Plane and solid geometry . obtuse. BOOK IX 437 Propositiox XIV. Theorem 954. In equal spheres, or in the same sphere, two spher-ical triangles are equal: I. If a side and the two adjacent angles of one areequal respectively to a side and the two adjacent anglesof the other; II. If two sides and the included angle of one areequal respectively to tivo sides and the included angleof the other; III. If the three sides of one are equal respectively tothe three sides of the other : provided tl%e equal parts are arranged in tlie same order. The proofs are left as exercises for the student. Hint. In e
Plane and solid geometry . obtuse. BOOK IX 437 Propositiox XIV. Theorem 954. In equal spheres, or in the same sphere, two spher-ical triangles are equal: I. If a side and the two adjacent angles of one areequal respectively to a side and the two adjacent anglesof the other; II. If two sides and the included angle of one areequal respectively to tivo sides and the included angleof the other; III. If the three sides of one are equal respectively tothe three sides of the other : provided tl%e equal parts are arranged in tlie same order. The proofs are left as exercises for the student. Hint. In each of the above cases prove the corresponding trihedral Aequal (§§ 702, 704) ; and thus show that the spherical ^ are equal. 955. Questions. Compare Prop. XIV, I and II, with § 702, I andII, and with §§ 105 and 107. Could the methods used there be employedin § 954 ? Is the method here suggested preferable ? why ? 956. Def. Two spherical polygons are symmetrical if the corresponding polyhedral angles are
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
