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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eiuſdẽ arcus 30. </
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<
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<
s
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">ex demonſtratis à Ioanne Regiom. </
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<
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xml:space
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">& </
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<
s
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xml:space
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">Petro Nonio, vt dictum eſt, & </
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<
s
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xml:space
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">nos pro ver@
<
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at que conceſſo ſumpſimus. </
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<
s
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xml:space
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">Igitur ſinus O φ, ęqualis eſt ſinui declinationis illius arcus Eclipticæ, qui 30.
<
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</
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<
s
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xml:space
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">gradus complectitur, eſt arcui QX, ſimilis. </
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<
s
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xml:space
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">Quare arcus H γ, æqualis eſt arcui declinationis illius ar-
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cus Eclipticæ 30. </
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<
s
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">grad. </
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<
s
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xml:space
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">qui ar cui QX, 30. </
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<
s
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xml:space
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">grad. </
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<
s
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xml:space
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">eſt ſimilis. </
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<
s
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xml:space
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">Eademq́, de cæteris arcubus zodiaci est ratio,
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quod erat demonſtr andum.</
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<
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</
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<
s
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xml:space
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">INVENIRI quoque poſſunt declinationes omnium ſignorũ Eclipticæ hoc modo. </
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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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">Alia deſcriptio
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pa@allelorã Ae-
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quatoris per ſi-
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gnorum prin-
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cipia ductorum.</
note
>
lemmatis A B C D, diuidatur in 12. </
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>
<
s
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xml:space
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">partes æquales, initio facto à puncto M, maximæ declinationis; </
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<
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quælibet duo puncta diuiſionum æqualiter à puncto M, remota, rectis lineis iungantur; </
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<
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xml:space
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<
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Analemmate lineæ punctis diſtinctæ, & </
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xml:space
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">in punctis l, p, E, q, u, rectam M ρ, ſecantes; </
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<
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xml:space
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">quæ omnes paral-
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lelæ inter ſe erunt, ex ſcholio propoſ. </
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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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">Hæ lineæ vbi rectam M ρ, ſecabunt, per ea
<
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<
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number
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15
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0036-01
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puncta, qualia ſunt l, p, E, q, u, du-
<
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cendæ erunt rectæ lineæ β λ, γ μ,
<
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& </
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<
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xml:space
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">c. </
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<
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xml:space
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">æquinoctiali lineæ H I, paral-
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lelæ pro diametris parallelorũ per
<
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ſignorum initia deſcriptorum; </
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>
<
s
xml:id
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xml:space
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">ita
<
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vt rurſus arcus H β, H γ, &</
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<
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xml:space
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">c. </
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<
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xml:space
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declinationes ſignorum Zodiaci.
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</
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<
s
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xml:space
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">Quod vt demonſtremus, intelligen-
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dus est circulus A B C D, eſſe
<
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Ecliptica, cuius ſignorũ initia ſunt
<
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<
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in illis punctis diuiſionum 12. </
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<
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vt M, ρ, ſint principia ♋ & </
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♑. </
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<
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xml:space
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">Deindemanente hac Eclipti-
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caimmobili, & </
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>
<
s
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xml:space
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">in coſitu, quem in
<
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Sphæra habet, poſito principio
<
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♋ M, in Meridiano circulo ſu-
<
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pra Horizontẽ, & </
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>
<
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xml:space
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">principio ♑,
<
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ρ, in eodem ſub Horizonte, intelli-
<
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gendus eſt idem circulus inſtar Co-
<
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/>
luri ſolſtitiorum circa diametrum
<
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<
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xlink:label
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M ρ, conuerti, donec rectus ſit ad
<
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Eclipticæ planum, & </
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>
<
s
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xml:space
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">punctum F,
<
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directo ad polum arcticum, & </
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<
s
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xml:space
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">G,
<
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ad antarcticum ſpectet, ita ut Ae-
<
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quator ad hunc Colurum rectus per rectam H I, ductus, faciat in plano Eclipticæ communem ſectionem,
<
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<
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position
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xlink:label
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xlink:href
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xml:space
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">3. vndec.</
note
>
