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 SECVNDVS.
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mit, quarum vna borealis eſt, & </
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<
s
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xml:space
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">CÆTERVM in vtroque horologio ducenda eſt per G, locum gnomonis ad lineam meri-
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linea quid, &
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quomodo in
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horologio Ver-
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ticali ducenda.</
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dianam perpendicularis A B, quæ quidem communis ſectio erit Horizontis, & </
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<
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diceturq́ue linea horizontalis.
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Cum enim & </
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Verticali propriè dicto æquidi-
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ſtans, & </
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<
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ſit ad Meridiani planũ, erit quo-
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que communis illorum ſectio
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ad idem planum Meridiani, ac
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proinde, per defi. </
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</
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">& </
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<
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">ad meridianam lineam HI,
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in Meridiani plano exiſtentem
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perpendicularis in puncto G, cũ
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in hoc puncto occurrat plano
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Meridiani: </
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<
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teſt. </
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monem, qui in puncto G, per-
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pendicularis eſt ad planum ho-
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rologij, ductus horologio occur
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<
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rit in G, tranſibit quoque com-
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munis ſectio Horizontis, & </
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rologij per idem punctum G.
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</
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<
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horologij per G, ad meridianam
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lineam H I, perpendicularis du-
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cta eſt, communis ſectio eſt Hori
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zontis, ac plani horologij, eſtq́; </
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æquinoctiali lineæ parallela, vt
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in ſcholio propoſ. </
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lib. </
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<
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">In omni horo-
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logio portio il-
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la, quæ ſupra li
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neam horizon-
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talem dcſcripta
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eſt, ſuperuaca
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nea eſt, ac pro-
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inde reſecãda.</
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ſtente in Horizonte, cum videli-
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cet oritur, vel occidit, vmbra ſty-
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li proijcitur in communem ſectionem Horizontis ac plani horologij, hoc eſt, in rectam A B, vt cõ
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ſtar ex propoſ. </
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">fit, vt toto reliquo tempore cuiuſque diei, cum Sol ſupta Horizon
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tem eleuatus eſt, eadem vmbra cadat in planum horologij infra lineam horizontalem. </
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<
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">Quare
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in omni horologio reſecanda eſt pars illa, quæ ſupra lineam horizontalem extat, tanquam ſuper-
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uacanea, ita vt in horologio Verticali, quod ad boream ſpectat, ſolum ea particula relinquatur,
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quæ inter horizontalem lineam, & </
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<
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gii borea lis in-
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fra lineam hori
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zontalem æqua
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lis eſt portioni
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horologii au-
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ſtralis ſupra ho
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rizontalem li-
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neam.</
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<
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<
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">HÆC autem pars Verticalis horologij borealis inter lineam horizontalem, & </
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<
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">arcum ♋,
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cõprehenſa, æqualis omnino eſt illi parti, quam linea horizõtalis ex Auſtrali horologio, tanquam
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ſuperfluã, abſcindit. </
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<
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">Tantũ enim diſtat in horologio boreali parallelus ♋, ab H, centro horologii,
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quantum ab eodem in Auſtrali parallelus ♑, abeſt, vt conſtat ex Analemmate huius propoſ. </
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ita probari poteſt. </
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<
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">Quoniam in triangulo D G K, ad ſiniſtram, duo anguli D, G, æquales ſunt duo
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bus angulis D, G, in triangulo D G N, ad dexteram; </
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<
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ticem conſtituti, æquales: </
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<
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">latera D G, D G, æqualia, propterea quòd vtrumque gno
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moni eſt æquale; </
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cum in triangulis D H K, D H N, & </
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<
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quoque latera H K, H N, æqualia; </
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<
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">ac proinde cum per K, tranſeat ſectio conica ♋, in boreali ho-
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<
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<
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rologio, & </
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<
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">per N, ſectio conica ♑, in auſtrali, tantum diſtabit in horologio boreali arcus ♋, ab
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H, quantum diſtat ab eodem puncto H, arcus ♑, in horologio Auſtrali. </
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<
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& </
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<
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<
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<
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vt demonſtratum eſt; </
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<
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">erit ſectio conica ♋, cuins diameter K Q, in horologio boreali, æqualis ſe-
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ctioni conicæ ♑, cuius diameter N Q, in horologio Auſtrali: </
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<
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rologij ita ſecat triangulum per axem in cono vmbræ ♋, vt à plano huius horologij ſecatur trian
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gulum per axem in cono vmbræ ♑, ob æqualitatem rectarum D K, D N, & </
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<
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D N H, vt oſtẽſum eſt. </
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<
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">Si igitur pars illa horologij Auſtralis abſciſſa à linea horizontali ſuperpona
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tur horologio boreali, (ita vt pars illa, quæ nunc eſt ſuperior, fiat inferior, & </
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ſuperior; </
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">& </
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<
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">pars quæ dextra eſt, inuerſo hoc modo, vt dictum eſt, horologio, quæ nimirum eſt ver-
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ſus A, fiat ſiniſtra, & </
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<
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