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 SECVNDVS.
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aut minus diſtantem à puncto H, intercepta.</
s
>
<
s
xml:id
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"
xml:space
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"/>
</
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>
<
p
style
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<
s
xml:id
="
echoid-s10799
"
xml:space
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preserve
">STYLVS ſiue gnomon ex poſteriori modo deſcribendi parallelos ſignorum, hoc eſt, ex figuraradio-
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0187-01
"
xlink:href
="
note-0187-01a
"
xml:space
="
preserve
">Quã ratione ex
<
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/>
figura radiorũ
<
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longitudo ſtyli,
<
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eiusq́; locus in
<
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horologio explo
<
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retur.</
note
>
rum, habetur, ſi e x puncto D, vbi radius Aequatoris axem A λ, ſecat, ad H I, perpendicularis ducatur,
<
lb
/>
D ρ, vel certè recta D ρ, faciens angulum ρ D I, æqualem angulo altitudinis poli. </
s
>
<
s
xml:id
="
echoid-s10800
"
xml:space
="
preserve
">Longitudo enim ſtyli
<
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/>
est ipſarecta D ρ: </
s
>
<
s
xml:id
="
echoid-s10801
"
xml:space
="
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">Locus verò eius eſt punctum ρ, diſtans ab H, centro horologij interuallo H ρ, in linea
<
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/>
meridiana, vel ab æquinoctiali linea F K, ſpatio I ρ, in eadem linea meridiana verſus centrum H.</
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>
<
s
xml:id
="
echoid-s10802
"
xml:space
="
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"/>
</
p
>
<
p
style
="
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">
<
s
xml:id
="
echoid-s10803
"
xml:space
="
preserve
">QVOD ſi magnitudo gnomonis data ſit, inueniemus hac ratione diſtantiam figuræ radiorum Zodia-
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0187-02
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xlink:href
="
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xml:space
="
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">Quomodo cx
<
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data ſtyli longi
<
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tudine inuenia
<
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tur diſtantia ra
<
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/>
diorum Zodia-
<
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/>
ci à puncto H,
<
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in figura radio-
<
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rum.</
note
>
ci à puncto H, in axe H D. </
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>
<
s
xml:id
="
echoid-s10804
"
xml:space
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preserve
">Nam horariæ lineæ ex H, procedentes eædem omnino manent, vt diximus, in
<
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/>
eadem altitudine poli. </
s
>
<
s
xml:id
="
echoid-s10805
"
xml:space
="
preserve
">In portione Analemmatis, quam propoſ. </
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>
<
s
xml:id
="
echoid-s10806
"
xml:space
="
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">1. </
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>
<
s
xml:id
="
echoid-s10807
"
xml:space
="
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">huius lib. </
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>
<
s
xml:id
="
echoid-s10808
"
xml:space
="
preserve
">deſcripſimus, abſcindatur ex
<
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A D, diametro Verticalis circuli protracta, recta D M, æqualis gnomoni dato, & </
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>
<
s
xml:id
="
echoid-s10809
"
xml:space
="
preserve
">per M, ipſi B C, diame
<
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<
note
position
="
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xlink:label
="
note-0187-03
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xlink:href
="
note-0187-03a
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xml:space
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">10</
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>
tro Horizontis parallela agatur N O, ſecans axem E D, in N, & </
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>
<
s
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="
echoid-s10810
"
xml:space
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">Aequatoris diametrũ F D, in O; </
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>
<
s
xml:id
="
echoid-s10811
"
xml:space
="
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">Pun
<
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ctum ergo D, in figura radiorum Zodiaci huius propoſ. </
s
>
<
s
xml:id
="
echoid-s10812
"
xml:space
="
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">in quo conueniunt omnes radij Zodiaci, diſtare de-
<
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bet ab H, interuallo D N, cuiuſmodi eſt punctum D, prope A, in dicta figura radiorum Zodiaci huius pro-
<
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/>
poſ. </
s
>
<
s
xml:id
="
echoid-s10813
"
xml:space
="
preserve
">Si enim ex illo puncto D, demittatur perpendicularis ad H D, pro radio Aequatoris, & </
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>
<
s
xml:id
="
echoid-s10814
"
xml:space
="
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">ſimul ex D,
<
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aliorum ſignorum radij emittantur, vt in Analemmate propoſ. </
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>
<
s
xml:id
="
echoid-s10815
"
xml:space
="
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">1. </
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>
<
s
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="
echoid-s10816
"
xml:space
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">ſuperioris lib. </
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>
<
s
xml:id
="
echoid-s10817
"
xml:space
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">deſcribemus beneficio li-
<
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nearum horariarum inter hoſce radios, & </
s
>
<
s
xml:id
="
echoid-s10818
"
xml:space
="
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">punctum H, comprehenſarum parallelos ſignorum, vt prius;
