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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M L, ita rectangulum ſub C E, E A, ad rectangulum ſub C M, M A. </
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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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<
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xml:space
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<
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xml:space
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">Apollonij, ſi circa diametrum maiorem AC, & </
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<
s
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xml:space
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">minorem H I, (Eſt enim A C, maior quàm
<
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H I, cum A C, diameter circuli A F C G, ęqualis ſit diametro F G, eiuſdem circuli) ellipſis deſcri-
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batur, & </
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>
<
s
xml:id
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xml:space
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">ex quouis puncto ipſi H E, parallela du-
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<
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catur, hoc eſt, ordinatim applicata ad diametrũ
<
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A C, quadratum ex H E, ad quadratum illius pa-
<
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rallelæ eſt, vt rectangulum ſub C E, E A, ad re-
<
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ctangulum ſub partibus diametri A C, quas pa-
<
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rallela illa facit. </
s
>
<
s
xml:id
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xml:space
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">Igitur punctum L, in illam El-
<
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lipſim cadet, cuius maior diameter A C, & </
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<
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<
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xml:space
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nor HI; </
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<
s
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xml:space
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">quandoquidem eſt, vt quadratum ex
<
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H E, ad quadratum ex L M, ita rectangulum ſub
<
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C E, E A, ad rectangulum ſub C M, M A; </
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>
<
s
xml:id
="
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xml:space
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">alias
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pars foret ęqualis toti. </
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>
<
s
xml:id
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xml:space
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preserve
">Si enim illa Ellipſis non
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tranſit per punctum L, tranſeat ſi fieri poteſt, per
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N. </
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<
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xml:space
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">Erit igitur per propoſ. </
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<
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xml:space
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<
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<
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xml:space
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">1. </
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<
s
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xml:space
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">Apollonij,
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vt rectangulum CE, E A, ad rectangulum ſub C M, M A, hoc eſt, vt quadratum ex H E, ad qua-
<
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dratum ex L M, ita quadaatum ex H E, ad quadratum ex N M. </
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<
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xml:space
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">Aequalia ſunt igitur quadrata ex
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L M, & </
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<
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">N M, atque adeò & </
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<
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xml:space
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">rectę L M, N M, ęquales, totum & </
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<
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xml:space
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">pars. </
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<
s
xml:id
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xml:space
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">Quod eſt abſurdum.
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</
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<
s
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xml:space
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">Tranſit ergo Ellipſis illa per punctum L, ac proinde punctum L, in Ellipſim cadit, cuius maior
<
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<
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">20</
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diameter A C, & </
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<
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">minor HI. </
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<
s
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xml:space
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">Eodem modo oſtendemus & </
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<
s
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xml:space
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">alia puncta, in quæ à circunferentia
<
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circuli. </
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>
<
s
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xml:space
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">A B C D, perpendiculares cadunt, in eadem Ellipſi eſſe. </
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<
s
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xml:space
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">Quocirca ſi à circunferentia cir-
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culi maximi in ſphæra, &</
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<
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<
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">Quod erat demon ſtrandum.</
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<
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<
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">HOC theorema proponitur à Federico Commandino vniuer ſalius in libello de horologiorum deſcri-
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ptione; </
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>
<
s
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xml:space
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">adeo vt etiamſi planum, in quo circulus A F C G, non ſecet circulum inclinatum A B C D, per
<
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centrum, vel nullo modo, & </
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<
s
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xml:space
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">ſiue A B C D, ſit maximus circulus in ſphæra, ſiue quicunque, tamen per-
<
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pendiculares ductæ à circunferentia circuli A B C D, ad planum A F C G, cadant in Ellipſim. </
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<
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">Nam ſi
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planum, in quo circulus A F C G, non ſecet circulum A B C D, per centrum, vel nullo modo, ita propo-
<
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ſitum colligit. </
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>
<
s
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xml:space
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">Ducto alio plano ipſi A F C G, æquidiſtante, quod circulum A B C D, ſecet in centro E, ſi-
<
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militer demonſtrabitur, vt prius, perpendiculares à circuli A B C D, circunferentia ad planum illud de-
<
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miſſas in Ellipſim cadere: </
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>
<
s
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xml:space
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">quæ quidem lineæ, cum vlterius productæ ad planum A F C G, quod illi æqui-
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diſtat, eandem poſitionem habeant, cadent & </
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<
s
xml:id
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xml:space
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">eoloco in Ellipſim, cuius maior diameter æqualis erit dia-
<
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metro A C, circuli A B C D, minor vero æqualis interuallo H I, perpendicularium B H, D I, quæ ab ex-
<
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tremitatibus alteri{us} diametri B D, ducuntur.</
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</
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<
s
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xml:space
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">NOS autem propoſuimus theorema de circulis maximis in ſphæra duntaxat, quia in his ſolis appare
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bit eius vſus in noſtra hac Gnomonica.</
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<
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<
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xml:space
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<
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<
s
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xml:space
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">IN circunferentia circuli maximi in ſphęra ad alium circulum ma-
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ximum inclinati ſumptis duobus punctis extremis diametri commu-
<
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nem eorum ſectionem ad rectos angulos ſecantis, quo loco perpendi-
<
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culares ab his ductæ ad alium circulum cadant, ſi nota fuerit inclina-
<
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tio, inueſtigare.</
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<
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</
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<
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<
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<
s
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xml:space
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">SIT in ſphęra circulus maximus A B C D, ad circulum maximum A F C E, inclinatus, ſitq́;
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</
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<
s
xml:id
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xml:space
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">eorum ſectio communis diameter A C, ad quam in plano circuli A B C D, per centrum G, alia
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diameter ducatur perpendicularis B D. </
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<
s
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xml:space
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">Oportet igitur inueſtigare, quo loco perpendiculares à
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punctis D, B, in planum circuli A F C E, demiſſę cadant. </
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<
s
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xml:space
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">In plano circuli A F C E, ducatur alia
<
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<
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xml:space
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">Inuentio pun-
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ctorum, in quæ
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cadunt perpen-
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diculares ab ex-
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tremitatibus,
<
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diametri circu-
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li ad alium cir-
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culum inclina-
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ti
<
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.</
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diameter E F, ad A C, perpendicularis, ſitq́; </
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<
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">angulus inclinationis, quę nota ponitur E G H, ita vt
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arcus E H, æqualis ſitarcui inclinationis circuli A B C D, ad circulum A F C E; </
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">ab H, ducatur
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HI, ad EF, perpendicularis. </
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<
s
xml:id
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xml:space
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">Dico perpendicularem à D, ad planum circuli A F C E, demiſſam
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cadere in punctum I. </
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<
s
xml:id
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xml:space
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">Ducto enim per E G, D G, plano faciente in ſphæra ſemicirculum E D F, ex
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propoſ. </
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<
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<
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<
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">1. </
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<
s
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xml:space
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">Theodoſii, erit hicad circulos A F C E, A B C D, rectus. </
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<
s
xml:id
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xml:space
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">(Nam cum C G, per-
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pendicularis ſit ad E G, D G, erit eadem quoque ad planum per E G, D G, ductum, id eſt, ad ſe-
<
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<
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">4. vndec.</
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micirculum E D F, recta, atque adeo & </
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<
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">plana circulorum A F C E, A B C D, per C G, ducta </
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