s
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xml:space
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metros F G, H I, datas deſcribatur Ellipſis, vel
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certè eius pars, ſecans A C, communem ſectio-
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nem Horizontis, ac Meridiani in K, puncto, per
<
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<
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quod ipſi A C, perpendicularis ducatur K L, ſe-
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cãs Horizontis circunferentiã in L. </
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<
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C L, æqualẽ eſſe arcui Meridiani circuli inter
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Horizontem, & </
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<
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</
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<
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ad Horizontẽ A B C D, rectus; </
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<
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xml:space
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in quo planum inclinatum ſecat Meridianum,
<
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ita vt arcus C M, ſit inter Horizontem, & </
s
>
<
s
xml:id
="
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xml:space
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num ipſum. </
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<
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xml:space
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">Ducantur quoque rectæ E L,
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E M, C L, C M. </
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<
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A C, communem ſectionem Horizontis, ac Meridiani, quòd Meridianus ad Horizontem rectus
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ſit; </
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<
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<
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<
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<
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xml:space
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">& </
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<
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xml:space
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">in Ellipſim, quam perpendiculares à punctis circunfe
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rentiæ plani inclinati, quorum vnum eſt M, in planum Horizontis cadentes efficiunt; </
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<
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eſt, perpendicularem ex M, cadere in punctum K, vbi Ellipſis rectam A C, ſecat. </
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<
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<
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ſit M K, eritq́ue propterea tam angulus E K M, quàm C K M, rectus, per definitionem 3. </
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<
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</
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<
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<
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">Quare tam quadratum ex E L, quadratis ex E K, K L, quàm quadratum ex E M, quadra
<
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<
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tis ex E K, K M, æquale erit: </
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tur enim ex centro ſphæræ ad eius ſuperficiem.) </
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<
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<
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<
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dratis ex E K, K M, æqualia; </
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<
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xml:space
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">Et dempto quadrato ex E K, cõmuni, æquale erit quadratum ex K L,
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quadrato ex K M, atq; </
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<
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<
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<
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C K M, latera K L, K C, lateribus K M, K C, ſint ęqualia, angulosq́ue contineant ęquales, vtpo-
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<
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te rectos; </
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<
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">ęqualis erit baſis C L, baſi C M, ac idcirco & </
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<
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">arcus C L, arcui C M, Meridiani inter Ho
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<
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rizontem, & </
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<
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<
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</
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<
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<
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<
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<
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<
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<
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">Arcus Metidia
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ni inter Hori-
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zontẽ & planũ
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inclinatum po-
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ſitus, quomodo
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inquiratur per
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ſinus.</
note
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Meridianum inclinatum E F, ſecans Meridianum in G, ſiue infra Horizontem, ſiue ſupra, vt C G,
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</
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arcus ſit inter Horizontem, & </
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num inclinatum interpoſitus. </
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<
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niam igitur in ſphęrico triangulo
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C F G, cuius angulus C, rectus eſt,
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quòd Meridianus rectus ſit ad Ho-
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<
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rizontem; </
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<
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xml:space
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pe cõplementi declinationis D F,
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à Verticali circulo, ad ſinum angu-
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li G, inclinationis plani E F, ad Me
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ridianum, ita eſt, per propoſ. </
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<
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</
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<
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per propoſ. </
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<
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<
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<
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<
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tè ex propoſ. </
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<
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gulorum ſphęricorum, ſinus arcus
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C G, inter Horizontem, & </
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<
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<
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inclinatum, ad ſinũ anguli F, inclinationis plani ad Horizontẽ; </
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<
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xml:space
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<
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anguli G, inclinationis ad Meridianũ, ad ſinum arcus C F, complementi declinationis à Verticali,
<
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ita ſinus anguli F, inclinationis ad Horizontẽ, ad ſinum arcus Meridiani C G, inter Horizontem,
<
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& </
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>
<
s
xml:id
="
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<
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<
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<
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ni propoſiti à circulo Verticali, atque inclinatione eiuſdem ad Horizontem. </
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>
<
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="
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xml:space
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">Item inclinatione
<
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eiuſdem ad Meridianum, ex propoſ. </
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>
<
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">antecedente; </
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>
<
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xml:space
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">ſi fiat, vt ſinus inclinationis ad Meridianum ad
<
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ſinum cõplementi declinationis à Verticali, ita ſinus inclinationis ad Horizontem, ad aliud, habe-
<
lb
/>
bitur ſinus illius arcus Meridiani, qui inter Horizontem, & </
s
>
<
s
xml:id
="
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xml:space
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">planum inclinatum interiicitur.</
s
>
<
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</
p
>
<
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>
<
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<
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<
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<
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<
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<
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xml:space
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li grad. </
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<
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echoid-s5353
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5354
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5355
"
xml:space
="
preserve
">inclinatio ad Horizontem grad. </
s
>
<
s
xml:id
="
echoid-s5356
"
xml:space
="
preserve
">52. </
s
>
<
s
xml:id
="
echoid-s5357
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5358
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s5359
"
xml:space
="
preserve
">Si igitur fiat, vt 91902. </
s
>
<
s
xml:id
="
echoid-s5360
"
xml:space
="
preserve
">ſinus inclinatio-
<
lb
/>
nis ad Meridianum ad 86602. </
s
>
<
s
xml:id
="
echoid-s5361
"
xml:space
="
preserve
">ſinum complementi declinationis à Verticali, ita 78854. </
s
>
<
s
xml:id
="
echoid-s5362
"
xml:space
="
preserve
">ſinus </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>