<
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/>
</
s
>
<
s
xml:id
="
echoid-s10819
"
xml:space
="
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">quos percurret extremitas vmbræ à gnomone dato D M, proiectæ, vt ex demonſtratis conſtat. </
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>
<
s
xml:id
="
echoid-s10820
"
xml:space
="
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">Nam ſi ex
<
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/>
dicto puncto D, demittatur ad H I B, perpendicularis D K, erit hæc æqualis gnomoni dato D M. </
s
>
<
s
xml:id
="
echoid-s10821
"
xml:space
="
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">Cum
<
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/>
enim angulus D H K, in triangulo D H K, figuræ radiorum Zodiaci huius propoſ. </
s
>
<
s
xml:id
="
echoid-s10822
"
xml:space
="
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">æqualis ſit angulo
<
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D N M, in triangulo D N M, portionis Analemmatis propoſ. </
s
>
<
s
xml:id
="
echoid-s10823
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s10824
"
xml:space
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">huius lib. </
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>
<
s
xml:id
="
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"
xml:space
="
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">(Vterque enim eſt angulus
<
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<
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">20</
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>
altitudinis poli) & </
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>
<
s
xml:id
="
echoid-s10826
"
xml:space
="
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">recti anguli ad K, & </
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>
<
s
xml:id
="
echoid-s10827
"
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="
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">M, æquales ſint; </
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>
<
s
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="
echoid-s10828
"
xml:space
="
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">ſit autem & </
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>
<
s
xml:id
="
echoid-s10829
"
xml:space
="
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">latus H D, lateri D N, æquale,
<
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ex constructione; </
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>
<
s
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="
echoid-s10830
"
xml:space
="
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">erunt & </
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>
<
s
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="
echoid-s10831
"
xml:space
="
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">reliqua latera, nempe D K, D M, inter ſe, & </
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>
<
s
xml:id
="
echoid-s10832
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xml:space
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">H K, N M, inter ſe æqualia.
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</
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>
<
s
xml:id
="
echoid-s10833
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xml:space
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<
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xlink:label
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xml:space
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">26. primi.</
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>
Quod est propoſitum. </
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>
<
s
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xml:space
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">Mutatis autem arcubus ſignorum, mutatur quoque ęquinoctialis linea, quæ tanto
<
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<
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="
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xlink:label
="
note-0187-06
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xlink:href
="
note-0187-06a
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xml:space
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">Deſcriptio pa-
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rallelorum, qui
<
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non per ſigno -
<
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rum initia, ſed
<
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per alia puncta
<
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Zodiaci tran-
<
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ſeunt, in eodem
<
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horologio.</
note
>
ſpatio in linea meridiana abeſt ſemper à centro H, quanta est portio rectæ H B, in figura radiorum huius
<
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propoſ. </
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>
<
s
xml:id
="
echoid-s10835
"
xml:space
="
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">inter H, & </
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>
<
s
xml:id
="
echoid-s10836
"
xml:space
="
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">radium Aequatoris inter cepta, vt & </
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>
<
s
xml:id
="
echoid-s10837
"
xml:space
="
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">paulo ante diximus.</
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>
<
s
xml:id
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echoid-s10838
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xml:space
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</
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>
<
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<
s
xml:id
="
echoid-s10839
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xml:space
="
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">IAM verò ſi accipiamus declinationes aliorum punctorum Zodiaci, eorum{q́ue} parallelos in prima fi-
<
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gura huius propoſ. </
s
>
<
s
xml:id
="
echoid-s10840
"
xml:space
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">vel eorum radios ex D, in tertia figura ducamus, deſcribemus eodem modo eorum pa-
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rallelos in prædicto horologio.</
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>
<
s
xml:id
="
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xml:space
