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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