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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LIBER QVARTVS.
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<
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xml:space
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">HANC autem conſtructionem hoc modo demonſtrabimus. </
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deſcriptionis
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horologii præ-
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dicti.</
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ſitum habentis intelligatur A B, Horizonti æquidiſtans, ita vt ſit communis ſectio plani horolo-
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gii, & </
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<
s
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">triangulum E F ψ, moueri concipiatur circa rectam E ψ, donec cum Hori-
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zonte coniungatur, in eoque iaceat. </
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<
s
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">Et quoniam D E F, angulus eſt declinationis plani à Vertica-
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li, erit reliquus A E F, angulus complementi dictæ declinationis, qualem nimirum facit Meri-
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dianus cum linea, quæ in plano declinante, & </
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<
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no per illam rectam ducto, & </
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<
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xml:space
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">Quare E F, in illo ſitu communis ſectio erit
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Meridiani, & </
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<
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tis, ac Meridiani, erit E F, axis mundi occurrens plano horologij in E, puncto, quod centrum erit
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horologii, in quo omnes horariæ lineæ conueniunt, vt in ſuperioribus demonſtratum eſt.</
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<
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">RVRSVS triangulo E F ψ, habente illum ſitum, quem diximus, intelligatur circa F ψ, con-
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uerti triangulum F n ψ, deorſum verſus, donec & </
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rectum: </
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<
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">quod tum demum fiet, cum recta ψ n, perpendicularis fuerit ad A B. </
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A B, perpendicularis exiſtens ad rectas ψ F, ψ n, recta erit ad planum trianguli ψ F n, per illas re-
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ctas ductum. </
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planum trianguli ψ F n, rectum erit; </
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<
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<
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ſtet. </
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">Quocirca cum F ψ n, angulus ſit inclinationis plani ad Horizontem, & </
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<
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">per rectam F ψ, in
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eo ſitu ducatur Horizon, iacebit ψ n, in plano inclinato, coniunctaq́; </
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plano exiſtente, atque adeò punctum n, in punctum p, cadet, ob æqualitatem rectarum ψ n, ψ p.
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</
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<
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<
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in plano Horizontis exiſtentis in dicto ſitu, tranſeat per rectam E F, vt demonſtrauimus, ac pro-
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inde & </
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">per rectam F n, in illo ſitu, (propterea quod F n, per defin. </
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<
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planum trianguli E F ψ, cum perpendicularis ſit, ex conſtructione, ad F ψ, cõmunem ſectione m
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triangulorum E F ψ, ψ F n, quorum vnum ad alterum rectum eſt) occurret Meridianus plano
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horologii inclinati in puncto p; </
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<
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">ac proinde recta E p, communis ſectio erit Meridiani, ac plani
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horologii inclinati. </
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<
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ad principium propoſ. </
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<
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">QVONIAM autem, triangulis E F ψ, ψ F n, in iiſdem poſitionibus adhuc conſtitutis, re-
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cta F G, ad ψ n, cõmunem ſectionem plani horologii, & </
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cti exiſtentis, perpendicularis eſt, exiſtitq́ue in plano trianguli F n ψ, erit per deſin. </
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<
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