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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lis ponitur arcui E L; </
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<
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<
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xml:space
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lelæ, propterea quòd anguli O G T, k T G, recti ſint, ex conſtructione; </
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<
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<
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les, & </
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<
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<
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tur recta G O, ad rectas O L, O k, perpendicula-
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ris eſt, erit eadem G O, ad planum per O L, O k, du-
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<
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ctum perpendicularis: </
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culi D E B F, per G O, ductum, ad idem planum
<
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<
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per O L, O K, ductum erit rectum. </
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<
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dicularis ex k, in planum D E B F, demiſſa cidet
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in rectam L N, communem ſectionem plani DE-
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<
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B F, & </
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<
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tem in Q, cadat, ita demonſtrabitur. </
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<
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ri poteſt, in aliud punctum, vt in R. </
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<
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tur L S, M P, parallelæ ſunt, erit vt L M, ad M G,
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<
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ita S P, ad P G; </
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<
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<
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xml:space
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S G, ad P G: </
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<
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xml:space
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les ſunt, per definitionem circuli; </
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<
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xml:space
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<
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L O, Q O, æquales, ob rectangula S O, P O. </
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erit quoque, vt E G, ad H G, ita L O, ad Q O; </
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permutando, vt E G, ad L O, ita H G, ad Q O; </
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</
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adeò vt quadratum ex E G, ad quadratum ex L O, ita quadratum ex H G, ad quadratum ex Q O:
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</
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<
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Sed eſt, ex propoſ. </
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<
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<
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">Apollonij, vt quadratum ex E G, ad quadratum ex L O, ita rectangu-
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gulum ſub B G, GD, ad rectangulum ſub B O, O D, quòd E G, L O, ſint ordinatim ductæ ad B D,
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diametrum circuli D E B F, nempe perpendiculares. </
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<
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">Erit ergo quoque vt rectangulum ſub B G,
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G D, ad rectangulum ſub B O, O D, ita quadratum ex H G, ad quadratum ex Q O. </
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<
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Ellipſis diametrorum D B, HI, ponatur tranſire per R, (eò quod in R, dicatur cadere perpendicu
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laris ex K, demiſſa,) eſt quoque, per eandem propoſitionem 21. </
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ſub B G, G D, ad rectangulum ſub B O, O D, ita quadratum ex H G, ad quadratum ex R O, quòd
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H G, R O, ſint ordinatim applicatę ad diametrum BD. </
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<
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dratum ex Q O, ita idem quadratum ex H G, ad quadratum ex R O. </
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<
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R O, ęqualia ſunt, ac propterea & </
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<
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<
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<
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</
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<
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">Perpendicularis ergo à k, demiſſa non cadit in aliud punctum, quàm in Q. </
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<
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ptis alijs punctis in circunferentia circuli A B C D, inueniemus, quo loco perpendicutares ab ip-
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ſis ductę in planum circuli D E B F, cadant. </
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<
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ra ad alium circulum, &</
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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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D B, H I, ita aptentur, vt ſeſe bifariam in G, & </
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<
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<
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<
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<
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<
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ſcribenda fit El
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lipſis, cuius dia-
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@@etri datæ ſint@</
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G D, G H, circuli deſcribantur: </
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<
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vtrinque, ſumantur arcus ęquales E L, L A, A B, B C,
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quotcunque, & </
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<
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@@
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at in altero ſemicirculo E B F; </
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<
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L, A, B, &</
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<
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<
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H M I, in partes, quæ ſimiles erunt partibus E L, L A,
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&</
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<
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<
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capitis 1. </
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<
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<
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culi maioris à D, vel B, hinc inde remota æqualiter
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connectantur lineis rectis; </
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<
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<
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cta circuli minoris ab H, vel I, hinc inde ęqualiter quo-
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que remota alijs lineis rectis; </
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<
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xml:space
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coierint quęque duæ lineæ, quę per diuiſiones ſibi re-
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ſpondentes tranſeunt, notentur, cadẽt ea omnia in El-
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lipſim, cuius diametri D B, H I, vt demonſtratum eſt.
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</
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<
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">Nam in ſuperiori figura oſtendimus punctum Q, vbi
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coeuntrectæ L N, P M, quarum illa minori diametro
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H I, hæc verò maiori D B, parallela eſt, cadere in El-
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lipſim, quæ quidem parallelæ ducuntur per puncta L,
<
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M, interſe reſpondentia, hoc eſt, auferentia arcus ſimiles E L, H M. </
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<
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">Cum ergo hic idem fiat, propterea
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quòd lineę omnes puncta correſpondentia connectentes parallelæ ſunt diametris H I, D B, ex ijs, quę in
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ſcholio propoſ. </
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<
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<
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<
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<
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<
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Idẽ fiet, etiã ſi arcus E L, L A, &</
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<
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">c. </
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<
s
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">nõ fint æquales, dummodo per puncta reſpondentia L, M, &</
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<
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xml:id
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echoid-s5176
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<
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xml:id
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echoid-s5177
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parallelæ diametris Ellipſis, &</
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echoid-s5178
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<
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echoid-s5179
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echoid-s5180
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coniungentem
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duxerimus, Ellipſis deſcripta erit. </
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echoid-s5181
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<
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xml:id
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echoid-s5182
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xml:space
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"/>
</
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</
div
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</
text
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</
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