Full text: Bithynius, Theodosius: Theodosii Tripolitae Sphaericorum libri tres

cus K O, arcui N A, & arcus K P, arcui N B, æ-
qualis, vt ſint quoque ſe
micirculi A M O, O F A; B G P, P H B. Eruntigi-
tur ſemicirculi A M O,
B H P, non coeuntes, cũ
ſe mutuo non ſecent. Eo
dem modo nõ coeuntes
erunt ſemicirculi B G P,
A F O. Dico arcus paral
lelorum A B, L E, M H,
interceptos inter ſemi-
circulos A M O, B H P,
non coeuntes ſimiles eſ-
ſe, necnon & arcus A B,
C D, F G, interceptos in
ter ſemicirculos B G P,
A F O, non concurren-
tes ſimiles eſſe: Arcus vero maximorum circulorum A C, A L, B D, B E, æ-
quales eſſe; necnon & arcus C F, L M, D G, E H: quorum illi inter paralle-
los A B, C D E, hi vero inter parallelos C D E, F G H, interijciuntur: Eo-
demq́; pacto æquales eſſe arcus A F, A M, B G, B H, inter parallelos A B,
F G H, interiectos. Per polum enim I, & puncta contactuum A, B, circuli
maximi deſcribantur Q A I R, S B I T, ſecantes parallelos in Q, S, V, X. Tranſibunt hi circuli maximi per polos quoque circulorum A F K, B H K; ac proinde bifariam ſecabunt ſegmenta C A L, D B E, C V L, D X E: necnõ
ſegmenta F A M, G B H, F Q M, G S H. Præterea ijdem circuli ad angulos
rectos ſecabunt parallelos A B, C D E, F G H, & maximos circulos A F K,
B H K. Quoniam igitur diametris circulorum æqualium A F K, B H K, inſi
ſtunt ad angulos rectos ſegmenta circulorum æqualia, nempe ſemicirculi in-
choati à punctis A, B, & per I, tranſeũtes, donec iterũ ſecent circulos A F K,
B H K; ſuntq́; arcus æquales A I, B I, quòd ex defin. poli recta I A, IB æqua
les ſint; qui quidem minores ſunt dimidijs ſemicirculorum partibus: (cum
enim dimidij ſint arcuum A I R, B I T, quòd, ex defin. poli, rectæ ex I, ad
puncta A, B, R, T, atque adeo arcus quoque ſint æquales: ſint autem arcus
A I R, B I T, ſemicirculo minores, quòd ſemicirculi tendant ex A, & B, per
I, vſque ad circulos A F K, B H K; erunt arcus A I, B I, minores dimidijs par
tibus illorum ſemicirculorum.) ſunt quoque æquales rectæ I C, I E, ex po-
li defin. erunt arcus A C, B E, æquales: Eſt autem A C, ipſi A L, & B E, ipſi
B D, æqualis, propterea quòd arcus C A L, D B E, bifariam ſecantur, vt de-
monſtratum eſt. Quatuor ergo arcus A C, A L, B E, B D, æquales ſunt. Eo-
dem modo oſtendemus, æquales eſſe quatuor arcus A F, A M, B H, B G; ac
propterea & reliquos C F, L M, E H, D G, qui quidem ſinguli inter binos
parallelos intercipiuntur. Quodſecundo loco proponebatur demonſtrandũ.

89.1.

1. huius.
11. 1. huius.
055-01
20 1. huius.
5. huius.
9. huius.
15. 1. huius.
28. tertij.
28. tertij.
11. huius.
9. huius.

QVIA vero arcus toti C A L, D B E, æquales ſunt, quòd ipſorum dimi
dia æqualia ſint, vt demonſtratum eſt; erunt & rectæ ſubtenſæ C L, D E, æ-
quales, quæ quidem arcubus quoque C V L, D X E, ſubtenduntur; ac pro-

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