Clavius, Christoph, Geometria practica

Table of contents

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[351.] THEOR. 5. PROPOS. 10.
[352.] THEOR. 6. PROPOS. 11.
[353.] COROLLARIVM.
[354.] THEOR. 7. PROPOS. 12.
[355.] PROBL. 6. PROPOS. 13.
[356.] PROBL. 7. PROPOS. 14.
[357.] THEOR. 8. PROPOS. 15.
[358.] PROBL. 8. PROPOS. 16.
[359.] COROLLARIVM.
[360.] SCHOLIVM.
[361.] PROBL. 9. PROPOS. 17.
[362.] PROBL. 10. PROPOS. 18.
[363.] PROBL. 11. PROPOS. 19.
[364.] PROBL. 12. PROPOS. 20.
[365.] THEOR. 9. ROPOS. 21.
[366.] PROBL. 13. PROPOS. 22.
[367.] PROBL. 14. PROPOS. 23.
[368.] PROBL. 15. PROPOS. 24.
[369.] PROBL. 16. PROPOS. 25.
[370.] PROBL. 17. PROPOS. 26.
[371.] COROLLARIVM.
[372.] PROBL. 18. PROPOS. 27.
[373.] THEOR. 10. PROPOS. 28.
[374.] SCHOLIVM.
[375.] THEOR. 11. PROPOS. 29.
[376.] SCHOLIVM.
[377.] THEOR. 12. PROPOS. 30.
[378.] THEOR. 13. PROPOS. 31.
[379.] THEOR. 14. PROPOS. 32.
[380.] PROBL. 19. PROPOS. 33.
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page |< < (360) of 450 > >|
388360GEOMETR. PRACT.
THEOR. 11. PROPOS. 29.
1. Arcvs tres FA, AB, BG, ſextæ partes circuliſunt, quod rectæ eos ſubtẽ-
dentes
ſemidiametri ſint circuli FABG, ex conſtructione.
Igitur FABG, ſemi-
280[Figure 280]1131. tertij. circulus eſt, cuius diameter FG;
ideoque 22ſchol. 27.
tertij
.
FEG, in ſemicirculo rectus:
Et diameter F G, re- ctæ AB, parallela, ob arcus A F, B G, æquales. Et
quoniã
, vt conſtat ex demonſtratione praxis ſcho-
lij
propoſ.
@0. & 11. lib. 1. Euclid. recta C D, ſecat re-
3329. primi. ctam AB, bifariam in M, &
ad angulos rectos; ſe- cabit eadem parallela quoque F G, ad angulosre-
44ſchol. 27.
tertij
.
ctos in C.
Eadem quoq; CD, ſecabit arcum A B, bifariamin E, ac propterea toti arcus EF, EG, ęqua
556. quanti. les erunt, videlicet quadrantes;
ideoq; rectæ EF, EG, latera ſunt quadrati in circulo F A B G, deſcri-
66ſchol. 34.
primi
.
pti, eiuſque diameter FG.
Igitur anguli F, G, ſemi- recti erunt: ac proinde cum anguliad C, recti ſint,
7732. primi. erunt quo que O E M, NEM, ſemirecti;
ideoq; & EOM, ENM, ſemirecti. Ac proinde tam latera E M, N O, quam E M, M N, 886. primi. qualia: atqueidcirco & OM, NM, inter ſe æqualia erunt; nec non & totæ OB,
NA
, æquales erunt.
Immo & EO, EN, erunt æquales, quod latera EM, 994. primi. laterib. EM, MN, æqualia ſint, cõprehendãtq; angulos æquales, vt pote rectos.
2. Deinde quialatera AN, AI, lateribus BO, BH, æqualia ſunt; ſuntq; an-
guli
N, O, ſemirecti æquales, &
vterque reliquorum angulorum I, H, minorre-
101019. primi. cto;
quod vterque minor ſit ſemirecto ad O, & N; propterea quod tam latus AN, minus eſt latere AI, ꝗ̃ latus B O, latere BH: eruntper ea, quæ ad finem lib.

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