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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ſa axis eſt Hyperbolarum, cum ſecet ordinatim applicatas ad angulos rectos, vt ex propoſ. </
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<
s
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">PRO Ellipſi denique duo rurſus lemmata præmittenda ſunt, quæ ſequuntur, quadrant{q́ue} in om-
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nem conum tam rectum, quàm ſcalenum.</
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<
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<
s
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">diametro tranſuerſa Ellipſis, inuenirelatus rectum Ellipſis.</
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ris recti Ellipſis,
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cuius tranſuer-
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ſa diameter in
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cono data ſit.</
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<
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">SIT datus conus A B C, in quo triangulum per axem A B C; </
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<
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pla@@ faciente Ellipſim E F, iuxta propoſ. </
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<
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<
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<
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<
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">Apollonij, ita vtrecta E F, ſit diame-
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ter tra@ſuerſa Ellipſis. </
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<
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<
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">Per A, ducatur
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A G, ipſi E F, parallela ſecans B C, productam in G; </
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<
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xml:space
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G, & </
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<
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">alterum latus trianguli per axem, ad A G, ita A G, ad G H. </
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<
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">Rurſ{us} fiat, vt G H,
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ad G B, rectam inter idem punctum G, & </
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<
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">alterum latus trianguli per axem, ita E F, dia-
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<
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xml:space
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meter tranſuerſa ad E I. </
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<
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">Dico E I, eſſe latus rectum Ellipſis, id eſt, eſſe rectam, iuxta quã
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poſſunt ordinatim applicatæ ad diametrum. </
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<
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B G, G C, rec
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tis inter punctum G, & </
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<
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<
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plicetur rectangulum C H, ſub G C, G H, contentum; </
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<
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">quod æquale crit quadrato ex A G;
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quòd tresrectæ C G, A G, G H, ſint continuè proportionales ex conſtructione; </
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<
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B G H, vna linea recta, propter duos angulos rectos ad G. </
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<
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ad G B, ita E F, ad E I; </
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">vt autem H G, ad G B, ita eſt H C, rectangulum ad rectangulũ
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C B, hoc eſt, quadratum ex A G, ad rectangulum ſub B G, G C, contentum. </
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<
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latus rectum eſt Ellipſis E F, ex propoſ. </
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<
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<
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<
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t
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a pars rectan-
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guli ſub diame-
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tro tianſuerſa
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Ellipſis, & latere
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recto compre-
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henſi applicetur
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ad tranſuerſam
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diametrum ex
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vtraque parte,
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ita vt deficiat fi
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gura quadrata.</
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ſunt or dinatim applicatæ &</
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<
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cto comprehenſi, ad tranſuerſam diametrum ex,
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vtraque parte applicare, ita vt de-
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ficiat figura quadrata.</
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<
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ctum E I, media proportionalis A B, quæ bifariam ſecetur in C. </
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<
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A B, rectangulo ſub E F, E I, æquale, atque adeò quadratum ex A C, quod ex ſc
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holio pro-
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<
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poſ. </
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<
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<
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A B, quartæ parti rectanguli ſub E F, E I, æquale
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crit. </
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<
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ad diametrum tranſuerſam E F, ex vtraque par-
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te æquale rectangulum, deficiens figura quadrata,
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hac arte. </
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<
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niam per ea, quæ ad definitiones ſecundas lib. </
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</
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<
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ctum E I, minus est diametro tranſuerſa E F, hoc
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est, diametro maiore Ellipſis, erit quoque A B, media proportionalis inter E F, E I, </
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