Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

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5442 rectæ A I, I G, rectis D K, K H, æquales ſunt; & reliquæ I L, K M, ex
ſemidiametris A L, D M, vt in prima figura, vbi puncta I, K, cadunt in ſe-
midiametros A L, D M, vel certe erunt & totæ I L, K M, æquales, vt in ſe-
cunda figura, vbi puncta I, K, cadunt in ſemidiametros A L, D M, productas

60[Figure 60] ad A, & D. Quia igit̃
I L, L B, rectis K M,
M E, æquales ſunt; cõ
tinentq́ue angulos ad
L, M, æquales, ob æ-
1127. tertij. qualitatẽ arcuũ A B,
D E; erunt & baſes
I B, K E, æquales.
224. primi. Quamobrem cum la-
tera G I, I B, lateri-
bus H K, K E, æqua-
lia ſint, contineantq́;
angulos G I B, H K E,
æquales, nimirum rectos, ex defin. 3. lib. 11. Eucl. erunt & baſes G B, H E, æ-
334. primi. quales. quod eſt propoſitum. Facilius idem concludetur, ſi perpendiculares
ex G, H, in plana circulorum A B C, D E F, demiſſæ cadant in puncta A, D,
vt in tertia figura. Nam quia rectæ G A, A B, rectis H D, D E, æquales ſunt,
4429. tertij. ob æquales arcus A G, D H, & A B, D E, continentq́; angulos æquales, vt-
pote rectos, ex defin. 3. lib. 11. Eucl. erunt baſes G B, H E, æquales. Si igitur
554. primi. in diametris circulorum æqualium, æqualia ſegmenta, & c. Quod erat oſten
dendum.

THEOREMA 13. PROPOS. 13.

6618.

SI in ſphæra ſint paralleli circuli, & deſcriban
tur maximi circuli, qui vnum quidem parallelo-
rum tangant, reliquos vero ſecent; circunferentię
parallelorum interceptæ inter eos maximorum
circulorum ſemicirculos, qui non concurrunt,
ſimiles erunt; maximorum vero circulorum cir-
cunferentiæ inter duos quoſcunque parallelos in-
terceptæ, erunt æquales.

SINT in ſphæra paralleli circuli A B, C D E, F G H, quieundem polũ
771. huius. habebunt, nempe I. Circuli autem maximi A F K, B H K, tangant parallelũ
A B, in punctis A, B, & reliquos ſecent in punctis F, C, L, M; H, E, D, G:
ſeipſos aũt mutuo ſecent in K, N, vt ſint ſemicirculi K M N, N F K; K G N,
N H K. Maximi enim circuli ſe ſecant mutuo bifariam. Sumatur quoque ar
8811. 1. huius.

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