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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Sol in P, exiſtet, altitudo{q́ue} Solis erit arcus I P, vt ex ijs, quæ propoſ. </
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<
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<
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ligi poteſt.</
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<
s
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xml:space
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">QVOD ſi quando recta P Q, ceciderit in punctum N, hoc est, ſi altitudo Solis inuenta fuerit æqua
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lis meridianæ altitudini Solis illius diei, exiſtet Sol in Meridiano circulo, ac propterea vmbra ipſa A B,
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erit linea meridiana.</
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<
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xml:space
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">PER idem Analemma eadem ferè ratione explorare nobis licebit declinationem cuiuſcunque plani
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propoſiti, etiamſi in plano Horizonti parallelo lineam meridianam non inueniamus, quemadmodum
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& </
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<
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<
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">Baptiſta Benedicto traditur in Gnomonica. </
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<
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xml:space
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">Quod vt fiat, ſit murus ad Horizontem rectus
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A B, in quo ducta recta C D,
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ni propoſiti, per
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Analẽma qua
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arte ſit exqui-
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renda.</
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Horizonti parallela, figatur
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in ea ſtylus C E, cuiusuis longi-
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tudinis ad murum rectus in
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puncto C, obſeruetur{q́ue} quo-
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cunque tempore, cum Sol pla-
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num muri illuminat, ſiue ante
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meridiem, ſiue poſt, extremitas
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vmbræ E F, quam ſtylus proij-
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cit, nempe punctũ F, per quod
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ad rectam C D, perpendicula-
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ris ducatur F D; </
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<
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xml:space
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">quæ dicto ci-
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tius ducetur hoc modo. </
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plicetur muro filum cum per-
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pendiculo, ita vt per punctum
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F, tranſeat, ſignetur in mu-
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ro punctum quodcunque D.
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</
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<
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">Nam linea recta per F, & </
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<
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">D, ducta perpendicularis erit ad C D, cum filum ad Horizontẽ ſit rectũ. </
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<
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enim fit, vt & </
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<
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xml:space
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">recta F D, quæ à filo perpendiculi non differt, vel certe ei parallela eſt, ad Horizontem,
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qui per rectam C D, ducitur, ſit perpendicularis; </
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<
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">atque adeo per definitionem 3. </
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<
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">lib. </
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<
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<
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">Euclidis, cum
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recta C D, in Horizonte rectos conſtituat angulos. </
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<
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xml:space
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">Ego loco ſtyli vtor hic quoque inſtrumento illo, quod
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ad initium huius ſcholij deſcripſimus. </
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<
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xml:space
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">Si enim applicetur muro A B, ita vt punctum D, in punctum C,
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cadat, & </
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<
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">latus D A, in rectam C D, recta D I, vergente deorſum verſus, fungetur latus D H, mune-
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re ſtyli ad murum recti. </
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<
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">Quare obſeruata extremitate vmbræ illius in puncto F, amouendum erit instru
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mentum, & </
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<
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">punctum C, diligenter notandum. </
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<
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">Itaque quoniam radius Solis E F, per E, verticem ſtyli,
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qui in centro mundi eſt, per propoſ. </
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<
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<
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">huius libri, in plano illius Verticalis exiſtit, qui tempore obſerua-
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tionis per centrum Solis ducitur, occurret hic Verticalis muro A B, in puncto F. </
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<
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">Quia verò tam planũ
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muri, quàm huius Verticalis rectum eſt ad Horizontem, erit quoque communis eorum ſectio ad Horizon-
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tem recta, atque adeo, per defin. </
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<
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<
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<
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<
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">Euclidis, perpendicularis ad rectam C D, in Horizonte exiſten
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tem. </
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<
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">Cum ergo F D, ſit ad C D, perpendicularis, erit F D, communis ſectio muri A B, & </
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">Verticalis
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tunc temporis per centrum Solis ducti, atque adeo idem Verticalis per punctum D, tranſibit. </
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<
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tur recta E D, erit communis ſectio Horizontis, & </
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<
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">eiuſdem Verticalis, cum vterque circulus per pun-
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<
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cta E, D, tranſeat; </
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<
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">atque adeo linea F D, ad Horizontem recta, perpendicularis erit, per defin. </
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<
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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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">Euclidis, ad rectam E D, in Horizonte exiſtentem: </
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<
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<
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">ad C D, perpendicularis oſtenſa. </
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<
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tur cum vtraque linea C D, E D, quarum illa in muro, hæc autem in Verticali per Solem tranſeunte exi-
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ſtit, ad F D, communem ſectionem muri, & </
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<
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<
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<
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<
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<
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Euclidis, C D E, angulus inclinationis muri ad dictum Verticalem. </
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<
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">Cui in plano muri æqualem exhibe-
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bimus hoc modo. </
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<
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xml:space
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">Ducta recta C G, ad C D, perpendiculari, fiat C G, ſtylo, vel lateri D H, inſtrumenti
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ad initium huius ſcholij deſcripti, æqualis, iungatur{q́ue} recta G D. </
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<
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">Dico angulum C D G, angulo C D E,
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æqualem eſſe. </
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<
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">Quoniam enim duo latera C E, C D, trianguli C D E, duobus lateribus C G, C D, trian-
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guli C D G, æqualia ſunt, angulosq́, comprehendunt æquales, vtpote rectos, (Eſt enim angulus E C D,
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rectus, per d@fin. </
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<
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<
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">lib. </
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<
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">11. </
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<
s
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xml:space
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">Euclidis, angulus verò G C D, ex conſtructione) erit quoque baſis E D, baſi
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<
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G D, & </
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<
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">angulus C D E, angulo C D G, æqualis. </
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<
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xml:space
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">Ex hoc autem angulo C D G, cognito inuestigabimus de-
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<
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">4. primi.</
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clinationem muri propoſiti à Verticali proprie dicto, hac ratione.</
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</
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<
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">POST QVAM vmbræ extremitas F, notata eſt, inquiratur ſtatim, antequã recta F D, ducatur,
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(quoniã ſi mora aliqua interceſſerit, vmbra mutabitur, & </
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<
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xml:space
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">Sol alium Verticalẽ occupabit, propter motum
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diurnũ) altitudo Solis, quæ in Analemmate ſuperiori, quod hic repetiuimus, ſupputetur ex punctis G, I,
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vſq;</
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<
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ad puncta Q, P. </
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<
s
xml:id
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xml:space
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">Iuncta enim recta PQ, erit diameter paralleli Horizõtis per centrũ Solis tempore
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obſeruationis ducti, vt ſupra demonſtrauimus, ſecans diametrum paralleli Solis in S, & </
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<
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Verticalis proprie dicti in R. </
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<
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">Deſcripto autem circa P Q, ex centro R, ſemicirculo P T Q, ducatur
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ex S, ad P Q, perpendicularis S T, ſecans circunferentiam ſemicirculi P T Q, in T, iungatur{q́ue}
<
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re-
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cta T R, quæ communis ſectio erit paralleli Horizontis, & </
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<
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">Verticalis circuli, quorum vterque tunc per
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Solis centrum ducitur; </
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<
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">adeo vt angulus acutus Q R T, vel P R T, ſit angulus declinationis dicti </
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