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</
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>
<
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<
s
xml:id
="
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xml:space
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">IMMO propoſito die primo cuiuſque menſis, vel alio quouis, ſi quæratur locus Solis illo die in Zo-
<
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<
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xlink:label
="
note-0187-07
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xlink:href
="
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xml:space
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">Deſcriptio pa-
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ralleli, in quo
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Sol exiſtit quo-
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libet die propo
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ſito, in eodẽ ho
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rologio.</
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>
diaco, & </
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>
<
s
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xml:space
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">declinatio, at que in prima figura huius propoſ. </
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>
<
s
xml:id
="
echoid-s10844
"
xml:space
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">eius parallelus, vel in figura radiorum eius ra-
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<
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position
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="
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xml:space
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">30</
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dius ex D, ducatur, deſcribetur eadem ratione in horologio linea quædam flexa, quam vmbræ extremitas
<
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percurret die illo propoſito.</
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>
<
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</
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>
<
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style
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<
s
xml:id
="
echoid-s10846
"
xml:space
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">HAC ratione deſcribi poſſunt in horologio dies feſti ſanctorum, hoc eſt, lineæ quædam inflexę, quas
<
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/>
<
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position
="
right
"
xlink:label
="
note-0187-09
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xlink:href
="
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xml:space
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">Deſcriptio die-
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rum feſtorũ in
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eodem horolo-
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gio.</
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>
vmbra ſtyli percurrit illis diebus.</
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>
<
s
xml:id
="
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xml:space
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</
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>
<
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<
s
xml:id
="
echoid-s10848
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xml:space
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">HIS autem omnibus parallelis ſignorum aſcribi poſſunt characteres ſignorum, dies menſium, qui-
<
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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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">Quid aſcriben-
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du ſit arcubus
<
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ſignorum in ho
<
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rologĩo delinea
<
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tis.</
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>
bus vmbrę extremitas illos percurrit; </
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>
<
s
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="
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"
xml:space
="
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">tempus ortus Solis & </
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>
<
s
xml:id
="
echoid-s10850
"
xml:space
="
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">occaſus, dierum & </
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>
<
s
xml:id
="
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xml:space
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">crepuſculorum magni-
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tudines, & </
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>
<
s
xml:id
="
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"
xml:space
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">alia huiuſmodi, cuiuſmodi eſſet in horologio Italico, & </
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>
<
s
xml:id
="
echoid-s10853
"
xml:space
="
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">Babylonico, de quibus propoſ. </
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>
<
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="
echoid-s10854
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">10. </
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<
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xml:space
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">& </
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<
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<
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11. </
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>
<
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="
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"
xml:space
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">huius lib. </
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>
<
s
xml:id
="
echoid-s10858
"
xml:space
="
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">agetur, tempus meridiei, & </
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>
<
s
xml:id
="
echoid-s10859
"
xml:space
="
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">c.</
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>
<
s
xml:id
="
