Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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vero latera AB, AC, ſunt inæqualia, ſit AC, maius, ex quo abſcindatur re-
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cta CE, minori lateri AB, æqualis, & </
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<
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">ex A, E, ad tertium latus BC, perpen
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diculares demittantur AD, EF, quarum vtraq;
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<
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">cadet intra triangulum, quando angulus B, ma-
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iori lateri AC, oppoſitus acutus eſt. </
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& </
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<
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ſit, quam B. </
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<
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xml:space
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">Quare perpendicularis AD, intra
<
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Schol. 13.
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ſecundi.
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Schol. 12.
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ſecundi.</
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triangulum cadet, ac proinde & </
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ris EF. </
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<
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">Quando vero angulus B, obtuſus eſt,
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cadet quidem AD, ſemper extra triangulum,
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at EF, cadere poteſt vel extra etiam, vel in pun
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ctum B, vel intra triangulum. </
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<
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">18. primi.
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Coroll. 4.
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ſexti.</
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dem erit demonſtratio. </
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<
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">Nam cum AD, EF, ſint
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parallelæ, erunt triangula CEF, CAD, ſimi-
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lia. </
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">4. ſexti.</
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in definitionibus ſinuum tradidimus, poſito ſinu toto CE, recta EF, ſit ſinus
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anguli C; </
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<
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CE, hoc eſt, latus AB, ad EF, ſinum anguli C, ita latus CA, ad AD, ſinum
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anguli ABD: </
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<
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">Et permutando, vt latus AB, ad latus AC, ita EF, ſinum
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anguli C, ad AD, ſinum anguli ABD, hoc eſt, in poſteriori triangulo, ad
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ſinum anguli ABC, cum duo anguli ad B, æquales ſint duobus rectis, & </
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<
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inde eundem ſinum habeant, vt in definitionibus ſinuum docuimus. </
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conſtat, ita eſſe minus latus AB, ad maius AC, vt eſt EF, ſinus anguli C, mi-
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nori lateri oppoſiti ad AD, ſinum anguli ABC, maiori lateri oppoſiti: </
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conuertendo, ita eſſe maius latus AC, ad minus AB, vt eſt AD, ſinus angu-
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li ABC, maiori lateri oppoſiti ad EF, ſinum anguli C, minori lateri oppo-
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ſiti. </
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C, ad ſinum anguli A: </
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<
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ſinum anguli C. </
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<
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inæqualia, (ſi forte æqualia non ſunt) ducas ad latus oppoſitum lineam per-
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pendicularem, & </
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facto ab altero puncto extremo maioris lateris, vbi cum tertio latere coniun-
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gitur, vt à nobis factum eſt, &</
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<
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<
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rectangulum ABC: </
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">de rectangulo enim in
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principio huius demonſtrationis iam eſt de-
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monſtratum. </
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AC, ita ſinum anguli C, ad ſinum anguli B:
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</
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<
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guli B, ad ſinum anguli C, &</
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A, vbi duo late-
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latus AB. # ſin. ang. C.
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latus AD. # ſin. ang. D.
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latus AC. # ſin. ang. B.
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ra aſſumpta co-
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eunt, ad tertiũ
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latus BC, per-
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pẽdiculari AD,
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quæ vel i@tra triangulum cadet, vel extra, prout anguli B, & </
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