Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ad angulũ IGE, vt mox demonſtrabimus: </
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BGC, æqualis; </
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rallelorũ OE, BC, factæ à plano AB, parallelæ; </
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<
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munes ſectiones eorundem planorum factæ à plano AE.) </
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<
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proportio rectę GI, ad rectam IK, hoc eſt, ad rectam ſibi æqualem IH, quàm
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anguli BGC, ad angulum DGE: </
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ita eſt arcus BC, ad arcum DE. </
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<
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ad rectam IH, quàm arcus BC, ad arcum DE: </
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GD, ad DN, hoc eſt, ita tota diameter DL, ad totam diametrum DM.
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(ſunt enim DN, OH, communes ſectiones planorum parallelorum DF,
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OE, factæ à plano AB, parallelæ.) </
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diametri ſphæræ ad DM, diametrum paralleli DF, quàm arcus BC, ad arcum
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DE. </
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li, &</
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">_QVOD_ autem maior ſit proportio rectæ _GI,_ ad rectam _IK,_ quàm anguli _IKE,_
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ad angulum _
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E,_ hoc theoremate propoſito demonſtrabimus.</
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<
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">IN omni triangulo rectangulo, ſi ab vno acutorum angulorum
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vtcunque ad latus oppoſitum linea recta ducatur; </
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<
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tio huius lateris ad eius ſegmentum, quod prope angulum rectum
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exiſtit, quàm anguli acuti, quem linea ducta cum prædicto latere, ef-
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fecit, ad reliquum angulum acutum trianguli.</
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<
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">SIT triangulum rectangulum EGI, habens angulum I, rectum,
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ducaturque ab angulo acuto IEG, ad latus oppoſitum GI, recta li-
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nea EK, vtcunque. </
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<
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">Dico maiorem eſſe proportionem rectæ GI, ad IK,
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quàm anguli acuti IKE, ad angulum acutum IGE. </
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per G, recta GA, ipſi EK, parallela, occurrens rectæ IE, protractæ
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in A. </
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erit angulus IEG, acutus, & </
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rea AEG, obtuſus. </
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in triangulo GEI, maius eſt latere GI;
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in triangulo verò AEG, minus latere
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AG. </
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ad interuallum GE, deſcriptus ſecabit
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rectam GI, productam vltra I, nempe
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in B, rectam vero GA, citra A, vt
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in C. </
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<
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maius eſt ſectore GCE, maior erit proportio trianguli GAE, ad
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triangulum GEI, quàm ſectoris GCE, ad triangulum GEI: </
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autcm maior adhuc proportio ſectoris GCE, ad triangulum GEI, quàm
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