rectam illam punctis not at am, quæ ipſam M ρ, ad angulos rectos ſecat in E, centro. </
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>
<
s
xml:id
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xml:space
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">Cum enim tam pla-
<
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num Eclipticæ, quàm Aequatoris ad Colurum ſit rectum, erit quoque communis illorum ſectio ad eundem
<
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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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">19. vndec.</
note
>
recta, at que adeo & </
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<
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xml:space
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">ad rectam M ρ, in eodem Coluro exiſtentem. </
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<
s
xml:id
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xml:space
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">Si igitur per punctum p, verbi gratia,
<
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concipiamus tranſire planum Aequatori par allelum, faciet id in plano Eclipticæ rectam punctis diſtin-
<
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ctam, & </
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>
<
s
xml:id
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xml:space
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">per p, tranſeuntem, at que alteri rectæ per E, ductæ, punctis{q́ue} diſtinctæ par allelam; </
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<
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xml:space
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<
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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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">16. vndec.</
note
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<
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quòd hæ lineæ per E, & </
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<
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xml:id
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xml:space
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">p, ductæ ſint ſectiones planorum parallelorum, nempe Aequatoris, & </
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<
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xml:id
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">plani ipſi
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paralleli, factæ à plano Eclipticæ. </
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<
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xml:space
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">In Sphera autem circulum efficiet ex propoſ. </
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>
<
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">1. </
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<
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<
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<
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<
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tori parallelum, cuius diameter per p, incedens parallela erit diametro Aequatoris H I; </
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<
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<
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<
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xlink:label
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">16. vndec.</
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H I, & </
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<
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xml:id
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xml:space
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">diameter huius circuli ſint ſectiones planorum parallelorum, nimirum Aequatoris, & </
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<
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<
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ipſi æquidiſtantis, factæ à plano Coluri ſolſtitiorum. </
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<
s
xml:id
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xml:space
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">Igitur recta γ ω, per p, ducta ipſi H I, parallela dia-
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meter eſt illius paralleli, qui in Ecliptica per puncta terminantia rectam illam punctis not at am, & </
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<
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p, ductam, tranſit, nempe per arcus 30. </
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<
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xml:id
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">grad. </
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<
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xml:space
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">ab æquinoctialibus punctis computatos; </
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<
s
xml:id
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xml:space
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">quæ quidem pun-
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cta æquinoctialia terminantur àrecta illa punctis notata, & </
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<
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xml:id
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xml:space
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">per centrum E, ducta. </
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<
s
xml:id
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xml:space
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">Quare cum arcus
<
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Coluri ſolſtitiorum inter Aequatorem, & </
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<
s
xml:id
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"
xml:space
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">parallelum circulum quemcunque interceptus metiatur decli-
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nationem illius paralleli ab Aequatore, erit arcus H γ, declinatio paralleli, cuius diameter γ μ, qui{q́ue}
<
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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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per ea puncta in Ecliptica incedit, quæ à recta punctis diſtincta, at que per punctum p, ducta terminan-
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tur. </
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<
s
xml:id
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xml:space
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>
<
s
xml:id
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xml:space
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">Quòd ſi circulus A B C D, non ſolum in 12. </
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>
<
s
xml:id
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xml:space
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">partes, ſed in ſingulos
<
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etiam diſtribuatur gradus, eadem{q́ue} fiant, quæ prius, deſcribemus eodem artificio diametros parallelorum
<
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per ſingulos gradus Eclipticæ incedentium.</
s
>
<
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xml:id
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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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">DENIQVE, ſi declinationes ſignorum, vel quorumlibet punctorum Eclipticæ, inuentæ per doctri-
<
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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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">Alia adhue de-
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ſcriptio paralle-
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lorũ per puncta
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Eclipticæ tran-
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ſeuntium.</
note
>
nam ſinuum, vt in coroll. </
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>
<
s
xml:id
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">huius propoſ. </
s
>
<
s
xml:id
="
echoid-s1237
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xml:space
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">docuimus, ſupputentur ab Aequatoris diametro H I, ad vtram-
<
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que partem in circulo Analemmatis, & </
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>
<
s
xml:id
="
echoid-s1238
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xml:space
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">per fines ſupputationum ipſi H I, parallelæ agantur, erunt hæ
<
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rurſus diametri parallelorum per initia ſignorum, vel per data puncta Eclipticæ, tranſeuntium, vt prius;
<
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/>
</
s
>
<
s
xml:id
="
echoid-s1239
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xml:space
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">quamuis vt in initio diximus, incerta eſt per hanc viam Analemmatis deſcriptio, propter declinationes,
<
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quæ uix ſine errore in circulo A B C D, ſupputari poſſunt, cum in eo minuta, & </
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>
<
s
xml:id
="
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xml:space
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">ſecunda graduum de-
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ſignari nequeant.</
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