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

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9684 ralleli; per ſingula autem puncta æquales circun ſerentias terminan-
tia, deſcribãtur paralleli circuli. Circunferentię maximi illins circuli
primo poſiti inter parallelos interceptæ, inæquales erunt, ſemperq́;
ea, quæ propior fuerit maximo parallelorum, remotiore maior erit.

IN _circunferentia maximi circuli_ A B, _ſit polus parallelorum, quem alĳ duo_
_maximi_ B C, A C, _ſecent ad angulos rectos, ſitque_ B C, _parall lorum maximus, &_
A C, _ad parallelos obliquus. Sumantur arcus non continui æquales_ D E, F G; _ac per_
D, E, F, G, _paralleli ducantur_ D H, E I, F K, G L. _Dico arcum_ H I, _maiorem eſſe arcu_
K L. _Aut enim arcus intermedius_ E F, _vtrique æqualium_ D E, F G, _commenſurabilis_
_eſt, aut incommenſurabilis. Sit primum commenſurabilis. Inuenta autem maxima_
114. decim. _menſura V, ſecentur tres arcus_ D E, E F, F G, _in partes ipſi_ V, _æquales, & per pun=_
_cta diuiſionum paralleli deſcribantur, vt in prima figura apparet. Quoniam igitur_

103[Figure 103] _arcus continui_ D P, P E, E O, _& c. æquales ſunt; erit arcus_ H T, _maior arcu_ T I,
225. huius._&_ T I, _maior, quàm_ I S, _& c. Quare cum_ H T, _maior ſit, quàm_ K Q, _&_ T I, _ma=_
_ior quam_ Q L; _erit totus_ H I, _maior toto_ K L. _Quod eſt propoſitum._

SED _iam_ E F, _incommenſurabilis ſit vtrique_ D E, F G. _Dico adhucarcum_ H I,
_maiorem eſſe arcu_ K L. _Sienim maior non eſt, erit vel minor, vel æqualis. Sit pri=_
_mum minor; & ex_ K L, _(vt in ſecunda ſigura) auferatur ipſi_ H I, _æqualis_ K M; _&_
_per_ M, _parallelus ducatur_ M N. _Deinde per Lemma 2. Propoſ._ 8. _huius lib. reperia=_
_tur arcus_ F O, _maior quidem, quàm_ F N, _minor verò quam_ F G, _& commenſurabi=_
_lis intermedio arcui_ E F: _Sitque_ E P, _ipſi_ F O, _(qui minor eſt, quàm_ F G, _atque_
_adeo minor etiam, quam_ D E, _ipſi_ F G, _æqualis) æqualis, ac per_ O, P, _paralleli de=_
_ſcribantur_ O R, P Q. _Quoniam igitur arcus non continui_ P E, F O, _æquales ſunt,_
_eſtque vtrique illorum commenſurabilis arcus intermedius_ E F; _erit, vt iam eſt de=_
_monſtratum in prima figura, arcus_ Q I, _maior arcu_ K R. _Ergo & multo maior erit,_
_quaàm_ K M; _ac proinde multo magis arcus_ H I, _maior erit quàm_ K M: _Sed &_ H I,
_equalis ponitur ipſi_ K M. _Quod eſt abſurdum. Non ergo_ H I, _minor eſt, quàm_ K L.

SIT _deinde, ſi fieripoteſt, arcus_ H I, _arcui_ K L, _æqualis, vt in tertia figura._
_Diniſis autem arcubus_ D E, F G, _bifariam in_ M, N, _ducantur per_ M, N, _paralleli_ M O,
N P. _Erit igitur arcus_ H O, _maior, quàm_ O I; _&_ K P, _maior, quàm_ P L. _Quare_
335. huius. O I, _minor erit, quam dimidium ipſius_ H I, _&_ K P, _maior dimidio ipſius_ K L.

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Scan	Original
91	79
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96	84
97	85
98	86
99	87
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103	91
104	92
105	93
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107	95
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Scan	Original
91	79
92	80
93	81
94	82
95	83
96	84
97	85
98	86
99	87
100	88
101	89
102	90
103	91
104	92
105	93
106	94
107	95
108	96
109
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111	99
112	100
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119	107
120	108