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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G X, & </
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<
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<
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">rectæ C T, L X, arcus{q́ue} C T, L X, æquales erunt. </
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<
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xml:space
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">Itaque quoniam arcus A S,
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arcui I V, æqualis est, & </
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<
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xml:space
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">arcus B
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S, arcui K V, ſuperabit A B, arcus primæ horæ ♋, eadem quantita-
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te arcum A S, horæ æquinoctialis, qua I K, arcus ab arcu I V, horæ æquinoctialis ſuperatur. </
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<
s
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xml:space
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">Ergo per
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ea, quæ dictaſunt, erit I K, arcus primæ horæ ♑; </
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<
s
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xml:space
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">at que adeò circulus maximus B F K, per primam ho-
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ram ♋, & </
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<
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xml:space
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ſit quoque per primam horam ♑. </
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<
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dem prorſus pacto demonſtr abimus ar-
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cum I K, eſſe duarum horarum ♑,
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quemadmodum & </
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<
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">arcus A C, duas ho-
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ras ♋, complectitur, & </
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<
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<
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duas horas Aequatoris; </
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<
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licet arcus T C, quo A C, arcus dua-
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rum horarum ♋, ſuperat arcum A T,
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duarum horarum æquinoctialium, ęqua-
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lis eſt arcui L X, quo I L, arcus ab ar-
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cu I X, duarum horarum æquinoctia-
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lium ſuperatur. </
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<
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xml:space
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">Cum igitur I K, oſten-
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ſus ſit arcus primæ horæ ♑, erit K L,
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arcus ſecundæ horæ. </
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<
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xml:space
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">Eadem{q́ue}, demon-
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ſtratio erit in reliquis horis inæquali-
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bus ♑, & </
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<
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">aliorum ſignorum, ſi loco
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parallelorum ♋, & </
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<
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alij duo oppoſiti, & </
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<
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">æquales. </
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<
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propoſitum.</
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<
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">OMNIA autem, quæ proximis
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">In ſphęra recta
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iidẽ circuli indi
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cãt horas à mer.
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vel med. noc &
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ab or. vel occ
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Nullæ autẽ ibi
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ſunt horę in-
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æquales.</
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duabus propoſ. </
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<
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ligenda ſunt in ſphæra obliqua tantum.
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</
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<
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">Nam in recta non eſt vllus parallelus perpetuo apparens, cum omnes paralleli ab Horizonte per il-
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lorum polos ducto bifariam ſecentur, vt conſtat ex propoſ. </
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<
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<
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<
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maximi circuli, inter quos eſt & </
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">Horizon, incedentes per polos mundi, ſecantes{q́ue}
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Aequatorem, ac proinde, per propoſ. </
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">& </
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<
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</
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<
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">partes æquales, indicabunt & </
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">horas à meridie vel media nocte, & </
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">ab ortu vel occaſu Solis. </
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<
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ræ autem inæquales ibi nuliæ ſunt, cum perpetuum ſit æquinoctium, ac proinde horæ æquinoctiales ſint
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partes duodecimæ cuiuslibet diei, quemadmodum & </
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<
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">horæ inæquales in ſphæra obliqua partes ſunt duo-
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decimæ cuiuſque diei.</
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<
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">THEOREMA 9. PROPOSITIO 11.</
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radius Solis ꝓ-
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iicitur in cõem
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ſectionem plani
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horologij, & cir
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culi maximi, in
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quo Sol exiſtit.</
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<
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">SOLE in quocunque circulo horario, vel alio maximo exiſtente,
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radius Solaris, atque adeò vmbra verticis ſtyli proijcitur in rectam li-
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neam, quæ communis ſectio eſt ipſius circuli horarij vel maximi, &</
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plani horologij.</
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<
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<
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">SIT circulus horarius, vel quicunque alius maximus A B C D, ſecans planum horologii
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E F G H, per rectam E G, ſitq́ ſtylus I K, cuius vertex I, in centro I, collocetur, per propoſ. </
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<
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co Sole in quocunque puncto L, exiſtente in circulo A B C D, radium eius, & </
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<
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<
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ſtyli I, proijci in rectam E G. </
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<
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">Nam radius L I, pertinens ad centrum I, per quod & </
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<
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culi A B C D, ducitur, à plano circuli A B C D, non recedet, Sole exiſtente in circunferentia
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ipſius circuli, ſed productus ſecabit circunferentiam eiuſdem circuli in puncto M, quod puncto
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L, opponitur, ita vt ipſe radius ſit circuli diameter. </
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<
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">Cum ergo recta E G, in plano eiuſdem
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circuli exiſtat, ſecabit radius L I M, rectam E G, in N, puncto; </
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<
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vmbra verticis ſtyli I, proiicietur in rectam E G, communem ſectionem circuli horarii A B-
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C D, & </
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<
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<
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">Eodem modo, ſi alius quidam circulus horarius, vel alius
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maximus A F C H, idem planum horologij E F G H, ſecet per rectam F H, & </
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<
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">Sol exiſtat in pun-
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cto O, circuli horarij, vel maximi, demonſtrabimus radium O I, & </
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<
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">vmbram eiuſdem verticis
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ſtyli I, proiici in rectam F H, propterea quod radius productus ad punctum oppoſitum P, re-
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ctam FH, in eodem plano circuli A F C H, exiſtentem ſecet in Q, puncto. </
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<
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