echoid-s10860
"
xml:space
="
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"/>
</
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>
<
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style
="
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<
s
xml:id
="
echoid-s10861
"
xml:space
="
preserve
">IN huius verò rei gratiam ducendæ ſunt quædam lineæ parallelæ ipſi lineę meridianæ tam ad ſini-
<
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ſtram, quàm ad dexteram, vt in ſecunda figur a huius propoſ. </
s
>
<
s
xml:id
="
echoid-s10862
"
xml:space
="
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">apparet. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Hę autem parallelę, quo remo-
<
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<
note
position
="
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"
xlink:label
="
note-0187-11
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xlink:href
="
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xml:space
="
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">40</
note
>
tiores erunt à meridiana linea, eo maiori temporis ſpatio vmbra gnomonis in horologio excipietur.</
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>
<
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xml:id
="
echoid-s10864
"
xml:space
="
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"/>
</
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>
<
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style
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<
s
xml:id
="
echoid-s10865
"
xml:space
="
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">RVRSVS quoniam Sol à ♑, per ♈, aſcendit vſque ad ♋; </
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>
<
s
xml:id
="
echoid-s10866
"
xml:space
="
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">à ♋, verò per ♎, vſque ad ♑, deſcen-
<
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dit, aſcribenda erunt ad priora ſigna, hæc verba. </
s
>
<
s
xml:id
="
echoid-s10867
"
xml:space
="
preserve
">A S C E N S V S S O L I S; </
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>
<
s
xml:id
="
echoid-s10868
"
xml:space
="
preserve
">ad poſteriora verò hæc.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s10869
"
xml:space
="
preserve
">D E S C E N S V S S O L I S. </
s
>
<
s
xml:id
="
echoid-s10870
"
xml:space
="
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">Exemplum habes in horologio ſuperiori. </
s
>
<
s
xml:id
="
echoid-s10871
"
xml:space
="
preserve
">Quod etiam intelligendum
<
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/>
eſt in alijs horologijs, vt in Verticali, Meridiano Aequinoctiali, & </
s
>
<
s
xml:id
="
echoid-s10872
"
xml:space
="
preserve
">c.</
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>
<
s
xml:id
="
echoid-s10873
"
xml:space
="
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"/>
</
p
>
<
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style
="
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">
<
s
xml:id
="
echoid-s10874
"
xml:space
="
preserve
">POSTREMO eoſdem parallelos, arcusve ſignorum in horologio, quod in ſcholio pręcedentis pro-
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0187-12
"
xlink:href
="
note-0187-12a
"
xml:space
="
preserve
">Qua atte arcus
<
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/>
ſignorum in ho
<
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/>
rologio, quod
<
lb
/>
centrum non
<
lb
/>
habear, deſcribẽ
<
lb
/>
di ſiut.</
note
>
poſ. </
s
>
<
s
xml:id
="
echoid-s10875
"
xml:space
="
preserve
">etiamſi cent rum eius non haberemus, eiſdem ferè rationibus, quibus in hac propoſ. </
s
>
<
s
xml:id
="
echoid-s10876
"
xml:space
="
preserve
">vſi ſumus, deſcribe
<
lb
/>
mus. </
s
>
<
s
xml:id
="
echoid-s10877
"
xml:space
="
preserve
">Nam quòd ad priorem rationem attinet, ſi deſcribatur Analemma pro data altitudine poli, vt in
<
lb
/>
propoſito exemplo ad latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s10878
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s10879
"
xml:space
="
preserve
">cum parallelis ſignorum, eorundem radijs, vt in conis ha-
<
lb
/>
beantur triangula per axem, at que adeò in recta R O, (quæ Horizonti B C, æquidiſtare debet ſecundum
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0187-13
"
xlink:href
="
note-0187-13a
"
xml:space
="
preserve
">50</
note
>
diſtantiam rectæ D G, ſtylo F M, ęqualis) diametri ſectionum conicarum; </
s
>
<
s
xml:id
="
echoid-s10880
"
xml:space
="
preserve
">at que puncta K, L, M. </
s
>
<
s
xml:id
="
echoid-s10881
"
xml:space
="
preserve
">Q, P,
<
lb
/>
N, ex puncto I, (vbi Aequatoris diameter rectam. </
s
>
<
s
xml:id
="
echoid-s10882
"
xml:space
="
preserve
">R O, diuidit) accepta transferantur in lineam meri-
<
lb
/>
dianam A B, ex puncto E, vbi æquinoctialis linea, ac meridiana ſe interſecant; </
s
>
<
s
xml:id
="
echoid-s10883
"
xml:space
="
preserve
">postremo verò circa dia-
<
lb
/>
metros ſectionum conicarum deſcribantur ſectiones conicæ, ſecundum doctrinam propoſ. </
s
>
<
s
xml:id
="
echoid-s10884
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s10885
"
xml:space
="
preserve
">ſuperioris lib.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10886
"
xml:space
="
preserve
">it a vt per illa puncta K, L, M, & </
s
>
<
s
xml:id
="
echoid-s10887
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s10888
"
xml:space
="
preserve
">in horologio tranſeant, deſcripti erunt paralleli ſignorum.</
s
>
<
s
xml:id
="
echoid-s10889
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s10890
"
xml:space
="
preserve
">QVOD verò attinet ad posteriorem rationem ex figura radiorum Zodiaci depromptam, it a rem
<
lb
/>
perficiemus. </
s
>
<
s
xml:id
="
echoid-s10891
"
xml:space
="
preserve
">Inradium Aequatoris D C, transferantur omnia interualla inter centrum B, (ex quo cir-
<
lb
/>
culus deſcriptus fuit, at que in partes 24. </
s
>
<
s
xml:id
="
echoid-s10892
"
xml:space
="
preserve
">æquales diuiſus) & </
s
>
<
s
xml:id
="
echoid-s10893
"
xml:space
="
preserve
">horas in ęquinoctiali linea C D, interiecta, à
<
lb
/>
puncto D, imprimendo puncta in ipſo radio Aequatoris. </
s
>
<
s
xml:id
="
echoid-s10894
"
xml:space
="
preserve
">Deinde in axe D G, abſcindatur recta D G,
<
lb
/>
æqualis portioni axis F G, in horologio, ad finem ſcholij ant ecedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s10895
"
xml:space
="
preserve
">deſcripto, & </
s
>
<
s
xml:id
="
echoid-s10896
"
xml:space
="
preserve
">per G, radio
<
lb
/>
Aequatoris D C, parallela agatur G H, in quam eodem modo à puncto G, transferantur ſpatia </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>