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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lineæ curuæ per puncta A, C, D, B, deſcriptæ æquales ſunt maiori axi AB, vt vult illa ꝓpoſitio Apollonij.</
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">INVENIEMVS quoque puncta F, G, pro clauiculorum locis hac ratione, & </
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rũ ad Ellipſim
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deſcribendam
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alia ratione in-
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ueniuntur.</
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propterea quod, cum minor axis fermè æqualis eſt maiori, arcus cir culorum ex C, vel D, deſcripti ualdè
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obliquè ſecant rectam A B.
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<
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dium eſt axis maioris, bifa-
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riã in H, deſcribatur ex H,
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ad interuallũ H B, vel H E,
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ſemicir culus B I E, & </
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<
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accõmodetur recta B I, dimi-
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dio minoris axis D E, æqua-
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lis, ducatur{q́ue} recta E I. </
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<
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rectã E I, æqualem eſſe tam
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rectæ E F, quàm rectæ E G,
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atque adeò, ſi abſcindantur
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rectæ E F, E G, ipſi E I,
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æquales, inuenta eſſe eadem
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puncta F, G, pro locis claui-
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culorum. </
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<
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dratum ex B E, æquale eſt
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quadratis ex E I, I B; </
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<
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quadratum ex D G, quadra-
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tis ex D E, E G, quàm qua-
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dratum ex D F, quadratis ex
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D E, E F, æquale: </
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<
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dratũ ex BE, tã quadrato ex
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D G, quàm quadrato ex D F,
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æquale, quod hæ lineæ æqua-
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les ſint ex conſtructione; </
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quadratũ ex B I, æquale qua-
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drato ex D E, quòd per con-
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ſtructionẽ æquales quoque ſint poſitæ rectæ B I, D E; </
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<
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">crit reliquũ quadratũ ex E I, reliquo quadrato tam ex
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E G, quàm ex E F, deſcripto æquale, ac proinde recta E I, rectis E G, E F, æqualis erit, quod eſt propoſitũ.</
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<
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lipſis circa datũ
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axem maiorem,
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& per datũ pun
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ctum deſcriba-
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tur.</
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re debeat Ellipſis circa axem A B, deſcripta, reperiemus minorem axem, hoc eſt, latitudinem Ellipſis,
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& </
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<
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">puncta F, G, in quibus affigendi ſunt clauiculi, hac ratione. </
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E, ad A B, perpendicularis C D, & </
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<
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ſi C D, parallela. </
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<
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">Deinde per ea, quæ in problemate tertio ſcholij propoſ. </
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<
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ſtr ata ſunt à nobis, fiat, vt rectangulum ſub A L, L B, contentum ad rectangulum contentum ſub A E,
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E B, hoc eſt, ad quadratum ex A E, vel E B, (Hoc enim rectangulum quadratum eſt, ob æqualitatem re-
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ctarum A E, E B) ita quadratum ex K L, ad aliud quadratũ, cuius latus ſit E D, vel E C. </
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monſtratis ab Apollonio propoſ. </
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<
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<
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<
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te docuimus, inueniemus puncta F, & </
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<
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<
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">ITA autem expedite quadratum lateris E D, vel E C, quæſiti comperiemus. </
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<
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">Ex E, ad interuallum
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E A, vel E B, ſemicir culus deſcribatur A M B, quem recta L K, producta ſecet in M; </
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<
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propoſ. </
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<
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<
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">Euclidis, recta L M, media proportionalis inter A L, L B, atq; </
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<
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ctangulo ſub A L, L B, cõtento æquale. </
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<
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">Vnde facili negotio reperiemus quadratũ, ad quod eandẽ propor-
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tionẽ habeat quadratũ ex L K, quã habet quadratũ ex L M, hoc eſt, rectangulũ ſub A L, L B, comprehen-
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ſum, ad quadratum ex E A, vel E B, hoc eſt, ad rectangulum ſub A E, E B, contentum, ſi tribus rectis
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<
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L M, E A, L K, quartam proportionalem inueniamus E D; </
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<
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quadrata ſupra rectas L M, E A, L K, E D, deſcripta, quam ipſęmet rectæ. </
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<
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quartam proportionalem E D, reperiemus. </
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<
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">Ductis rectis duabus N O, N P, facientibus angulum in N,
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quemcunque, ſumatur N Q, ipſi L M, & </
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<
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<
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agatur per O, ipſi Q R, parallela O P. </
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<
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<
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">cum ſit, vt N Q, hoc eſt,
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<
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L M, ad Q O, hoc eſt, ad E A, ita N R, hoc eſt, L K, ad R P. </
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<
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habebimus minoris axis dimidium E D, & </
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<
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<
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">CAETERVM loco clauiculorum vti poterimus inſtrumento quodam ad ſimilitudinẽ circini fabri-
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pro Ellipſi per
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filum deſcriben
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da.</
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cato, cuius crura in extremitatibus ſint reſecta, & </
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<
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">frusta abſciſſa ita adaptata, vt hinc inde poſſint di-
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moueri, & </
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<
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">cochleolis aſtringi, vt quãtumuis dilatentur circini crura, ſemper fruſta illa cochleolis aſtricta
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recta ſint ad planũ, in quo Ellipſis deſcribenda eſt. </
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<
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naliculos quoſdam per circuitum inciſos, ita vt filum in ijs circumuolutum neque ſurſum aſcendat, </
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