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

Scan	Original
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68
81	69
82	70
83	71
84	72
85	73
86	74
87	75
88	76
89	77
90	78
91	79
92	80
93	81
94	82
95	83
96	84
97	85
98	86
99	87
100	88

4937 li B G A, D G A, B G C, D G C, ex definit. 3. lib. 11. Eucl. Quare diameter
A C, cum per centrum circuli A B C D, tranſeat, ſecetq̃; rectam B D, ad
angulos rectos, bifariam eam ſecabit. Itaque cum latera A G, G B, æqualia
113. tertij. ſint lateribus A G, G D, contineantq́; angulos æquales, nempe rectos, erunt
224. primi. baſes A B, A D, ſubtendentes arcus A B, A D, inter ſe æquales, ac proinde
3328. terij.& arcus A B, A D, æquales erunt. Eodem modo oſtendemus arcus C B, C D,
æquales eſſe; nec non & arcus E B, E D; & F B, F D. Circulus igitur A F C E,
ſegmenta B A D, B C D, B E D, B F D, bifariam diuidit. Quapropter ſi in
ſphæra duo circuli ſe mutuo ſecent, & c. Quod demonſtrandum erat.

SCHOLIVM.

_DVO_ alia theoremata in alia verſione hoc loco adduntur, hæc videlicet.

SI in ſphæra duo circuli ſe mutuo ſecent, circulus alius eorum
4413. ſegmenta bifariam ſecans, it per polos eorum, eſtq́; circulus ma-
ximus.

_IN_ eadẽ figura ſecent ſe mutuo duo circuli _A B C D, E D F B,_ in punctis _B, D,_ &
alius quiſpiã circulus _A F C E,_ ſecet ſegmenta _B A D, B C D, B E D, B F D,_ bifariã. _D_i
co ciculũ _A F C E,_ ire per polos ipſorũ, eſſeq́; circulũ maximũ. Quoniã enim arcus _A D,_
_A B,_ æquales ſunt, nec nõ _C D, C B,_ erũt toti arcus _A D C, A B C,_ æquales, & propte
rea ſemicirculi. _E_odemq́; modo ſemicirculi erũt _E D F, E B F. C_irculus igitur _A F C E,_
bifariam ſecat circulos _A B C D, E D F B,_ atque adeo communes ſectiones _A C, E F,_
ſe interſecantes in _G,_ ipſorum diametri ſunt. _Q_uòd ſi connectantur rectæ _B G, D G,_
cum tria puncta _B, G, D,_ in vtroque plano circulorum _A B C D, EDFb_, ſint, at-
que adeo in communi ipſorum ſectione; ſit autem communis eorum ſectio linea recta;
553. vndec. recta erit _B G D. Q_uoniam vero ſubtenſæ rectæ _D A, D C,_ ſubtenſis rectis B _A_, B _C,_
6629. tertij. ſingulæ ſingulis æquales ſunt, ob æquales arcus, anguloſq́; continent æquales, nem-
7731. tertij. pe rectos in ſemicirculis exiſtentes; æquales erunt anguli _D A C, BAC. Q_uod etiã
884. primi. ita probari poterit. _Q_uoniam latera _D A, A C,_ lateribus _BA, A C,_ æqualia ſunt,
baſiſq́; _D C,_ baſi _BC,_ æqualis, erunt anguli _D A C, BAC,_ æquales. Rurſus quia
998. primi. latera _A D, A G,_ lateribus _Ab, A G,_ æqualia ſunt, angulosq́; continent æqua-
10104. primi. les, vt demonſtratum eſt; æquales erunt anguli _A G D, A G B,_ ac propterea recti.
Perpendicularis igitur eſt _BGD,_ ad rectam _A C, E_odem modo oſtendemus rectam
eandem _BGD,_ ad _E F,_ perpendicularem eſſe. _Q_uare eadem _BGD,_ perpendicula-
ris erit ad planum circuli _A F C E,_ per rectas _A C, E F,_ ductum; ac proinde &
11114. vndec. vtrumque planum circulorum _AbCD, EDFb,_ per rectam _BGD,_ ductum ad
idem planum circuli _A F C E,_ rectum erit: & vicißim circulus _A F C E,_ ad circu-
121218. vndec. los _AbCD, EDFb,_ rectus erit. _I_taque circulus _A F C E,_ circulos _A B C D,_
1313Schol. 15. 1.
huius. _E D F B,_ & bifariam & ad angulos rectos ſecat, _Q_uare maximus eſt, tranſitq́; per
ipſorum polos. _Q_uod eſt propoſitum.

Page concordance

Text layer

Text normalization

Search

Scan	Original
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68
81	69
82	70
83	71
84	72
85	73
86	74
87	75
88	76
89	77
90	78
91	79
92	80
93	81
94	82
95	83
96	84
97	85
98	86
99	87
100	88

Scan	Original
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68
81	69
82	70
83	71
84	72
85	73
86	74
87	75
88	76
89	77
90	78
91	79
92	80
93	81
94	82
95	83
96	84
97	85
98	86
99	87
100	88

Scan	Original
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68
81	69
82	70
83	71
84	72
85	73
86	74
87	75
88	76
89	77
90	78
91	79
92	80
93	81
94	82
95	83
96	84
97	85
98	86
99	87
100	88