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 PRIMVS.
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los æquales illis, quos ordinatim applicatæ cum diametro Paraboles conſtituunt. </
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<
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niet hæc ratio conis Scalcnis, cum triangulum per axem ad coni baſim rectum eſt, quia tunc, ex 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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xml:space
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">ordinatim applicatæ ſunt ad diametrum Paraboles perpendiculares, quemadmodum in
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cono recto, ita vt E H, ſit quoque axis Parabolæ.</
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<
s
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xml:space
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">PRO hyperbolis verò oppoſitis demonſtranda ſunt duo alia lemmata, quæ omni cono tam recto,
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quàm ſcaleno conucniunt; </
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<
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<
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">diametro tranſuerſa Hyperbolarum oppoſitarum, inuenire
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ris recti hyper-
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bolarũ oppoſi-
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tarum, quatũ
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diameter tranſ-
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uerſa in cono
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data ſit.</
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latus rectum Hyperboles.</
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<
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xml:space
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">SIT datus conus A B C, in quo triangulum per axem A B C, producatur {q́ue} conus vnà
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cum triangulo per axem ad verticem A, vt fiant duo coni A B C, A D E, ad verticem
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A, coniuncti. </
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<
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">Secetur quoque vtraque ſuperficies conica plano non per verticem facien
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te ſectiones F G H, I K L, quæ hyperbolæ ſunt oppoſitæ, ex propoſ. </
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<
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<
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<
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<
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quarum diameter tranſuerſa communis F I, & </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0051-01
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tera recta æqualia. </
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<
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ita inueniem{us}. </
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<
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xml:space
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">Per A, ducatur A M, ipſi F I,
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parallela ſecans B C, in M; </
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<
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">fiat{q́ue} vt C M, altera
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parsbaſis, ad A M, ita A M, ad M N. </
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<
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fiat, vt M N, ad B M, alteram baſis partem, ita
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xml:space
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<
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xml:space
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">12. ſexti.</
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F I, tranſuerſa diameter ad F O. </
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<
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xml:space
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">Dico F O, eſſe la-
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tusrectum vtriuſque Hyperboles; </
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<
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ctam, iuxta quam poſſunt ordinatim applicatæ ad
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diametrum vtriuſque hyperboles. </
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<
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ctangulum B C, contentum ſub baſis partibus B M,
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M C; </
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<
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">& </
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<
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">ad M C, applicetur rectangulum C N, ſub
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<
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<
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M C, M N, contentum, quod æquale erit quadrato
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rectæ A M, propterea quòdtres rectæ M C, A M,
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M N, continuè proportionales ſunt ex conſtructio-
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ne: </
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<
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">erit{q́ue} B M N, vna linearecta, quòd duo an-
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<
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guli ad M, recti ſint. </
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<
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M N, ad B M, ita F I, ad F O; </
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<
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">Vt autem M N, ad B M, ita eſt rectangulum C N, hoc est,
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<
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quadratum ex A M, ad rectangulum B C, ſub baſis partibus B M, M C, contentum; </
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<
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quoque vt quadratum ex A M, adrectangulum ſub B M, M C, ita tranſuerſa diameter
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F I, ad rectam F O. </
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<
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xml:space
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">Eſt igitur F O, latus rectum hyperboles, ex 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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nij, hoc eſt, Recta, iuxta quam poſſunt or dinatim applicatæ, &</
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<
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<
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quarta pats ſub
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diametro trãſ-
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uerſa hyperbo-
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les, & latere re-
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cto cõprehenſi
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applicetur ad
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diametrũ trã
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ſ-
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uerſam ex vtra-
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que parte, ita vt
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excedat figura
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quadraata.</
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<
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<
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<
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<
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re recto comprehenſi ad tranſuerſam diametrum ex vtraque parte applicare, ita vt
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excedatfigura quadrata.</
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<
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<
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<
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<
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ctum F O, media proportionalis A B, quæ bifariam ſecetur in C. </
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<
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<
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<
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ex A B, æquale rectangulo ſub F I, F O; </
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<
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">at que adeo quadratum ex A C, quod ex ſcholio
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<
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propoſ. </
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<
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<
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<
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<
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">Euclidis, quarta pars eſt quadrati ex A B, quartæ parti rectanguli ſub F I,
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F O, æquale erit. </
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<
s
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">Huic igitur quadrato ex A C, applicabim{us} ad diametrum tranſuer ſam
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F I, ex vtraque parte, æquale rectangulum excedens figura quadrata, hoc modo. </
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<
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recta F I, bifariam in D, fiat angulus rectus H K L, & </
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<
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K L, rectæ D I, æqualis, connectatur{q́ue} recta H L, quæ maior erit, quàm recta K L, hoc
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eſt, quàm D I, propterea quòd H L, maiori angulo opponatur, quàm K L. </
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<
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F I, in vtramque partem, abſcindantur vtrinque ex D, rectæ D Q, D R, ipſi H L, æqua-
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les. </
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<
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