Clavius, Christoph - In Sphaeram Ioannis de Sacro Bosco commentarius

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12588Comment. in I. Cap. Sphæræ tres lin eę AC, DF, FE, ita ſeſe

25[Figure 25] habe bũt, vt quælibet duæ ſint
reliq ua maiores. Si igitur ex
ipſis conficiatur triangulum
A G C, effectum erit, quod
proponitur. Erunt enim late-
1122. primi. ra AG, GC, & inter ſe ęqualia,
& ſimul ſumpta æqualia late-
ribus AB, BC, ſimul ſumptis:
addito igitur communi A C,
erunt triangula ABC, AGC,
iſoperimetra. Propoſito igi-
tur triangulo, cuius duo latera ſint inæqualia, ſupra reliquum latus triangulũ,
& c. d eſcripſimus. quod faciendum erat.

SCHOLIVM.

Cadet autem neceſſario punctum G, extra triangulum A B C: Sinamque ca-
2220. primi. deret in latus A B, ut ad punctum H, eßet ducta recta H C, minor quàm H B, B C, ſi-
mul, & ob id triangulum A H C, non eſſet iſoperimetrum triangulo A B C, c{ui}us con
trarium ex conſtructione eſt demonſtratum. Multo minus cadet punctum G, intra trian.
gu lum A B C. Quare extra cadet, quod eſt propoſitum.

THEOR. 7. PROPOS. 8.

Dvorvm triangulorum iſoperimetrorum eandem habentium ba-
33Iſoſeeles
triangulũ
maius eſt
triãgulo ſi
bi Iſoperi-
metro non
@ſoſcele. ſim, quorum unius duo latera ſint æqualia, alterius uero inæqualia; maius
erit illud, cuius duo latera æqualia ſunt.

Estg triangulum A B C, cuius latus A B, maius ſit latere B C, conſti-
tuaturq́ue ſuper baſim A C, (per præcedentẽ

26[Figure 26] propoſi.) triangulo A B C, triangulum Iſo-
perimetrum A D C, habens latera A D, D C,
æqualia & inter ſe, & lateribus A B, B C, ſi-
mul ſumptis. Dico triangulum A D C, maius
eſſe triangulo A B C. Producatur enim A D,
ad partes D, ſitq́ue D E, æqualis ipſi A D, ſiue
4420. primi. ipſi D C. Ducantur quoque rectæ D B, B E.
Quoniam igitur A B, B E, maiores ſunt, quã
A E, hoc eſt, quàm A D, D C, ſimul hoc eſt,
quàm A B, B C, ſimul; ablata communi A B,
erit B E, maior quam BC. Et quia latera E D,
D B, trianguli E D B, æqualia ſunt lateribus
C D, D B, trianguli C D B. Cum ergo baſis
B E, baſe B C, maior ſit, erit angulus E D B,
maior angulo C D B. Quare angulus E D B,
5525. primi. maior eſt, quàm dimidium anguli E D C:

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Scan	Original
111	74
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125	88
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140	103

Scan	Original
111	74
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115	78
116	79
117	80
118	81
119	82
120	83
121	84
122	85
123	86
124	87
125	88
126	89
127	90
128	91
129	92
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131	94
132	95
133	96
134	97
135	98
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137	100
138	101
139	102
140	103