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

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

Table of contents

[41.] THEOR. 10. PROP. 11.

[42.] THEOR. 11. PROP. 12.

[43.] SCHOLIVM.

[44.] THEOREMA 12. PROPOS. 13.

[45.] SCHOLIVM.

[46.] THEOR. 13. PROPOS. 14.

[47.] THEOREMA 14. PROPOS. 15.

[48.] SCHOLIVM.

[49.] I.

[50.] II.

[51.] III.

[52.] IIII.

[53.] THEOREMA 15. PROPOS. 16.

[54.] COROLLARIVM.

[55.] SCHOLIVM.

[56.] LEMMA.

[57.] THEOR. 16. PROPOS. 17.

[58.] PROBL. 2. PROP. 18.

[59.] PROBL. 3. PROPOS. 19.

[60.] SCHOLIVM.

[61.] PROBL. 4. PROP. 20.

[62.] PROBL. 5. PROP. 21.

[63.] SCHOLIVM.

[64.] I.

[65.] II.

[66.] THEOR. 17. PROPOS. 22.

[67.] SCHOLIVM.

[68.] FINIS LIBRI PRIMI THEODOSII.

[69.] THEODOSII SPHAE RICORVM LIBER SECVNDVS.

[70.] DEFINITIO.

42

THEODOSII

SPHAE RICORVM
LIBER SECVNDVS.

44[Figure 44]

DEFINITIO.

IN ſphæra circuli ſe mutuo tangere di-
cuntur, cum communis ſectio plano-
rum vtrumque circulum tetigerit.

THEOREMA 1. PROPOS. 1.

111

IN ſphæra paralleli circuli circa eoſdem po-
los ſunt.

IN ſphæra A B C D E F, paralleli circuli

45[Figure 45] ſint B F, C E. Dico eos circa eoſdem polos
eſſe. Sint enim A, D, poli circuli B, F, & cõ-
2221. 1. huius. nectatur recta A D, quæ ad circulum B F, re-
cta erit, tranſibitq́; per centrum ſphæræ.
3310. 1. huius. Quoniam igitur recta A D, ad circulũ B F,
perpendicularis eſt, erit quoque ad circulũ
parallelum C E, perpendicularis. Quare cũ
44Schol. 14.
vndec. tranſeat per centrum ſphæræ, vt oſtenſum
eſt, cadet in polos circuli C E. Sunt ergo
558. 1. huius. A, D, poli circuli C E: ſunt autem & poli
circuli B F. In ſphæra igitur paralleli circu-
li B F, C E, circa eoſdem polos A, D, ſunt. Quod erat demonſtrandum.

THEOREMA 2. PROPOS. 2.

662

IN ſphæra circuli, qui ſunt circa eoſdem po-
los, ſunt paralleli.

Text layer

Text normalization

Search