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

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3523

LEMMA.

IN omni circulo quadratum ſemidiametri dimidium eſt qua-
drati in ipſo circulo deſcripti.

_IN_ circulo, cuius centrum E, ductæ ſint duæ diametri A C, B D,

32[Figure 32] ſeſe ad angulos rectos ſecantes in E, cen-
tro. lunctis igitur rectis A B, B C, C D,
_D A,_ quadratum erit A B C D, in circu
lo inſcriptum, vt conſtat ex propoſ. 6. lib.
4. Eucl. Quoniam vero quadrata ex ſemi-
diametris æqualibus E A, E B, æqualia
inter ſe, æqualia ſimul ſunt quadrato ex
A B; dimidium erit quadratum ſemidia
1147. primi. metri E A, quadrati ex A B, quod in cir
culo deſcribitur. Quod eſt propoſitum. Ex
quo conſtat, in ſuperiorifigura, quadratum ſemidiametri B E, dimidium
eſſe quadrati ex C B, quod æquale ponitur ei, quod in circulo A B, in-
ſcribitur.

THEOR. 16. PROPOS. 17.

2227.

SI in ſphæra ſit circulus, à cuius polo in ipſius
circunferentiam ducta recta linea æqualis ſit late-
ri quadrati in ſcripti in maximo circulo, ipſe circu
lus maximus erit.

33[Figure 33]

IN ſphæra ſit circulus A B, à cuius polo
C, ad eius circunferentiam recta ducta C A,
æqualis ſit lateri quadrati in maximo circulo
ſphæræ deſcripti. Dico A B, circulum eſſe ma
ximum. Per rectam enim A C, & centrũ ſphæ
ræ planum ducatur, faciens in ſphæra circulũ
331. huius. A C B, qui maximus erit, cum per ſphæræ cen
446. huius. trum ducatur. Ducatur quoq; ex C, recta li-
nea C B, ad B, punctũ, in quo circulus maxi-
mus A C B, circulũ A B, ſecat; eritq́; per deſi
nit. poli, recta C B, rectæ C A, æqualis. Cũ
ergo A C, ponatur latus quadrati in maximo circulo A C B, deſcripti, erit
quoque C B, latus eiuſdem quadrati; atque adeò duo arcus A C, C B, qua-
drantes erunt conſicientes ſemicirculũ A C B, quòd quatuor latera quadra-
ti æqualia ſubtendãt quatuor circuli arcus æquales. Recta igitur A B, com-
5528. tertij.

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105	93
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107	95
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109
110
111	99
112	100
113	101
114	102
115	103
116	104
117	105
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122	110
123	111
124	112
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126	114
127	115
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Scan	Original
101	89
102	90
103	91
104	92
105	93
106	94
107	95
108	96
109
110
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118

Scan	Original
101	89
102	90
103	91
104	92
105	93
106	94
107	95
108	96
109
110
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118