Full text: 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

GNOMONICES pta eſt æqualis, ita E T, ſinus totus ad T X, ſinum Verticalis circunferentiæ A T: Si fiat, vt ſinus ho
rariæ circunferentiæ, hoc eſt, vt ſinus complementi altitudinis Solis ſupra Verticalem circulum,
nis, ita ſinus totus ad aliud, inue-
nietur ſinus circunferentiæ Ver-
ticalis; ac propterea ipſa circũfe-
rentia Verticalis nota ſiet.

476.1.

4. ſexti.
Verticalis.

POSTREMO, quoniam
in triangulis E Q N, E S V, eſt vt
E Q, ſinus circunferentiæ de-
ſcenſiuæ (Nam ſupra in horizon
tali circunferentia demonſtraui-
mus, rectam E Q, ipſi O P, ſinui
circunferentiæ deſcenſiuæ eſſe
æqualem) ad Q N, quæ ipſi k L,
hoc eſt, ipſi a m, ſinui | comple-
menti declinationis, ſumpta eſt
æqualis, ita E S, ſinus totus ad
S V, ſinum complementi circun
ferentiæ horizontalis A S; Si
fiat, vt ſinus @circunferentiæ de-
ſcenſiuæ, id eſt, vt ſinus comple-
menti altitudinis Solis ſupra Ho
ti declinationis, ita ſinus totus
plementi horizontalis circunferentiæ; atque ob id complementum hoc, vnà cum circunferen-
tia horizontali, cognitum erit.

476.1.

4. ſex@@.
10
20
Horizontalis

EÆDEM circunferentiæ facilius adhuc reperiẽtur, Sole in Verticali circulo exiſtente. Tunc
enim perpendicularis k L, ca-
dit in punctum n, vbi paralleli
diameter diametrum Vertica-
lis interſecat, vt in tertia figura
cap 4. quam hic repetiuimus,
apparet, & obid rectæ E Q S,
E Y, M N, à recta A E, nõ dif-
ferent: Recta item O P, ipſi
k L, æqualis eſt, vt in cap. 4. demonſtrauimus, atque adeo
recta E R T, in punctum P, ca-
det: Item L f, E g, perpendicu
lares ad E Y, à rectis O P, E B,
diſcrepabunt.

476.1.

Quando Sol in
Verticali circu-
lo exiſtit, facili-
medictæ circu@
feren@@æ re@@@
[...] .
30
40

ITAQVE quoniam eſt,
vt a m, quatenus ſinus totus in
parallelo dato, ad K L, quate-
nus ſinus rectus eſt diſtantiæ
Solis à meridie in eodem pa-
rallelo, ita a m, quatenus ſinus
eſt complementi declinationis
dati paralleli, nempe pars ſinus
totius in maximo circulo, puta in Meridiano, ad K L, quatenus pars eſt ſinus totius in eodem cir-
culo maximo, hoc eſt, ad O P, vel L f, ipſi K L, æqualem, quatenus ſinus eſt cõplementi circunfe-
rentiæ hectemoriæ f g, & ſinus rectus deſcenſiuæ circunferentiæ A P, & Verticalis A T: Si fiat, vt
ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis ad aliud, inue-
nietur ſinus O P, arcus A P, cuius complementum fg, dabit circunferentiam hectemoriam, ip-
ſemet vero arcus A P, erit circunferentia deſcenſiua, & Verticalis.

476.1.

50
Hectemoria.
Deſcenſiua, &
Verticalis.

HORARIA autem circunferentia, & meridiana erit quadrans Meridiani B M, propterea
quòd, vt diximus, rectæ N M, E Y, à recta A E, non differunt.

476.1.

Horatia, & Me-
ridiana.

HORIZONTALIS denique circunferentia A S, nihil tunc eſt. Nam puncta A, & S,

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