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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182162GNOMONICES lia ſunt lateribus H D, D F, trianguli H D F, in horologio, quòd D F, ipſi E F, cui æqualis eſt ſum
pta D C, in radio Aequatoris, æqualis ſit; (Cum enim latera E I, I F, trianguli E I F, lateribus D I,
I F, trianguli D I F, æqualia ſint, angulosq́; contineant æquales, nempe rectos; Nam E I F, rectus eſt
ex conſtructione, at F I D, rectus eſt, ex defin. 3. lib. 11. Euclidis, quòd F I, communis ſectio Aequa

134[Figure 134] toris, & plani horolo
gii ad Meridianum,
1119. vndec. hoc eſt, ad triãgulum
D H I, in plano Meri-
diani ſitũ, atq; adeo
ad rectã D I, perpen-
2210 dicularis eſt, in pun-
cto I; æquales erunt
334. primi. baſes E F, D F,) angu
losq́, continent æqua
les, vtpote rectos; Nã
H D C, in proxima
figura rectus eſt, ex
cõſtructione, at vero
& H D F, in horo-
logio rectus eſt, pro-
4420 pterea quòd axis HD,
rectus ad planũ Ae-
quatoris, ad rectam
F D, in eo exiſtentem
perpendicularis eſt,
in pũcto D, ex defin.
3. lib. 11. Euclidis; æquales erunt baſes H C, H F, & anguli D H C, D H F. Quare ſi triangulum
554. primi. H D C, circa axem H D, in horologio moueri concipiatur, donec cum triangulo H D F, coniun-
tur, & recta H C, rectæ H F, in plano horologij congruat, cadet radii æquinoctialis punctum C, in
punctum F, ob æqualitatem angulorum C H D; F H D, & linearum H C, H F, & radii ♋, punctũ
6630 Z, cadet in punctum α, propterea quod & recta H α, æqualis ſumpta eſt rectæ H Z, per conſtru-
ctionem, vel F α, ipſi C Z. Per punctum ergo α, horæ quintæ à meridie incedit ſectio conica ♋,
cum in ipſum radius cancri incidat in illa reuolutione trianguli D H C, circa axem D H, in horo-
logio, vt oſtendimus. Non aliter probabimus & punctum T, in illa circumlatione radiorum Zo-
diaci cadere in R; & β, punctum radii ♋, in γ; & ſic de cæteris lineis horariis, quæ æquinoctia-
lem lineam interſecant, dicendum eſt.

PRO hora vero ſexta à mer. vel med. noc. quæ lineam æquinoctialem non ſecat, ſed ei ęqui-
diſtat, ducenda eſt H V, ad axem H D, perpendicularis in figura radiorum Zodiaci, ſiue radio Ae-
quatoris D C, parallela; quia hac ratione, in illa circumductione radiorum, recta H V, recte H δ,
in horologio congruet, propter æqualitatem angulorum rectorum D H V, D H δ; Eſt enim angu
7740 lus D H V, rectus, ex conſtructione, angulus vero D H δ, ad axem conſtitutus rectus quoque eſt,
per defin. 3. lib. 11. Euclidis, propterea quòd H δ, linea ſextæ horæ, communis nimirum ſectio pla
ni horologii, & circuli horæ ſextæ, ad Meridianum, (ad quem vtrumque illorum rectum eſt) hoc
eſt, ad triangulum D H I, ac proinde & ad rectam D H, in puncto H, perpendicularis eſt. Quam-
8819. vndec. obrem punctum θ, radij ♋, cadet in δ, ob ęqualitatem, ex conſtructione, rectarum H θ, H δ:
Sumpta enim eſt in horologio recta H δ, rectæ H θ, in figura radiorum æqualis. Pro hora deni-
que ſeptima à meridie, vel quinta à med. noc. & aliis, quæ æquinoctialem lineam nõ ſecant, ſi opus
fuerit, (In noſtro exemplo nulla alia hora indigemus, cum arcus ♋, ſecet lineas horarum ſeptimæ à
mer. & quintæ à med. noc. in punctis ualde remotis à centro H) ducendæ ſunt lineæ, quæ ex alte-
ra parte, nempe ſiniſtra, cum linea H V, horæ ſextæ angulos faciant æquales angulis, quos lineæ ra-
9950 dium Aequatoris ex parte dextra ſecantes, & quæ ad horas æquinoctialem lineam ſecantes in ho-
rologio pertinent, cum eadem linea horæ ſextæ faciunt, quales ſunt H X, H Y, & c. Nam hoc mo.
do facient huiuſmodi lineæ cum axe H D, in figura radiorum Zodiaci angulos X H D, Y H D,
æquales angulis, quos lineæ horariæ reſpondentes in horologio cum axe H D, faciunt: nimirum
angulum X H D, in dicta figura æqualem angulo κ H D, in horologio. Cum enim duo anguli
X H λ, X H D, in figura radiorum æquales ſint duobus angulis D H k, D H κ, in horologio; quòd
tam hi, quàm illi duobus ſint rectis æquales: Sit autem angulus X H λ, in dicta figura angulo
101013. primi. D H K, in horologio æqualis; (Nam angulus X H λ, in eadem figura æqualis eſt angulo C H D,
eiuſdem figuræ, per pronunciatum 3. lib. 1. Euclidis, quòd & anguli toti recti V H λ, V H D, in-
ter ſe, & ablati V H X, V H C, inter ſe, per conſtructionem, æquales ſint; angulus autem C H D,
dictæ figuræ æqualis eſt angulo D H F, in horologio, vt demõſtratũ eſt, atq; adeò & angulo D H

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