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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lia ſunt lateribus H D, D F, trianguli H D F, in horologio, quòd D F, ipſi E F, cui æqualis eſt ſum
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pta D C, in radio Aequatoris, æqualis ſit; </
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<
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xml:space
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">(Cum enim latera E I, I F, trianguli E I F, lateribus D I,
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I F, trianguli D I F, æqualia ſint, angulosq́; </
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<
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<
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xml:space
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">Nam E I F, rectus eſt
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ex conſtructione, at F I D, rectus eſt, ex defin. </
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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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">Euclidis, quòd F I, communis ſectio Aequa
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toris, & </
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<
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gii ad Meridianum,
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hoc eſt, ad triãgulum
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D H I, in plano Meri-
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diani ſitũ, atq; </
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<
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ad rectã D I, perpen-
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<
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dicularis eſt, in pun-
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cto I; </
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<
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">æquales erunt
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xlink:label
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xml:space
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">4. primi.</
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baſes E F, D F,) angu
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losq́, continent æqua
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les, vtpote rectos; </
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<
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xml:space
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">Nã
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H D C, in proxima
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figura rectus eſt, ex
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cõſtructione, at vero
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& </
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<
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xml:space
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">H D F, in horo-
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logio rectus eſt, pro-
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pterea quòd axis HD,
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rectus ad planũ Ae-
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quatoris, ad rectam
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F D, in eo exiſtentem
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perpendicularis eſt,
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in pũcto D, ex defin.
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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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<
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xml:space
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">Euclidis; </
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<
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">æquales erunt baſes H C, H F, & </
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<
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">anguli D H C, D H F. </
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<
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xml:space
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">Quare ſi triangulum
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H D C, circa axem H D, in horologio moueri concipiatur, donec cum triangulo H D F, coniun-
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tur, & </
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<
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xml:space
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">recta H C, rectæ H F, in plano horologij congruat, cadet radii æquinoctialis punctum C, in
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punctum F, ob æqualitatem angulorum C H D; </
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<
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<
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">linearum H C, H F, & </
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<
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">radii ♋, punctũ
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Z, cadet in punctum α, propterea quod & </
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<
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xml:space
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">recta H α, æqualis ſumpta eſt rectæ H Z, per conſtru-
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ctionem, vel F α, ipſi C Z. </
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<
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xml:space
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">Per punctum ergo α, horæ quintæ à meridie incedit ſectio conica ♋,
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cum in ipſum radius cancri incidat in illa reuolutione trianguli D H C, circa axem D H, in horo-
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logio, vt oſtendimus. </
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<
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diaci cadere in R; </
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<
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xml:space
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">& </
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<
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">β, punctum radii ♋, in γ; </
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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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">ſic de cæteris lineis horariis, quæ æquinoctia-
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lem lineam interſecant, dicendum eſt.</
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<
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<
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<
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<
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<
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">quæ lineam æquinoctialem non ſecat, ſed ei ęqui-
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diſtat, ducenda eſt H V, ad axem H D, perpendicularis in figura radiorum Zodiaci, ſiue radio Ae-
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quatoris D C, parallela; </
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<
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xml:space
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">quia hac ratione, in illa circumductione radiorum, recta H V, recte H δ,
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in horologio congruet, propter æqualitatem angulorum rectorum D H V, D H δ; </
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<
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lus D H V, rectus, ex conſtructione, angulus vero D H δ
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, ad axem conſtitutus rectus quoque eſt,
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per defin. </
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<
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xml:space
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<
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<
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">11. </
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<
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xml:space
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">Euclidis, propterea quòd H δ, linea ſextæ horæ, communis nimirum ſectio pla
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ni horologii, & </
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<
s
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">circuli horæ ſextæ, ad Meridianum, (ad quem vtrumque illorum rectum eſt) hoc
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eſt, ad triangulum D H I, ac proinde & </
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<
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">ad rectam D H, in puncto H, perpendicularis eſt. </
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<
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xml:space
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">Quam-
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<
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obrem punctum θ, radij ♋, cadet in δ, ob ęqualitatem, ex conſtructione, rectarum H θ, H δ:
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</
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<
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">Sumpta enim eſt in horologio recta H δ, rectæ H θ, in figura radiorum æqualis. </
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que ſeptima à meridie, vel quinta à med. </
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<
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<
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">& </
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<
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">aliis, quæ æquinoctialem lineam nõ ſecant, ſi opus
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fuerit, (In noſtro exemplo nulla alia hora indigemus, cum arcus ♋, ſecet lineas horarum ſeptimæ à
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mer. </
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<
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<
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<
s
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xml:space
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">in punctis ualde remotis à centro H) ducendæ ſunt lineæ, quæ ex alte-
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ra parte, nempe ſiniſtra, cum linea H V, horæ ſextæ angulos faciant æquales angulis, quos lineæ ra-
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<
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dium Aequatoris ex parte dextra ſecantes, & </
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<
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">quæ ad horas æquinoctialem lineam ſecantes in ho-
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rologio pertinent, cum eadem linea horæ ſextæ faciunt, quales ſunt H X, H Y, &</
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<
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<
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</
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<
s
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xml:space
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">do facient huiuſmodi lineæ cum axe H D, in figura radiorum Zodiaci angulos X H D, Y H D,
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æquales angulis, quos lineæ horariæ reſpondentes in horologio cum axe H D, faciunt: </
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<
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angulum X H D, in dicta figura æqualem angulo κ H D, in horologio. </
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<
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xml:space
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">Cum enim duo anguli
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X H λ, X H D, in figura radiorum æquales ſint duobus angulis D H k, D H κ, in horologio; </
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<
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tam hi, quàm illi duobus ſint rectis æquales: </
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<
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D H K, in horologio æqualis; </
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<
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xml:space
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">(Nam angulus X H λ, in eadem figura æqualis eſt angulo C H D,
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eiuſdem figuræ, per pronunciatum 3. </
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<
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<
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<
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<
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ter ſe, & </
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<
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<
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dictæ figuræ æqualis eſt angulo D H F, in horologio, vt demõſtratũ eſt, atq; </
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<
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<
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