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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non deſcribitur ſemicirculus circa diametrum B C, quia non ſecaret rectã E M. </
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<
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xml:space
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ſemicirculi ſe interſecant in recta E M, in deſcriptione Ellipſis, vt@emicirculi F P H, R V S, in
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priori Ellipſi, v@i rectę E P, E V, æquales ſunt, atque perpendiculares k P, T V, ſumptę
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pſis ęquales in tertijs figuris.</
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<
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<
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harũ media -
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runi figurar@
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vbi eſt P, po-
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ne M, & loco
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M, repone P.</
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<
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<
s
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xml:space
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">SED iam demonſtremus, ſectionem conicam tranſire in plano per puncta Q, P, &</
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<
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ſuperioris de-
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ſcriptionis.</
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diametrum D E, atque adeo lineam per ipſa puncta in plano aptè deſcriptam, eſſe conicam ſectio-
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nem, vt diximus. </
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<
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xml:space
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">Ducto in primis figuris per rectam F H, plano, quod baſi coni æquidiſtet, erit
<
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ſectio facta F X H, circulus, per 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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ctio ſit recta X Y, quæ per K, tranſibit, vbi ſe ſecant rectæ D E, F H, & </
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<
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xml:space
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">vbi circulus F X H, per rectã
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F H, ductus ſectioni conicæ occurrit. </
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<
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xml:space
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">Et quoniam plana B C, F H, parallela ſecantur plano D E, fa-
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ciente conicam ſectionem, erunt communes ſectiones Z α X Y, parallelæ: </
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<
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xml:space
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ctam B C, perpendicularis, (vt enim fiat ſectio aliqua conica, neceſſe eſt, vt ſectio communis pla-
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ni ſecantis, & </
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<
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xml:space
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">baſis coni, qualis eſt recta Z α, perpendicularis ſit ad baſim trianguli per axem, vt
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conſtat
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ex propoſ. </
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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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">Apollonii) & </
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<
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xml:space
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">anguli B E Z, F K X, æquales ſunt, propte-
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<
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rea quòd rectæ B E, E Z, rectis F K, k X, ſunt parallelæ. </
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<
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">Igitur erit & </
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<
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que adeo X K, ad F H, perpendicularis, ac proinde X K, in ſemicirculo F X H, media erit propor-
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tionalis inter F K, K H, ex 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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ratione media eſt proportionalis inter F E, E H, hoc eſt, inter eaſdẽ F k, K H, in primis figuris, at-
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que adeo ipſi X K, in primis figuris æqualis: </
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<
s
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xml:space
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">(ſumptæ enim ſunt E F, E H, in ſecundis figuris, ip-
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ſis K.</
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<
s
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xml:space
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">F, K H, in primis æquales) Eſt autem eadem E P, in ſecundis figuris, ipſi k P, in tertiis æqua-
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lis. </
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<
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<
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">k P, in tertiis figuris, ipſi K X, in primis, ęqualis eſt. </
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<
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xml:space
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per X, in conica ſuperficie tranſeat ſectio conica, tranſibit eadem in plano per punctum P; </
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<
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niam hac ratione, poſito puncto K, tertiarum figurarum in puncto k, primarum, ita vt diameter
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k D, tertiarum congruat diametro k D, primarum, congruet perpendicularis k P, in tertiis figu-
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ris, perpendiculari k X, in primis; </
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<
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xml:space
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rectarũ k P, k X,) & </
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<
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<
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demq́ue ratione oſtendemus, ſectionem eandem tranſire per punctum Q, & </
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<
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xml:space
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ſunt. </
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<
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<
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<
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<
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